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Lacoste]{Louis \textsc{Lacoste}} % Sous la supervision de Pierre -\date{29 juin 2023} - -\begin{document} - -% titre -\begin{frame}[noframenumbering,plain] - \maketitle -\end{frame} - -\section{Contexte du modèle} -\label{sec:contexte-du-modele} -\begin{frame} - \frametitle{Contexte écologique} - \begin{itemize} - \item Faire de la détection de structure sur un réseau (SBM, LBM) mais intérêt à le faire sur plusieurs - \item De nombreux réseaux disponibles \parencite{WebLifeEcological} et décrivant des interactions similaires - \item Re-grouper les réseaux selon leur similarité (\emph{clustering} de réseaux) - \item Transférer de l'information grâce à la collection (par exemple reconstitution de données manquantes) - \item Déterminer des structures d'interactions fines de manière agnostique % Pas d'idee preco - %\item Vérifier si le regroupement est lié à des co-variables - \end{itemize} -\end{frame} -\begin{frame} - \frametitle{Réseaux bipartites\footnote{Ou \emph{bipartis}. Voir~\cite{larousseDefinitionsBipartiBipartite}.}} - \begin{columns}[c] - \begin{column}{0.48\textwidth} - \centering - Réseau bipartite\\ - \begin{tikzpicture}[scale=.6] - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1.5pt] - \tikzstyle{every state}=[draw, text=black,scale=0.95, transform shape] - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape] - \tikzstyle{every node}=[fill=blueind] - - \node[state, draw=black!50] (A1) at (0,5) {\textbf{R1}}; - \node[state, draw=black!50] (A2) at (2.5,5) {\textbf{R2}}; - \node[state, draw=black!50] (A3) at (5,5) {\textbf{R3}}; - - \tikzstyle{every node}=[fill=greenind, shape=rectangle] - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] - \node[state, draw=black!50] (B1) at (0,0) {\textbf{C1}}; - \node[state, draw=black!50] (B2) at (1.25,0) {\textbf{C2}}; - \node[state, draw=black!50] (B3) at (2.5,0) {\textbf{C3}}; - \node[state, draw=black!50] (B4) at (3.75,0) {\textbf{C4}}; - \node[state, draw=black!50] (B5) at (5,0) {\textbf{C5}}; - \path (A1) edge [] (B1); - \path (A1) edge (B2); - \path (A1) edge (B3); - \path (A1) edge (B4); - \path (A2) edge (B3); - \path (A2) edge (B4); - \path (A3) edge (B5); - \path (A2) edge (B5); - \end{tikzpicture} - \end{column} - \hfill - \begin{column}{0.48\linewidth} - Matrice d'incidence - \smallskip - $X=\left( - \begin{array}{rrrrr} - 1 & 1 & 1 & 1 & 0 \\ - 0 & 0 & 1 & 1 & 1 \\ - 0 & 0 & 0 & 0 & 1 \\ - \end{array}\right) - $\\ - \end{column} - \end{columns} - \smallskip - Permet de décrire des interactions impliquant deux agents dont les rôles - sont de natures différentes.\\ - Par exemple : hôtes-parasites, plantes-pollinisateurs, graines-disperseurs \dots -\end{frame} -\begin{frame} - \frametitle{Latent Block Model (LBM\footnotemark[2])} - %DONE remplacer i \in bullet par Zi = \bullet - Proposé par~\cite{govaertEMAlgorithmBlock2005}. - \begin{columns} - \begin{column}{0.40\linewidth} - \begin{figure}[H] - \center - \begin{tikzpicture}[scale=0.35] - \tikzstyle{every state}=[draw, text=black,scale=0.95, transform shape] - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape] - \tikzset{edge_proba/.style={draw=white, fill=none, text=black}} - - \tikzstyle{every node}=[fill=blueind] - \node[edge_proba] (pi1) at (1,5.7) {\textbf{$\pi_{{\color{blueind}\bullet}}$}}; - \node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}}; - \node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}}; - \node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}}; - - \tikzstyle{every node}=[fill=cyanind] - \node[edge_proba] (pi2) at (6.75,5.7) {\textbf{$\pi_{{\color{cyanind}\bullet}}$}}; - \node[state, draw=black!50] (R21) at (6.25,5) {\textbf{R21}}; - \node[state, draw=black!50] (R22) at (7.25,5) {\textbf{R22}}; - - \tikzstyle{every node}=[fill=electricblue] - \node[edge_proba] (pi3) at (10,5.7) {\textbf{$\pi_{{\color{electricblue}\bullet}}$}}; - \node[state, draw=black!50] (R31) at (10,5) {\textbf{R31}}; - - \tikzstyle{every node}=[fill=burntorange, shape=rectangle] - \node[edge_proba] (pi3) at (0.5,-0.7) {\textbf{$\rho_{{\color{burntorange}\bullet}}$}}; - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] - \node[state, draw=black!50] (B1) at (0,0) {\textbf{C11}}; - \node[state, draw=black!50] (B2) at (1,0) {\textbf{C12}}; - \tikzstyle{every node}=[fill=goldenyellow, shape=rectangle] - \node[edge_proba] (pi3) at (4,-0.7) {\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}}; - \node[state, draw=black!50] (B3) at (3.5,0) {\textbf{C21}}; - \node[state, draw=black!50] (B4) at (4.5,0) {\textbf{C22}}; - \tikzstyle{every node}=[fill=peach, shape=rectangle] - \node[edge_proba] (pi3) at (10,-0.7) {\textbf{$\rho_{{\color{peach}\bullet}}$}}; - \node[state, draw=black!50] (B5) at (10,0) {\textbf{C31}}; - - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1.5pt,draw opacity=0.2] - - \path (R11) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[left, fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$} (B1); - \path (R11) edge (B2); - \path (R11) edge (B3); - \path (R11) edge (B4); - - \path (R12) edge [] (B1); - \path (R12) edge (B2); - \path (R12) edge (B3); - \path (R12) edge (B4); - - \path (R13) edge [] (B1); - \path (R13) edge (B2); - \path (R13) edge (B3); - \path (R13) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{goldenyellow}\bullet}}$} (B4); - - \path (R21) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, right, fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$} (B3); - \path (R21) edge (B4); - \path (R21) edge (B5); - - \path (R22) edge (B3); - \path (R22) edge (B4); - \path (R22) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{peach}\bullet}}$} (B5); - - \path (R31) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, right, fill=none] {$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$} (B5); - - \end{tikzpicture} - \caption{Exemple de LBM\footnotemark} - \label{fig:LBMvisu} - \end{figure} - \end{column} - \begin{column}{0.51\linewidth} - Pour \begin{itemize} - \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ blocs fixés en ligne - \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ blocs fixés en colonne - \end{itemize} - \begin{block}{Paramètres} - \begin{itemize} - \item $\pi_{\bullet} = \mathbb{P}(Z_i = \bullet)$ en ligne et $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne - \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$ - \end{itemize} - \end{block} - \end{column} - \end{columns} - - \footnotetext{Que j'appellerai par la suite BiSBM} - -\end{frame} -\begin{frame} - \frametitle{\emph{colSBM}} - Le modèle \emph{colSBM} \parencite{chabert-liddellLearningCommonStructures2023}.\\ - % Difficulté estimer les parametres - - % DONE Modifier les realisations pour variabilite, mettre iid au dessus du sim et inverser modele et realisations - \smallskip - \definecolor{yellow}{RGB}{255,190,60} - \begin{center} - \begin{adjustbox}{trim=0 0 0 1cm} - \begin{tikzpicture}[scale=.32] - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=.5pt, bend left] - \tikzstyle{every state}=[draw, text=black,scale=0.95, transform shape] - \tikzset{edge_proba/.style={draw=white, fill=none, text=black}} - - \tikzstyle{every node}=[fill=yellow] - \node[state, draw=black!50] (A1) at (0,2) {\textbf{A1}}; - \node[state, draw=black!50] (A2) at (1.5, 2) {\textbf{A2}}; - \node[state, draw=black!50] (A3) at (0.75,3.25) {\textbf{A3}}; - - \tikzstyle{every node}=[fill=blueind] - \node[state, draw=black!50] (B1) at (4.5,3) {\textbf{B1}}; - \node[state, draw=black!50] (B2) at (4,4.75) {\textbf{B2}}; - \node[state, draw=black!50] (B3) at (5.5,6) {\textbf{B3}}; - \node[state, draw=black!50] (B4) at (7,4.75) {\textbf{B4}}; - \node[state, draw=black!50] (B5) at (6.5,3) {\textbf{B5}}; - - \tikzstyle{every node}=[fill=greenind] - \node[state, draw=black!50] (C1) at (5,0) {\textbf{C1}}; - \node[state, draw=black!50] (C2) at (7,1) {\textbf{C2}}; - - - \path (A1) edge[bend right] (A2); - \path (A1) edge node[midway, left, fill=none] {$\alpha_{{\color{yellow}\bullet}{\color{yellow}\bullet}}$} (A3); - \path (A3) edge (A2); - - \path (A3) edge node[midway, above, fill=none] {$\alpha_{{\color{yellow}\bullet}{\color{blueind}\bullet}}$} (B3); - - \path (B1) edge (B2); - \path (B2) edge (B3); - \path (B3) edge (B4); - \path (B4) edge (B5); - \path (B5) edge (B1); - - \path (B1) edge[bend left=0] (B4); - \path (B5) edge[bend left=0] (B2); - - \path (A2) edge[bend right] node[midway, below, fill=none] {$\alpha_{{\color{yellow}\bullet}{\color{greenind}\bullet}}$} (C1); - \path (C1) edge[bend right] node[midway, below, fill=none] {$\alpha_{{\color{greenind}\bullet}{\color{greenind}\bullet}}$} (C2); - \path (C2) edge[bend right] node[midway, right, fill=none] {$\alpha_{{\color{greenind}\bullet}{\color{blueind}\bullet}}$} (B4); - - \node[font=\small, text justified,draw=none, fill=none] at (4.5,-1.5) {SBM}; - - - - % Sampled network - \begin{scope}[xshift=-16cm,yshift=4cm] - \node[font=\small, text justified, fill=none] at (10, -2.5) {$\overset{iid}{\sim}$}; - \tikzstyle{every node}=[fill=gray, scale=0.95] - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=.5pt, bend left] - \tikzstyle{every state}=[draw, text=black,scale=0.95, transform shape] - - \node[state, draw=black!50] (A1) at (0,0) {\textbf{10}}; - \node[state, draw=black!50] (A2) at (1, 0) {\textbf{2}}; - \node[state, draw=black!50] (A3) at (0.5,1) {\textbf{5}}; - - \node[state, draw=black!50] (B2) at (2,2.75) {\textbf{9}}; - \node[state, draw=black!50] (B3) at (3.5,4) {\textbf{6}}; - \node[state, draw=black!50] (B4) at (5,2.75) {\textbf{3}}; - \node[state, draw=black!50] (B5) at (4.5,1) {\textbf{7}}; - - \node[state, draw=black!50] (C1) at (3,-0.5) {\textbf{4}}; - - \path (A1) edge[bend right] (A2); - \path (A1) edge (A3); - \path (A3) edge (A2); - - \path (A3) edge (B3); - - \path (B2) edge (B3); - \path (B3) edge (B4); - \path (B4) edge (B5); - - \path (B5) edge[bend left=0] (B2); - - \path (A2) edge[bend right] (C1); - - \node[text width=3cm,font=\small, text justified, rotate=90, fill=none, below = -0.8cm of C1] (dots) {\dots}; - - \end{scope} - \begin{scope}[xshift=-16cm,yshift=-4cm] - \tikzstyle{every node}=[fill=gray, scale=0.95] - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=.5pt, bend left] - \tikzstyle{every state}=[draw, text=black,scale=0.95, transform shape] - - \node[state, draw=black!50] (A2) at (1, 0) {\textbf{2}}; - \node[state, draw=black!50] (A3) at (0.5,1) {\textbf{1}}; - - \node[state, draw=black!50] (B1) at (2.5,1) {\textbf{5}}; - \node[state, draw=black!50] (B2) at (2,2.75) {\textbf{10}}; - \node[state, draw=black!50] (B4) at (5,2.75) {\textbf{8}}; - \node[state, draw=black!50] (B5) at (4.5,1) {\textbf{7}}; - - \node[state, draw=black!50] (C2) at (5,0) {\textbf{3}}; - - - - \path (A3) edge (A2); - - - \path (B1) edge (B2); - \path (B4) edge (B5); - \path (B5) edge (B1); - - \path (B1) edge[bend left=0] (B4); - \path (B5) edge[bend left=0] (B2); - - \path (C2) edge[bend right] (B4); - \end{scope} - \end{tikzpicture} - \end{adjustbox} - \end{center} - Pour $Q = |\{{\color{yellow}\bullet},{\color{blueind}\bullet},{\color{greenind}\bullet}\}|$ blocs fixés : - \begin{block}{Paramètres} - \begin{itemize} - \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ - \item $\alpha_{{\color{greenind}\bullet}{\color{blueind}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{greenind}\bullet}, Z_j = {\color{blueind}\bullet})$ - \end{itemize} - \end{block} -\end{frame} -\section{Extension de \emph{colSBM} aux réseaux bipartites} -\label{sec:extension-de-colsbm-aux-reseaux-bipartites} -\begin{frame} - \frametitle{Collections bipartites} - \begin{center} - \begin{adjustbox}{trim=0 0 1 1.5cm} - \begin{tikzpicture}[scale=.33] - \begin{scope}[xshift=18cm, yshift=2cm] - \tikzstyle{every state}=[draw=none, text=black,scale=0.75, transform shape] - \tikzset{edge_proba/.style={draw=white, fill=none, text=black}} - - \tikzstyle{every node}=[fill=blueind] - \node[edge_proba] (pi1) at (1,5.7) {\textbf{$\pi_{{\color{blueind}\bullet}}$}}; - \node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}}; - \node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}}; - \node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}}; - - \tikzstyle{every node}=[fill=cyanind] - \node[edge_proba] (pi2) at (6.75,5.7) {\textbf{$\pi_{{\color{cyanind}\bullet}}$}}; - \node[state, draw=black!50] (R21) at (6.25,5) {\textbf{R21}}; - \node[state, draw=black!50] (R22) at (7.25,5) {\textbf{R22}}; - - \tikzstyle{every node}=[fill=electricblue] - \node[edge_proba] (pi3) at (10,5.7) {\textbf{$\pi_{{\color{electricblue}\bullet}}$}}; - \node[state, draw=black!50] (R31) at (10,5) {\textbf{R31}}; - - \tikzstyle{every node}=[fill=burntorange, shape=rectangle] - \node[edge_proba] (rho1) at (0.5,-1) {\textbf{$\rho_{{\color{burntorange}\bullet}}$}}; - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] - \node[state, draw=black!50] (B1) at (0,0) {\textbf{C11}}; - \node[state, draw=black!50] (B2) at (1,0) {\textbf{C12}}; - \tikzstyle{every node}=[fill=goldenyellow, shape=rectangle] - \node[edge_proba] (rho2) at (4,-1) {\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}}; - \node[state, draw=black!50] (B3) at (3.5,0) {\textbf{C21}}; - \node[state, draw=black!50] (B4) at (4.5,0) {\textbf{C22}}; - \tikzstyle{every node}=[fill=peach, shape=rectangle] - \node[edge_proba] (rho3) at (10,-1) {\textbf{$\rho_{{\color{peach}\bullet}}$}}; - \node[state, draw=black!50] (B5) at (10,0) {\textbf{C31}}; - - \node[font=\small, text justified,draw=none, fill=none, below = 0.05cm of rho2] {BiSBM}; - - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1.5pt,draw opacity=0.2] - - \path (R11) edge (B2); - \path (R11) edge (B3); - \path (R11) edge (B4); - - \path (R12) edge [] (B1); - \path (R12) edge (B2); - \path (R12) edge (B3); - \path (R12) edge (B4); - - \path (R13) edge [] (B1); - \path (R13) edge (B2); - \path (R13) edge (B3); - - \path (R21) edge (B4); - \path (R21) edge (B5); - - \path (R22) edge (B3); - \path (R22) edge (B4); - - \path (R11) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[left, fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$} (B1); - \path (R13) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{goldenyellow}\bullet}}$} (B4); - \path (R21) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, anchor=center, fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$} (B3); - \path (R22) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{peach}\bullet}}$} (B5); - \path (R31) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, right, fill=none] {$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$} (B5); - \end{scope} - - \begin{scope}[xshift=3cm, yshift = 1cm] - \node[text justified, fill=none] at (10, 3.5) {$\overset{iid}{\sim}$}; - \begin{scope}[yshift = 6cm] - \tikzstyle{every state}=[draw, text=black,scale=0.75, transform shape] - - \tikzstyle{every node}=[fill=gray] - \node[state, draw=black!50] (R11) at (0,1.25) {\textbf{1}}; - \node[state, draw=black!50] (R12) at (1,1.25) {\textbf{2}}; - \node[state, draw=black!50] (R13) at (2,1.25) {\textbf{3}}; - \node[state, draw=black!50] (R21) at (3,1.25) {\textbf{4}}; - \node[state, draw=black!50] (R31) at (5,1.25) {\textbf{6}}; - - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] - \node[state, draw=black!50] (B1) at (0.5,-1) {\textbf{1}}; - - \node[state, draw=black!50] (B31) at (2.5,-1) {\textbf{3}}; - \node[state, draw=black!50] (B4) at (3.5,-1) {\textbf{4}}; - - \node[state, draw=black!50] (B5) at (4.5,-1) {\textbf{5}}; - - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] - \path (R11) edge (B1); - \path (R11) edge (B31); - \path (R11) edge (B4); - - \path (R12) edge [] (B1); - \path (R12) edge (B31); - \path (R12) edge (B4); - - \path (R13) edge [] (B1); - \path (R13) edge (B31); - \path (R13) edge (B4); - - \path (R21) edge (B31); - \path (R21) edge (B4); - \path (R21) edge (B5); - - - \path (R31) edge (B5); - \end{scope} - \node[text width=3cm,font=\small, text justified, rotate=90, fill=none] (dots) at (2.5, 7.5){\dots}; - - \begin{scope}[yshift = 0cm] - \tikzstyle{every state}=[draw, text=black,scale=0.75, transform shape] - - \tikzstyle{every node}=[fill=gray] - \node[state, draw=black!50] (R11) at (0,2.25) {\textbf{4}}; - \node[state, draw=black!50] (R13) at (2,2.25) {\textbf{6}}; - \node[state, draw=black!50] (R21) at (3,2.25) {\textbf{3}}; - \node[state, draw=black!50] (R22) at (4,2.25) {\textbf{5}}; - \node[state, draw=black!50] (R31) at (5,2.25) {\textbf{2}}; - - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] - \node[state, draw=black!50] (B1) at (0.5,0) {\textbf{5}}; - \node[state, draw=black!50] (B2) at (1.5,0) {\textbf{1}}; - - \node[state, draw=black!50] (B4) at (3.5,0) {\textbf{2}}; - - \node[state, draw=black!50] (B5) at (4.5,0) {\textbf{4}}; - - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] - \path (R11) edge (B1); - \path (R11) edge (B2); - \path (R11) edge (B4); - - \path (R13) edge [] (B1); - \path (R13) edge (B2); - \path (R13) edge (B4); - - \path (R21) edge (B4); - \path (R21) edge (B5); - - \path (R22) edge (B4); - \path (R22) edge (B5); - - \path (R31) edge (B5); - \end{scope} - \end{scope} - \end{tikzpicture} - \end{adjustbox} - \end{center} - - Pour - \begin{itemize} - \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ blocs fixés en ligne - \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ blocs fixés en colonne - \end{itemize} - \begin{block}{Paramètres} - \begin{itemize} - \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ en ligne et $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne - \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$ - \end{itemize} - \end{block} -\end{frame} - -\begin{frame} - \frametitle{Différents modèles} - \begin{block}{\emph{iid-colBiSBM}} - $\bm{\pi} = (\pi_1, \dots \pi_{Q_1})$ et $\bm{\rho} = (\rho_1, \dots \rho_{Q_2})$ %{$\forall q \in \llbracket 1, Q_1 - 1\rrbracket, \pi_q > 0$ et $\forall r \in \llbracket 1, Q_2 - 1\rrbracket, \rho_r > 0$} - , tous les réseaux partagent les mêmes paramètres\footnotemark - \end{block} - - \begin{block}{\emph{$\pi\rho$-colBiSBM}} - $\bm{\pi} = ((\pi_{\color{black}1}^{\color{red}m}, \dots \pi_{\color{black}Q_1}^{\color{red}m}))_{m=1,\dots M}$ et $\bm{\rho} = ((\rho_{\color{black}1}^{\color{red}m}, \dots \rho_{\color{black}Q_2}^{\color{red}m}))_{m=1,\dots M}$ %{$\forall q \in \llbracket 1, Q_1 - 1\rrbracket, \pi_q > 0$ et $\forall r \in \llbracket 1, Q_2 - 1\rrbracket, \rho_r > 0$} - \small \\ - avec $\forall q,m \in \llbracket 1, Q_1 \rrbracket \times \llbracket 1, M \rrbracket, \pi_q^m \in \left[ 0,1 \right]$ - et $\forall r,m \in \llbracket 1, Q_2 \rrbracket \times \llbracket 1, M \rrbracket, \rho_r^m \in \left[ 0,1 \right]$ - \end{block} - Et également deux autres modèles ($\pi$-colBiSBM et $\rho$-colBiSBM) où seulement une des deux dimensions est libre. - \footnotetext{Dans tous les modèles la structure de connectivité est supposée identique au sein de la collection.} -\end{frame} -\begin{frame} - \frametitle{Estimation des paramètres} - % DONE dire que tau i q m c' est la proba que Zim = q, approximation de la proba variationnelle. Parce qu on impose lindependance - Maximisation d'une borne inférieure de la log-vraisemblance des données observées. - \begin{multline*} - \ell (\bm{X};\bm{\theta}) \geq \color{red}\sum_{m=1}^{M} \bigg( \color{black} \sum_{i = 1}^{n_1^m}\sum_{j=1}^{n_2^m}\sum_{q \in \mathcal{Q}_{1,m}} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{1,m}_{i,q} \tau^{2,m}_{j,r} \log f(X^{m}_{ij}; \alpha_{qr}) \\ - + \sum_{i=1}^{n_1^m} \sum_{q \in \mathcal{Q}_{1,m}} \tau^{1,m}_{i,q} \log \pi_{\color{black}q}^{\color{gray}m} + \sum_{j=1}^{n_2^m} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{2,m}_{j,r} \log \rho_{\color{black}r}^{\color{gray}m} \\ - - \sum_{i=1}^{n_1} \tau^{1,m}_{i,q} \log \tau^{1,m}_{i,q} - \sum_{j=1}^{n_2} \tau^{2,m}_{j,r} \log \tau^{2,m}_{j,r} \color{red}\bigg) \color{black} =: J(\bm{\tau};\bm{\theta}) $$ - \end{multline*} - - \begin{block}{Approximation variationnelle} - $\tau_{i,q}^{1,m} = P(Z_i = q | X^m_{ij})$ et $\tau_{j,r}^{2,m} = P(W_j = r | X^m_{ij})$ tels que $P(Z_i = q, W_j = r | X^m_{ij}) = \tau_{i,q}^{1,m}\times\tau_{j,r}^{2,m}$ - \end{block} - -\end{frame} - -\begin{frame} - \frametitle{Sélection de modèle : choix de $(Q_1,Q_2)$ - Approche gloutonne} - % DONE But maximiser un critere le BICL, deplacer voir St Clair dans la note - % VEM a Q1 Q2 fixer - % Choix de Q1 Q2 par maximisation du BICL - % Itemize dans la box : init, explo voisin, arrets - \underline{Le VEM se fait à $Q_1, Q_2$ fixés}, il faut donc déterminer les \enquote*{meilleures} coordonnées. - Nous maximisons un BIC-L\footnote{\emph{Bayesian Information Criterion - Like}, en adaptant les formules de~\cite{chabert-liddellLearningCommonStructures2023}}. - - Détermination d'un premier mode par approche \emph{gloutonne} \smallskip - \begin{columns} - \begin{column}{0.5\linewidth} - \begin{tikzpicture} - \draw[step=1cm, help lines] (-2,-2) grid (2,2); - \draw[fill=gray, draw=gray] (0,0) circle [radius=0.225cm]; - \draw[fill=blueind, draw=blueind] (1,0) circle [radius=0.225cm]; - \draw[fill=blueind, draw=blueind] (0,1) circle [radius=0.225cm]; - \draw[fill=red, draw=red] (-1,0) circle [radius=0.225cm]; - \draw[fill=red, draw=red] (0,-1) circle [radius=0.225cm]; - - % Légende - \node[font=\tiny, text justified,fill=none, rotate=-45] (Splits) at (0.5,0.5){{\color{blueind} Splits}}; - \node[font=\tiny, text justified,fill=none, rotate=-45] (Merges) at (-0.5,-0.5){{\color{red} Merges}}; - - % Splitting - \draw[>=stealth,->,thick, draw=blueind] (0.225,0) -- +(0.55,0); - \draw[>=stealth,->,thick, draw=blueind] (0,0.225) -- +(0,0.55); - - % Merging - \draw[>=stealth,->,thick, draw=red] (-0.225,0) -- +(-0.55,0); - \draw[>=stealth,->,thick, draw=red] (0,-0.225) -- +(0,-0.55); - - % Axes - \draw[>=to,->,thick] (-2,-2) -- +(1,0); - \node[font=\small, fill=none] (Q_1) at (-0.75,-2) {$Q_1$}; - \draw[>=to,->,thick] (-2,-2) -- +(0,1); - \node[font=\small, fill=none] (Q_2) at (-2,-0.75) {$Q_2$}; - - \end{tikzpicture} - \end{column} - \begin{column}{0.5\linewidth} - \begin{block}{Exploration gloutonne} - \begin{itemize} - \item Initialisation sur $(1,2)$ et $(2,1)$ - \item Exploration des 4 voisins et déplacement sur le meilleur des 4 - \item Arrêt après 2 étapes successives sans augmentation du BIC-L - \end{itemize} - \end{block} - \end{column} - \end{columns} -\end{frame} -\begin{frame} - \frametitle{Sélection de modèle : choix de $(Q_1,Q_2)$ - Fenêtre glissante} - \begin{columns} - \begin{column}{0.60\linewidth} - \begin{figure} - \includegraphics[scale=0.22]{img/moving_window.png} - \caption{Exemple de parcours de fenêtre glissante} - \end{figure} - \end{column} - \begin{column}{0.4\linewidth} - \definecolor{mypurple}{RGB}{128,0,128} - \begin{tikzpicture} - - \tikzstyle{model}=[circle,draw=none,fill=gray] - \tikzstyle{split}=[>=stealth,->,thick, draw=blueind] - \tikzstyle{merge}=[>=stealth,->,thick, draw=red] - \draw[step=1cm, help lines] (-2,-2) grid (2,2); - \node[model] (mode) at (0,0) {{\color{red}X}}; - - \onslide<2->{ - \draw[color=red, line width=1pt] (-1.5,-1.5) rectangle ++(3,3); - } - \onslide<3-3>{ - \node[model] (bottom_left) at (-1,-1) {}; - \node[model, opacity=0.6] (row_1) at (0,-1) {}; - \node[model, opacity=0.6] (col_1) at (-1,0) {}; - - \draw[split] (bottom_left) -- (col_1); - \draw[split] (-1.75,0) -- (col_1); - \draw[split] (bottom_left) -- (row_1); - \draw[split] (0,-1.75) -- (row_1); - } - \onslide<4->{ - \node[model] (bottom_left) at (-1,-1) {}; - \node[model, draw=blue] (row_1) at (0,-1) {}; - \node[model, draw=blue] (col_1) at (-1,0) {}; - } - \onslide<4-4>{ - \node[model, opacity=0.6] (row_2) at (1,-1) {}; - \node[model, opacity=0.6] (col_2) at (-1,1) {}; - - \draw[split] (col_1) -- (col_2); - \draw[split] (-1.75,1) -- (col_2); - \draw[split] (row_1) -- (row_2); - \draw[split] (1,-1.75) -- (row_2); - \draw[split] (row_1) -- (mode); - \draw[split] (col_1) -- (mode); - } - \onslide<5->{ - \node[model, draw=blue] (row_2) at (1,-1) {}; - \node[model, draw=blue] (col_2) at (-1,1) {}; - \node[model, draw=blue] (mode) at (0,0) {{\color{red}X}}; - } - \onslide<5-5>{ - \node[model, opacity=0.6] (row_3) at (1,0) {}; - \node[model, opacity=0.6] (col_3) at (0,1) {}; - - \draw[split] (col_2) -- (col_3); - \draw[split] (row_2) -- (row_3); - \draw[split] (mode) -- (row_3); - \draw[split] (mode) -- (col_3); - } - \onslide<6->{ - \node[model, draw=blue] (row_3) at (1,0) {}; - \node[model, draw=blue] (col_3) at (0,1) {}; - } - \onslide<6-6>{ - \node[model, opacity=0.6] (top_right) at (1,1) {}; - \draw[split] (col_3) -- (top_right); - \draw[split] (row_3) -- (top_right); - } - \onslide<7->{ - \node[model, draw=blue] (top_right) at (1,1) {}; - } - \onslide<8->{ - \node[model, draw=mypurple] (top_right) at (1,1) {}; - \node[model, draw=mypurple] (row_3) at (1,0) {}; - \node[model, draw=mypurple] (col_3) at (0,1) {}; - \node[model, draw=mypurple] (row_2) at (1,-1) {}; - \node[model, draw=mypurple] (col_2) at (-1,1) {}; - \node[model, draw=mypurple] (mode) at (0,0) {{\color{red}X}}; - \node[model, draw=red] (bottom_left) at (-1,-1) {}; - \node[model, draw=mypurple] (row_1) at (0,-1) {}; - \node[model, draw=mypurple] (col_1) at (-1,0) {}; - - \draw[merge] (1,1.75) -- (top_right); - \draw[merge] (1.75,1) -- (top_right); - \draw[merge] (0,1.75) -- (col_3); - \draw[merge] (1.75,0) -- (row_3); - \draw[merge] (1.75,-1) -- (row_2); - \draw[merge] (-1,1.75) -- (col_2); - - \draw[merge] (top_right) -- (col_3); - \draw[merge] (top_right) -- (row_3); - \draw[merge] (col_3) -- (col_2); - \draw[merge] (row_3) -- (row_2) ; - \draw[merge] (row_3) -- (mode); - \draw[merge] (col_3) -- (mode); - \draw[merge] (col_2) --(col_1); - \draw[merge] (row_2) -- (row_1); - \draw[merge] (mode) -- (row_1); - \draw[merge] (mode) -- (col_1); - \draw[merge] (col_1) -- (bottom_left); - \draw[merge] (row_1) -- (bottom_left); - } - \end{tikzpicture} - \end{column} - \end{columns} -\end{frame} - -\begin{frame} - \frametitle{Clustering de réseaux} - \begin{columns} - \begin{column}{0.2\linewidth} - \begin{block}{Objectif} - Déterminer une partition qui maximise la somme du BICL de ses sous-collections. - \end{block} - \end{column} - \begin{column}{0.78\linewidth} - \begin{tikzpicture} - \tikzstyle{instruct}=[font=\small, text justified, rectangle,draw,fill=yellow!50] - \tikzstyle{first_col}=[rectangle, text justified, draw,fill=gray!50] - \tikzstyle{second_col}=[scale=0.55, circle, draw,fill=red!50] - \tikzstyle{test}=[font=\small, text justified, diamond, aspect=2.5,thick, - draw=blue,fill=yellow!50,text=blue] - \tikzstyle{es}=[font=\small, text justified, rectangle,draw,rounded corners=4pt,fill=cyanind!25] - - \node[es] (liste) at (0,4) {Donner une collection à partitionner}; - \node[instruct, text width=5cm, below = 0.45cm of liste] (1-collection) {Ajuster \emph{colBiSBM}}; - \node[first_col, right = 0.5cm of 1-collection] (1-col-obj) {}; - \node[instruct, text width=5cm, below = 0.45cm of 1-collection] (dissimi) {Calculer une matrice de dissimilarité de la collection}; - \node[instruct, text width=5cm, below = 0.45cm of dissimi] (2-sous-collection) {Séparer la \emph{collection en 2 sous-collections} et ajuster les \emph{colBiSBM}}; - \node[second_col, right = 0.25cm of 2-sous-collection] (1-sec-col-obj) {1}; - \node[second_col, right = 0.25cm of 1-sec-col-obj] (1-sec-col-obj) {2}; - \node[test,below = 0.45cm of 2-sous-collection, scale=0.5] (BICL-test) {$\sum_{i=1}^{2} (\text{BIC-L}(\tikz[baseline=-0.25cm]{\node[second_col] {i};} )) > \text{BIC-L}(\tikz[baseline=-0.25cm]{\node[first_col] {};})$?}; - \node[es, right = 0.55cm of BICL-test] (sortie) {Renvoyer \tikz{\node[rectangle, draw, fill=gray!50, rounded corners=0pt] {};}}; - \node[es, left = 0.45cm of dissimi, text width = 2cm] (recursion) {Recommencer sur \tikz{\node[second_col] {1};} et \tikz{\node[second_col] {2};} }; - - \tikzstyle{suite}=[->,>=stealth,thick,rounded corners=4pt] - \draw[suite] (liste) -- (1-collection); - \draw[suite] (1-collection) -- (dissimi); - \draw[suite] (dissimi) -- (2-sous-collection); - \draw[suite] (2-sous-collection) -- (BICL-test); - \draw[suite] (BICL-test) -| node[near start, above, fill=none] {Oui} (recursion); - \draw[suite] (recursion.north) |- (1-collection.west); - \draw[suite] (BICL-test) -- node[near start, above, fill=none] {Non} (sortie); - - \end{tikzpicture} - \end{column} - \end{columns} - \blfootnote{Même approche que~\cite{chabert-liddellLearningCommonStructures2023}} -\end{frame} - -\section{Application} -\label{sec:application} -\begin{frame} - \frametitle{Application, données plantes pollinisateurs} - \small - Voici des résultats du modèle \emph{iid-colBiSBM} sur des données - plantes-pollinisateurs (~\cite{doreRelativeEffectsAnthropogenic2021} - et~\cite{thebaultDatabasePlantpollinatorNetworks2020}) - % DONE Ajouter un tableau avec le nombre de réseaux dans chaque sous-collection - \begin{columns} - \begin{column}{0.48\linewidth} - \includegraphics[scale=0.32]{img/annual_time_span_vs_iid.png} - \begin{center} - \begin{tabular}{ |c|c|c|c|c|c| } - \hline - \thead{N° de \\collection} & 1 & 2 & 3 & 4 & 5 \\ - \hline - \thead{Nombre de \\réseaux} & 38 & 45 & 1 & 20 & 19 \\ - \hline - \end{tabular} - \end{center} - \end{column} - \begin{column}{0.48\linewidth} - \begin{figure}[H] - \includegraphics[width=0.45\textwidth]{img/iid-meso-1.png} - \includegraphics[width=0.45\textwidth]{img/iid-meso-2.png} - \includegraphics[width=0.45\textwidth]{img/iid-meso-3.png} - \includegraphics[width=0.45\textwidth]{img/iid-meso-4.png} - \includegraphics[width=0.45\textwidth]{img/iid-meso-5.png} - \caption{Connectivités de la partition} - \end{figure} - \end{column} - \end{columns} -\end{frame} -\section{Conclusion} -\label{sec:conclusion} -\begin{frame} - \frametitle{Conclusion et perspectives} - % DONE Ajouter une slide conclusion perspective - % Rappeler les modeles avec clustering - % Evoquer l'analyse de reseaux corrigés pour l'échantillonnage - % Lien vers le package - - \begin{itemize} - \item 4 modèles dont 3 qui ont une flexibilité sur au moins une des dimensions (adaptabilité aux données) - \item Partitionner un ensemble de réseaux selon leurs structures - \item Comparer les \emph{clusterings} de réseaux obtenus entre données brutes et données corrigées (par exemple par la méthode \emph{CoOPLBM}\footnote{~\cite{anakokDisentanglingStructureEcological2022}}) - \end{itemize} - - \bigskip - \centering - Le package est disponible sur GitHub : \faGithub \url{https://github.com/Chabert-Liddell/colSBM} - - \bigskip - \huge - Merci pour votre attention ! - -\end{frame} -\renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}} -\begin{frame}[noframenumbering,plain,allowframebreaks] - \frametitle{Bibliographie} - \printbibliography -\end{frame} - -\end{document} \ No newline at end of file diff --git a/presentation/animation.gif b/presentation/animation.gif new file mode 100644 index 0000000..c9677d1 Binary files /dev/null and b/presentation/animation.gif differ diff --git a/presentation/presentation.bbl-SAVE-ERROR b/presentation/presentation.bbl-SAVE-ERROR new file mode 100644 index 0000000..7889bd3 --- /dev/null +++ b/presentation/presentation.bbl-SAVE-ERROR @@ -0,0 +1,521 @@ +% $ biblatex auxiliary file $ +% $ biblatex bbl format version 3.3 $ +% Do not modify the above lines! +% +% This is an auxiliary file used by the 'biblatex' package. +% This file may safely be deleted. It will be recreated by +% biber as required. +% +\begingroup +\makeatletter +\@ifundefined{ver@biblatex.sty} + {\@latex@error + {Missing 'biblatex' package} + {The bibliography requires the 'biblatex' package.} + \aftergroup\endinput} + {} +\endgroup + + +\refsection{0} + \datalist[entry]{none/apasortcite//global/global/global} + \entry{WebLifeEcological}{online}{}{} + \field{sortinit}{1} + \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a} + \field{labeldatesource}{nodate} + \field{labeltitlesource}{title} + \field{title}{Web of {{Life}}: Ecological Networks Database} + \field{urlday}{17} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{urldateera}{ce} + \verb{file} + \verb /home/polarolouis/Zotero/storage/9WZE8QLQ/map.html + \endverb + \verb{urlraw} + \verb https://www.web-of-life.es/map.php + \endverb + \verb{url} + \verb https://www.web-of-life.es/map.php + \endverb + \keyw{networks,site} + \endentry + \entry{larousseDefinitionsBipartiBipartite}{online}{}{} + \name{author}{1}{}{% + {{un=0,uniquepart=base,hash=d7507e4ee9a344124ebcf84871b83290}{% + family={Larousse}, + familyi={L\bibinitperiod}, + given={Éditions}, + giveni={É\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{fullhash}{d7507e4ee9a344124ebcf84871b83290} + \strng{fullhashraw}{d7507e4ee9a344124ebcf84871b83290} + \strng{bibnamehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authorbibnamehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authornamehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authorfullhash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authorfullhashraw}{d7507e4ee9a344124ebcf84871b83290} + \field{sortinit}{2} + \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a} + \field{labeldatesource}{nodate} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{shorttitle} + \field{abstract}{biparti, bipartite - Définitions Français : Retrouvez la définition de biparti, bipartite, ainsi que les difficultés... - synonymes, homonymes, difficultés, citations.} + \field{langid}{french} + \field{shorttitle}{Définitions} + \field{title}{Définitions : biparti, bipartite - Dictionnaire de français Larousse} + \field{urlday}{17} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{urldateera}{ce} + \verb{file} + \verb /home/polarolouis/Zotero/storage/MA2VH6NX/9503.html + \endverb + \verb{urlraw} + \verb https://www.larousse.fr/dictionnaires/francais/biparti/9503 + \endverb + \verb{url} + \verb https://www.larousse.fr/dictionnaires/francais/biparti/9503 + \endverb + \endentry + \entry{govaertEMAlgorithmBlock2005}{article}{}{} + \name{author}{2}{}{% + {{un=0,uniquepart=base,hash=e362e82efc56e96877c249de27098dd7}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=5554bf45de9d6150691084d7cde5594c}{% + family={Nadif}, + familyi={N\bibinitperiod}, + given={M.}, + giveni={M\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{bibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorbibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authornamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \field{sortinit}{3} + \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.} + \field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}} + \field{issn}{1939-3539} + \field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence} + \field{month}{4} + \field{number}{4} + \field{title}{An {{EM}} Algorithm for the Block Mixture Model} + \field{volume}{27} + \field{year}{2005} + \field{dateera}{ce} + \field{pages}{643\bibrangedash 647} + \range{pages}{5} + \verb{doi} + \verb 10.1109/TPAMI.2005.69 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/6IG45HH2/govaert2005.pdf.pdf;/home/polarolouis/Zotero/storage/TL8M3XRF/Govaert et Nadif - 2005 - An EM algorithm for the block mixture model.pdf;/home/polarolouis/Zotero/storage/2Y48IB26/1401917.html + \endverb + \keyw{Approximation algorithms,Classification algorithms,Clustering algorithms,Clustering methods,Data mining,EM algorithm,Index Terms- Block mixture model,Maximum likelihood estimation,Parameter estimation,Partitioning algorithms,Self organizing feature maps,Sparse matrices,variational approximation.} + \endentry + \entry{chabert-liddellLearningCommonStructures2023}{online}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=b2590d483a7fe284c2cdda3920206a4e}{% + family={Chabert-Liddell}, + familyi={C\bibinithyphendelim L\bibinitperiod}, + given={Saint-Clair}, + giveni={S\bibinithyphendelim C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=06c8f96f3a1aba5140a38275380f781f}{% + family={Donnet}, + familyi={D\bibinitperiod}, + given={Sophie}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{fullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{fullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{bibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorbibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authornamehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{authorfullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorfullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \field{sortinit}{4} + \field{sortinithash}{9381316451d1b9788675a07e972a12a7} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.} + \field{day}{27} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{month}{3} + \field{title}{Learning Common Structures in a Collection of Networks. {{An}} Application to Food Webs} + \field{type}{article} + \field{urlday}{22} + \field{urlmonth}{5} + \field{urlyear}{2023} + \field{year}{2023} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{doi} + \verb 10.48550/arXiv.2206.00560 + \endverb + \verb{eprint} + \verb 2206.00560 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/M74TXGCF/Chabert-Liddell et al. - 2023 - Learning common structures in a collection of netw.pdf;/home/polarolouis/Zotero/storage/A35M8KNP/2206.html + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \keyw{Statistics - Applications,Statistics - Methodology} + \endentry + \entry{anakokDisentanglingStructureEcological2022}{online}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=fe9e51991c906363fdb9789340eb02b8}{% + family={Anakok}, + familyi={A\bibinitperiod}, + given={Emre}, + giveni={E\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=0e7741d31a239c4be11fc31138a136c1}{% + family={Fontaine}, + familyi={F\bibinitperiod}, + given={Colin}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=f23dbf986aa073f9022baede42ef0479}{% + family={Thebault}, + familyi={T\bibinitperiod}, + given={Elisa}, + giveni={E\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{fullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{fullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \strng{bibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorbibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authornamehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{authorfullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorfullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \field{sortinit}{6} + \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated in simulation studies. The practical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.} + \field{day}{29} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{langid}{english} + \field{month}{11} + \field{title}{Disentangling the Structure of Ecological Bipartite Networks from Observation Processes} + \field{urlday}{14} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{year}{2022} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{eprint} + \verb 2211.16364 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/LQ3FINZG/Anakok et al. - 2022 - Disentangling the structure of ecological bipartit.pdf + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \keyw{Statistics - Methodology} + \endentry + \enddatalist + \datalist[entry]{none/global//global/global/global} + \entry{WebLifeEcological}{online}{}{} + \field{sortinit}{1} + \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a} + \field{labeldatesource}{nodate} + \field{labeltitlesource}{title} + \field{title}{Web of {{Life}}: Ecological Networks Database} + \field{urlday}{17} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{urldateera}{ce} + \verb{file} + \verb /home/polarolouis/Zotero/storage/9WZE8QLQ/map.html + \endverb + \verb{urlraw} + \verb https://www.web-of-life.es/map.php + \endverb + \verb{url} + \verb https://www.web-of-life.es/map.php + \endverb + \keyw{networks,site} + \endentry + \entry{larousseDefinitionsBipartiBipartite}{online}{}{} + \name{author}{1}{}{% + {{un=0,uniquepart=base,hash=d7507e4ee9a344124ebcf84871b83290}{% + family={Larousse}, + familyi={L\bibinitperiod}, + given={Éditions}, + giveni={É\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{fullhash}{d7507e4ee9a344124ebcf84871b83290} + \strng{fullhashraw}{d7507e4ee9a344124ebcf84871b83290} + \strng{bibnamehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authorbibnamehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authornamehash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authorfullhash}{d7507e4ee9a344124ebcf84871b83290} + \strng{authorfullhashraw}{d7507e4ee9a344124ebcf84871b83290} + \field{sortinit}{2} + \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a} + \field{labeldatesource}{nodate} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{shorttitle} + \field{abstract}{biparti, bipartite - Définitions Français : Retrouvez la définition de biparti, bipartite, ainsi que les difficultés... - synonymes, homonymes, difficultés, citations.} + \field{langid}{french} + \field{shorttitle}{Définitions} + \field{title}{Définitions : biparti, bipartite - Dictionnaire de français Larousse} + \field{urlday}{17} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{urldateera}{ce} + \verb{file} + \verb /home/polarolouis/Zotero/storage/MA2VH6NX/9503.html + \endverb + \verb{urlraw} + \verb https://www.larousse.fr/dictionnaires/francais/biparti/9503 + \endverb + \verb{url} + \verb https://www.larousse.fr/dictionnaires/francais/biparti/9503 + \endverb + \endentry + \entry{govaertEMAlgorithmBlock2005}{article}{}{} + \name{author}{2}{}{% + {{un=0,uniquepart=base,hash=e362e82efc56e96877c249de27098dd7}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=5554bf45de9d6150691084d7cde5594c}{% + family={Nadif}, + familyi={N\bibinitperiod}, + given={M.}, + giveni={M\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{bibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorbibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authornamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \field{sortinit}{3} + \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.} + \field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}} + \field{issn}{1939-3539} + \field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence} + \field{month}{4} + \field{number}{4} + \field{title}{An {{EM}} Algorithm for the Block Mixture Model} + \field{volume}{27} + \field{year}{2005} + \field{dateera}{ce} + \field{pages}{643\bibrangedash 647} + \range{pages}{5} + \verb{doi} + \verb 10.1109/TPAMI.2005.69 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/6IG45HH2/govaert2005.pdf.pdf;/home/polarolouis/Zotero/storage/TL8M3XRF/Govaert et Nadif - 2005 - An EM algorithm for the block mixture model.pdf;/home/polarolouis/Zotero/storage/2Y48IB26/1401917.html + \endverb + \keyw{Approximation algorithms,Classification algorithms,Clustering algorithms,Clustering methods,Data mining,EM algorithm,Index Terms- Block mixture model,Maximum likelihood estimation,Parameter estimation,Partitioning algorithms,Self organizing feature maps,Sparse matrices,variational approximation.} + \endentry + \entry{chabert-liddellLearningCommonStructures2023}{online}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=b2590d483a7fe284c2cdda3920206a4e}{% + family={Chabert-Liddell}, + familyi={C\bibinithyphendelim L\bibinitperiod}, + given={Saint-Clair}, + giveni={S\bibinithyphendelim C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=06c8f96f3a1aba5140a38275380f781f}{% + family={Donnet}, + familyi={D\bibinitperiod}, + given={Sophie}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{fullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{fullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{bibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorbibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authornamehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{authorfullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorfullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \field{sortinit}{4} + \field{sortinithash}{9381316451d1b9788675a07e972a12a7} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.} + \field{day}{27} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{month}{3} + \field{title}{Learning Common Structures in a Collection of Networks. {{An}} Application to Food Webs} + \field{type}{article} + \field{urlday}{22} + \field{urlmonth}{5} + \field{urlyear}{2023} + \field{year}{2023} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{doi} + \verb 10.48550/arXiv.2206.00560 + \endverb + \verb{eprint} + \verb 2206.00560 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/M74TXGCF/Chabert-Liddell et al. - 2023 - Learning common structures in a collection of netw.pdf;/home/polarolouis/Zotero/storage/A35M8KNP/2206.html + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \keyw{Statistics - Applications,Statistics - Methodology} + \endentry + \entry{anakokDisentanglingStructureEcological2022}{online}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=fe9e51991c906363fdb9789340eb02b8}{% + family={Anakok}, + familyi={A\bibinitperiod}, + given={Emre}, + giveni={E\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=0e7741d31a239c4be11fc31138a136c1}{% + family={Fontaine}, + familyi={F\bibinitperiod}, + given={Colin}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=f23dbf986aa073f9022baede42ef0479}{% + family={Thebault}, + familyi={T\bibinitperiod}, + given={Elisa}, + giveni={E\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{fullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{fullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \strng{bibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorbibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authornamehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{authorfullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorfullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \field{sortinit}{6} + \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated in simulation studies. The practical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.} + \field{day}{29} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{langid}{english} + \field{month}{11} + \field{title}{Disentangling the Structure of Ecological Bipartite Networks from Observation Processes} + \field{urlday}{14} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{year}{2022} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{eprint} + \verb 2211.16364 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/LQ3FINZG/Anakok et al. - 2022 - Disentangling the structure of ecological bipartit.pdf + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \keyw{Statistics - Methodology} + \endentry + \enddatalist +\endrefsection +\endinput + diff --git a/presentation/presentation.pdf b/presentation/presentation.pdf new file mode 100644 index 0000000..021de6c Binary files /dev/null and b/presentation/presentation.pdf differ diff --git a/presentation/presentation.tex b/presentation/presentation.tex new file mode 100644 index 0000000..4e0d52b --- /dev/null +++ b/presentation/presentation.tex @@ -0,0 +1,357 @@ +\documentclass{beamer} +\usetheme{Boadilla} + +% importations +\usepackage[french]{babel} % pour dire que le texte est en francais +\usepackage{csquotes} +\usepackage[T1]{fontenc} % pour les font postscript +\usepackage[cyr]{aeguill} % Police vectorielle TrueType, guillemets francais +\usepackage{epsfig} % pour gérer les images +\usepackage{amsmath,amsthm, stmaryrd} % très bon mode mathématique +\usepackage{amsfonts,amssymb,bm, bbold}% permet la definition des ensembles +\usepackage{algorithm2e} % pour les algorithmes +\usepackage{algpseudocode} % pour les algorithmes +\usepackage{graphicx} +\usepackage{float} % pour le placement des figure +\usepackage{url} % pour une gestion efficace des url +\usepackage{hyperref} % pour les hyperliens dans le document +\usepackage{tikz} % For graph plots +\usepackage[outline]{contour} +\usepackage{adjustbox} % To resize tikzpictures +\usepackage{fontawesome5} +\usepackage{makecell} + +% Beamer +\setbeamertemplate{headline}{% + \begin{beamercolorbox}[ht=2.25ex,dp=3.75ex]{section in head/foot} + \insertnavigation{\paperwidth} + \end{beamercolorbox}% +}% +\beamertemplatenavigationsymbolsempty % Pas de bar de navigation +\setbeamerfont{caption}{size=\scriptsize} % Petit titre de figures + +% bibliographie +\usepackage[style=apa,sorting=none]{biblatex} +\addbibresource{../references.bib} + +% Images +\graphicspath{{../img/}{../figure/}} + +% Tikz +%% Tikz Related +\usetikzlibrary{calc,shapes,backgrounds,arrows,automata,shadows,positioning} +\usetikzlibrary{arrows,shapes,positioning,shadows,trees,calc,backgrounds,automata,positioning} +\usetikzlibrary{decorations.pathreplacing,calligraphy,external,petri} + +%% Tikz sets +\tikzset{ + basic/.style = {draw, text width=3cm, font=\sffamily, rectangle}, + root/.style = {basic, rounded corners=2pt, thin, align=center, + fill=green!30}, + level 2/.style = {basic, rounded corners=6pt, thin,align=center, fill=green!60, + text width=8em}, + level 3/.style = {basic, thin, align=left, fill=pink!60, text width=3.5cm} +} + +% Couleurs +% pour tickz multilevel +\definecolor{ao(english)}{rgb}{0.0, 0.5, 0.0} +\definecolor{redorg}{RGB}{215, 48, 39} +\definecolor{orangeorg}{RGB}{253, 174, 97} + +\definecolor{blueind}{RGB}{016, 101, 171} +\definecolor{cyanind}{RGB}{058, 147, 195} +\definecolor{electricblue}{RGB}{142, 196, 222} + +\definecolor{greenind}{RGB}{112, 130, 56} + +\definecolor{burntorange}{RGB}{179, 021, 041} +\definecolor{goldenyellow}{RGB}{215, 095, 076} +\definecolor{peach}{RGB}{246, 164, 130} + +\definecolor{gray}{RGB}{128, 128, 128} + +% Footnote +\makeatletter +\newcommand\blfootnote[1]{% + \begingroup + \renewcommand{\@makefntext}[1]{\noindent\makebox[1.8em][r]#1} + \renewcommand\thefootnote{}\footnote{#1}% + \addtocounter{footnote}{-1}% + \endgroup +} +\makeatother + + +\subtitle{Séminaire des stagiaires} +\title[Collections de réseaux bipartites]{Détection de structure dans des réseaux bipartites} +\author[L. Lacoste]{Louis \textsc{Lacoste}} % Sous la supervision de Pierre +\date{4 juillet 2024} + +\begin{document} + +% titre +\begin{frame}[noframenumbering,plain] + \maketitle +\end{frame} + +\section{Contexte du modèle} +\label{sec:contexte-du-modele} +\begin{frame} + \frametitle{Contexte écologique} + \begin{itemize} + \item Faire de la détection de structure sur un réseau (SBM, LBM) mais intérêt à le faire sur plusieurs + \item De nombreux réseaux disponibles \parencite{WebLifeEcological} et décrivant des interactions similaires + \item Re-grouper les réseaux selon leur similarité (\emph{clustering} de réseaux) + \item Transférer de l'information grâce à la collection (par exemple reconstitution de données manquantes) + \item Déterminer des structures d'interactions fines de manière agnostique % Pas d'idee preco + %\item Vérifier si le regroupement est lié à des co-variables + \end{itemize} +\end{frame} +\begin{frame} + \frametitle{Réseaux bipartites\footnote{Ou \emph{bipartis}. Voir~\cite{larousseDefinitionsBipartiBipartite}.}} + \begin{columns}[c] + \begin{column}{0.65\textwidth} + \begin{figure}[ht] + \centering + \begin{tikzpicture}[scale=.65] + \input{../tikz/plantpollinatornetwork.tex} + \end{tikzpicture} + \caption{Exemple d'un réseau plantes-pollinisateurs} + \label{fig:plantes-pollin} + + \end{figure} + \end{column} + \hfill + \begin{column}{0.35\linewidth} + \centering + \begin{align*} + X = \begin{pmatrix} + 1 & 1 & 1 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 1 \\ + 1 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 + \end{pmatrix} + \end{align*} + \footnotesize + Matrice d'adjacence associée + \end{column} + \end{columns} + \smallskip + Permet de décrire des interactions impliquant deux agents dont les rôles + sont de natures différentes.\\ + Par exemple : hôtes-parasites, plantes-pollinisateurs, graines-disperseurs \dots +\end{frame} + +\begin{frame} + \frametitle{Latent Block Model (LBM\footnotemark[2])} + %DONE remplacer i \in bullet par Zi = \bullet + Proposé par~\cite{govaertEMAlgorithmBlock2005}. + \begin{columns} + \begin{column}{0.40\linewidth} + \begin{figure}[H] + \center + \begin{tikzpicture}[scale=0.35] + \input{../tikz/lbm.tex} + \end{tikzpicture} + \caption{Exemple de LBM\footnotemark} + \label{fig:LBMvisu} + \end{figure} + \end{column} + \begin{column}{0.51\linewidth} + Pour \begin{itemize} + \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ blocs fixés en ligne + \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ blocs fixés en colonne + \end{itemize} + \begin{block}{Paramètres} + \begin{itemize} + \item $\pi_{\bullet} = \mathbb{P}(Z_i = \bullet)$ en ligne et $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne + \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$ + \end{itemize} + \end{block} + \end{column} + \end{columns} + + \footnotetext{Que j'appellerai par la suite BiSBM} + +\end{frame} + +\section{Extension de \emph{colSBM} aux réseaux bipartites} +\label{sec:extension-de-colsbm-aux-reseaux-bipartites} +\begin{frame} + \frametitle{Collections bipartites} + \begin{tikzpicture}[scale=0.33] + \input{../tikz/collbm-iid.tex} + \end{tikzpicture} + + \begin{itemize} + \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ blocs fixés en ligne + \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ blocs fixés en colonne + \end{itemize} + \begin{block}{Paramètres} + \begin{itemize} + \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ en ligne et $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne + \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$ + \end{itemize} + \end{block} +\end{frame} + +\begin{frame} + \frametitle{Différents modèles} + \only<1>{ + \begin{tikzpicture}[scale=0.33] + \input{../tikz/collbm-iid.tex} + \end{tikzpicture} + \begin{block}{\emph{iid-colBiSBM}} + $\bm{\pi} = (\pi_1, \dots \pi_{Q_1})$ et $\bm{\rho} = (\rho_1, \dots \rho_{Q_2})$ + \end{block} + } + \only<2>{ + \begin{tikzpicture}[scale=0.33] + \input{../tikz/collbm-pirho.tex} + \end{tikzpicture} + \begin{block}{\emph{$\pi\rho$-colBiSBM}} + $\bm{\pi} = ((\pi_{\color{black}1}^{\color{red}m}, \dots \pi_{\color{black}Q_1}^{\color{red}m}))_{m=1,\dots M}$ et $\bm{\rho} = ((\rho_{\color{black}1}^{\color{red}m}, \dots \rho_{\color{black}Q_2}^{\color{red}m}))_{m=1,\dots M}$ %{$\forall q \in \llbracket 1, Q_1 - 1\rrbracket, \pi_q > 0$ et $\forall r \in \llbracket 1, Q_2 - 1\rrbracket, \rho_r > 0$} + \small \\ + avec $\forall q,m \in \llbracket 1, Q_1 \rrbracket \times \llbracket 1, M \rrbracket, \pi_q^m \in \left[ 0,1 \right]$ + et $\forall r,m \in \llbracket 1, Q_2 \rrbracket \times \llbracket 1, M \rrbracket, \rho_r^m \in \left[ 0,1 \right]$ + \end{block} + } + Dans tous les modèles la structure de connectivité ($\bm{\alpha}$) est supposée identique au sein de la collection. +\end{frame} +\begin{frame} + \frametitle{Estimation des paramètres} + % DONE dire que tau i q m c' est la proba que Zim = q, approximation de la proba variationnelle. Parce qu on impose lindependance + Maximisation d'une borne inférieure de la log-vraisemblance des données observées. + \begin{multline*} + \ell (\bm{X};\bm{\theta}) \geq \color{red}\sum_{m=1}^{M} \bigg( \color{black} \sum_{i = 1}^{n_1^m}\sum_{j=1}^{n_2^m}\sum_{q \in \mathcal{Q}_{1,m}} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{1,m}_{i,q} \tau^{2,m}_{j,r} \log f(X^{m}_{ij}; \alpha_{qr}) \\ + + \sum_{i=1}^{n_1^m} \sum_{q \in \mathcal{Q}_{1,m}} \tau^{1,m}_{i,q} \log \pi_{\color{black}q}^{\color{gray}m} + \sum_{j=1}^{n_2^m} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{2,m}_{j,r} \log \rho_{\color{black}r}^{\color{gray}m} \\ + - \sum_{i=1}^{n_1} \tau^{1,m}_{i,q} \log \tau^{1,m}_{i,q} - \sum_{j=1}^{n_2} \tau^{2,m}_{j,r} \log \tau^{2,m}_{j,r} \color{red}\bigg) \color{black} =: J(\bm{\tau};\bm{\theta}) $$ + \end{multline*} + + \begin{block}{Approximation variationnelle} + $\tau_{i,q}^{1,m} = P(Z_i = q | X^m_{ij})$ et $\tau_{j,r}^{2,m} = P(W_j = r | X^m_{ij})$ tels que $P(Z_i = q, W_j = r | X^m_{ij}) = \tau_{i,q}^{1,m}\times\tau_{j,r}^{2,m}$ + \end{block} + +\end{frame} + +\begin{frame} + \frametitle{Sélection de modèle : choix de $(Q_1,Q_2)$ - Approche gloutonne} + % DONE But maximiser un critere le BICL, deplacer voir St Clair dans la note + % VEM a Q1 Q2 fixer + % Choix de Q1 Q2 par maximisation du BICL + % Itemize dans la box : init, explo voisin, arrets + \underline{Le VEM se fait à $Q_1, Q_2$ fixés}, il faut donc déterminer les \enquote*{meilleures} coordonnées. + Nous maximisons un BIC-L\footnote{\emph{Bayesian Information Criterion - Like}, en adaptant les formules de~\cite{chabert-liddellLearningCommonStructures2023}}. + + Détermination d'un premier mode par approche \emph{gloutonne} \smallskip + \begin{columns} + \begin{column}{0.5\linewidth} + \begin{tikzpicture} + \input{../tikz/greedy-exploration.tex} + \end{tikzpicture} + \end{column} + \begin{column}{0.5\linewidth} + \begin{block}{Exploration gloutonne} + \begin{itemize} + \item Initialisation sur $(1,2)$ et $(2,1)$ + \item Exploration des 4 voisins et déplacement sur le meilleur des 4 + \item Arrêt après 2 étapes successives sans augmentation du BIC-L + \end{itemize} + \end{block} + \end{column} + \end{columns} +\end{frame} +\begin{frame} + \frametitle{Sélection de modèle : choix de $(Q_1,Q_2)$ - Fenêtre glissante} + \begin{columns} + \begin{column}{0.6\textwidth} + \begin{figure} + \input{../tikz/moving-window.tex} + \caption{Fenêtre glissante} + \end{figure} + \end{column} + \begin{column}{0.4\textwidth} + \only<3>{\begin{block}{} + Initialisation du modèle si nécessaire + \end{block}} + \only<9>{\begin{block}{} + Localisation du nouveau mode + \end{block}} + \only<10>{\begin{block}{} + Déplacement sur le nouveau mode puis itération + \end{block}} + \end{column} + \end{columns} + + +\end{frame} + +\begin{frame} + \frametitle{Clustering de réseaux} + \begin{tikzpicture} + \tikzstyle{instruct}=[font=\small, text justified, rectangle,draw,fill=yellow!50] + \tikzstyle{first_col}=[rectangle, text justified, draw,fill=gray!50] + \tikzstyle{second_col}=[scale=0.55, circle, draw,fill=red!50] + \tikzstyle{test}=[font=\small, text justified, diamond, aspect=2.5,thick, + draw=blue,fill=yellow!50,text=blue] + \tikzstyle{es}=[font=\small, text justified, rectangle,draw,rounded corners=4pt,fill=cyanind!25] + + \node[es] (liste) at (0,4) {Donner une collection à partitionner}; + \node[instruct, text width=5cm, below = 0.45cm of liste] (1-collection) {Ajuster \emph{colBiSBM}}; + \node[first_col, right = 0.5cm of 1-collection] (1-col-obj) {}; + \node[instruct, text width=5cm, below = 0.45cm of 1-collection] (dissimi) {Calculer une matrice de dissimilarité de la collection}; + \node[instruct, text width=5cm, below = 0.45cm of dissimi] (2-sous-collection) {Séparer la \emph{collection en 2 sous-collections} et ajuster les \emph{colBiSBM}}; + \node[second_col, right = 0.25cm of 2-sous-collection] (1-sec-col-obj) {1}; + \node[second_col, right = 0.25cm of 1-sec-col-obj] (1-sec-col-obj) {2}; + \node[test,below = 0.45cm of 2-sous-collection, scale=0.5] (BICL-test) {$\sum_{i=1}^{2} (\text{BIC-L}(\tikz[baseline=-0.25cm]{\node[second_col] {i};} )) > \text{BIC-L}(\tikz[baseline=-0.25cm]{\node[first_col] {};})$?}; + \node[es, right = 0.55cm of BICL-test] (sortie) {Renvoyer \tikz{\node[rectangle, draw, fill=gray!50, rounded corners=0pt] {};}}; + \node[es, left = 0.45cm of dissimi, text width = 2cm] (recursion) {Recommencer sur \tikz{\node[second_col] {1};} et \tikz{\node[second_col] {2};} }; + + \tikzstyle{suite}=[->,>=stealth,thick,rounded corners=4pt] + \draw[suite] (liste) -- (1-collection); + \draw[suite] (1-collection) -- (dissimi); + \draw[suite] (dissimi) -- (2-sous-collection); + \draw[suite] (2-sous-collection) -- (BICL-test); + \draw[suite] (BICL-test) -| node[near start, above, fill=none] {Oui} (recursion); + \draw[suite] (recursion.north) |- (1-collection.west); + \draw[suite] (BICL-test) -- node[near start, above, fill=none] {Non} (sortie); + + \end{tikzpicture} + \blfootnote{Même approche que~\cite{chabert-liddellLearningCommonStructures2023}} +\end{frame} + +\section{Application} +\label{sec:application} + +\section{Conclusion} +\label{sec:conclusion} +\begin{frame} + \frametitle{Conclusion et perspectives} + % DONE Ajouter une slide conclusion perspective + % Rappeler les modeles avec clustering + % Evoquer l'analyse de reseaux corrigés pour l'échantillonnage + % Lien vers le package + + \begin{itemize} + \item 4 modèles dont 3 qui ont une flexibilité sur au moins une des dimensions (adaptabilité aux données) + \item Partitionner un ensemble de réseaux selon leurs structures + \item Comparer les \emph{clusterings} de réseaux obtenus entre données brutes et données corrigées (par exemple par la méthode \emph{CoOPLBM}\footnote{~\cite{anakokDisentanglingStructureEcological2022}}) + \end{itemize} + + \bigskip + \centering + Le package est disponible sur GitHub : \faGithub \url{https://github.com/Chabert-Liddell/colSBM} + + \bigskip + \huge + Merci pour votre attention ! + +\end{frame} +\renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}} +\begin{frame}[noframenumbering,plain,allowframebreaks] + \frametitle{Bibliographie} + \printbibliography +\end{frame} + +\end{document} \ No newline at end of file diff --git a/rapport.pdf b/rapport.pdf deleted file mode 100644 index 27ce4ea..0000000 Binary files a/rapport.pdf and /dev/null differ diff --git a/presentation_UMR.tex b/rapport/presentation_UMR.tex similarity index 100% rename from presentation_UMR.tex rename to rapport/presentation_UMR.tex diff --git a/rapport/rapport.bbl-SAVE-ERROR b/rapport/rapport.bbl-SAVE-ERROR new file mode 100644 index 0000000..3de9be5 --- /dev/null +++ b/rapport/rapport.bbl-SAVE-ERROR @@ -0,0 +1,1977 @@ +% $ biblatex auxiliary file $ +% $ biblatex bbl format version 3.3 $ +% Do not modify the above lines! +% +% This is an auxiliary file used by the 'biblatex' package. +% This file may safely be deleted. It will be recreated by +% biber as required. +% +\begingroup +\makeatletter +\@ifundefined{ver@biblatex.sty} + {\@latex@error + {Missing 'biblatex' package} + {The bibliography requires the 'biblatex' package.} + \aftergroup\endinput} + {} +\endgroup + + +\refsection{0} + \datalist[entry]{apa/apasortcite//global/global/global} + \entry{AccueilMIAParisSaclay}{online}{}{} + \field{sortinit}{A} + \field{sortinithash}{2f401846e2029bad6b3ecc16d50031e2} + \field{labeldatesource}{nodate} + \field{labeltitlesource}{title} + \field{title}{Accueil | {{MIA Paris-Saclay}}} + \field{urlday}{3} + \field{urlmonth}{7} + \field{urlyear}{2023} + \field{urldateera}{ce} + \verb{file} + \verb /home/polarolouis/Zotero/storage/I7FWTZC3/mia-ps.inrae.fr.html + \endverb + \verb{urlraw} + \verb https://mia-ps.inrae.fr/ + \endverb + \verb{url} + \verb https://mia-ps.inrae.fr/ + \endverb + \endentry + \entry{anakokDisentanglingStructureEcological2022}{online}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=fe9e51991c906363fdb9789340eb02b8}{% + family={Anakok}, + familyi={A\bibinitperiod}, + given={Emre}, + giveni={E\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=0e7741d31a239c4be11fc31138a136c1}{% + family={Fontaine}, + familyi={F\bibinitperiod}, + given={Colin}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=f23dbf986aa073f9022baede42ef0479}{% + family={Thebault}, + familyi={T\bibinitperiod}, + given={Elisa}, + giveni={E\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{fullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{fullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \strng{bibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorbibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authornamehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{authorfullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorfullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \field{sortinit}{A} + \field{sortinithash}{2f401846e2029bad6b3ecc16d50031e2} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated in simulation studies. The practical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.} + \field{day}{29} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{langid}{english} + \field{month}{11} + \field{title}{Disentangling the Structure of Ecological Bipartite Networks from Observation Processes} + \field{urlday}{14} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{year}{2022} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{eprint} + \verb 2211.16364 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/LQ3FINZG/Anakok et al. - 2022 - Disentangling the structure of ecological bipartit.pdf + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \keyw{Statistics - Methodology} + \endentry + \entry{biernackiAssessingMixtureModel2000}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=255c9c519676be165266b81a64bfee7e}{% + family={Biernacki}, + familyi={B\bibinitperiod}, + given={C.}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=d4c385b68696de3eb64ee9e356c030b6}{% + family={Celeux}, + familyi={C\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=e362e82efc56e96877c249de27098dd7}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{b7345cdc8a5fd7a8ac9f253a305026a2} + \strng{fullhash}{4f27942f3e82511621b18e076e78f9a9} + \strng{fullhashraw}{4f27942f3e82511621b18e076e78f9a9} + \strng{bibnamehash}{4f27942f3e82511621b18e076e78f9a9} + \strng{authorbibnamehash}{4f27942f3e82511621b18e076e78f9a9} + \strng{authornamehash}{b7345cdc8a5fd7a8ac9f253a305026a2} + \strng{authorfullhash}{4f27942f3e82511621b18e076e78f9a9} + \strng{authorfullhashraw}{4f27942f3e82511621b18e076e78f9a9} + \field{sortinit}{B} + \field{sortinithash}{d7095fff47cda75ca2589920aae98399} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{We propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood. For this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. Then, the integrated completed likelihood (ICL) is approximated using the Bayesian information criterion (BIC). Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data.} + \field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}} + \field{issn}{1939-3539} + \field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence} + \field{month}{7} + \field{number}{7} + \field{title}{Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood} + \field{volume}{22} + \field{year}{2000} + \field{dateera}{ce} + \field{pages}{719\bibrangedash 725} + \range{pages}{7} + \verb{doi} + \verb 10.1109/34.865189 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/MK9H446U/Biernacki et al. - 2000 - Assessing a mixture model for clustering with the .pdf + \endverb + \keyw{Bayesian methods,Context modeling,Gaussian distribution,Numerical simulation,Probability distribution,Robustness} + \endentry + \entry{chabert-liddellLearningCommonStructures2023}{online}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=b2590d483a7fe284c2cdda3920206a4e}{% + family={Chabert-Liddell}, + familyi={C\bibinithyphendelim L\bibinitperiod}, + given={Saint-Clair}, + giveni={S\bibinithyphendelim C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=06c8f96f3a1aba5140a38275380f781f}{% + family={Donnet}, + familyi={D\bibinitperiod}, + given={Sophie}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{fullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{fullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{bibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorbibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authornamehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{authorfullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorfullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \field{sortinit}{C} + \field{sortinithash}{4d103a86280481745c9c897c925753c0} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.} + \field{day}{27} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{month}{3} + \field{title}{Learning Common Structures in a Collection of Networks. {{An}} Application to Food Webs} + \field{type}{article} + \field{urlday}{22} + \field{urlmonth}{5} + \field{urlyear}{2023} + \field{year}{2023} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{doi} + \verb 10.48550/arXiv.2206.00560 + \endverb + \verb{eprint} + \verb 2206.00560 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/M74TXGCF/Chabert-Liddell et al. - 2023 - Learning common structures in a collection of netw.pdf;/home/polarolouis/Zotero/storage/A35M8KNP/2206.html + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \keyw{Statistics - Applications,Statistics - Methodology} + \endentry + \entry{daudinMixtureModelRandom2008}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=de4bdd0bb56d35c0db284d95b0eae35f}{% + family={Daudin}, + familyi={D\bibinitperiod}, + given={J.-J.}, + giveni={J\bibinithyphendelim J\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7099f7ae5fb227f549cc71bbc6d525ab}{% + family={Picard}, + familyi={P\bibinitperiod}, + given={F.}, + giveni={F\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=9f772e002ea2fcde759c25cd69c5299c}{% + family={Robin}, + familyi={R\bibinitperiod}, + given={S.}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{8db2758afbcd0c9a4aff2a9e81bcccaf} + \strng{fullhash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{fullhashraw}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{bibnamehash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{authorbibnamehash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{authornamehash}{8db2758afbcd0c9a4aff2a9e81bcccaf} + \strng{authorfullhash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{authorfullhashraw}{1ca792ce8b7d10d284e9b70bf8d15647} + \field{sortinit}{D} + \field{sortinithash}{6f385f66841fb5e82009dc833c761848} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The Erdös–Rényi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it does not fit well to real-world networks. The vertices of those networks are often structured in unknown classes (functionally related proteins or social communities) with different connectivity properties. The stochastic block structures model was proposed for this purpose in the context of social sciences, using a Bayesian approach. We consider the same model in a frequentest statistical framework. We give the degree distribution and the clustering coefficient associated with this model, a variational method to estimate its parameters and a model selection criterion to select the number of classes. This estimation procedure allows us to deal with large networks containing thousands of vertices. The method is used to uncover the modular structure of a network of enzymatic reactions.} + \field{day}{1} + \field{issn}{1573-1375} + \field{journaltitle}{Statistics and Computing} + \field{langid}{english} + \field{month}{6} + \field{number}{2} + \field{shortjournal}{Stat Comput} + \field{title}{A Mixture Model for Random Graphs} + \field{urlday}{16} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{18} + \field{year}{2008} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{173\bibrangedash 183} + \range{pages}{11} + \verb{doi} + \verb 10.1007/s11222-007-9046-7 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/439HK27B/Daudin et al. - 2008 - A mixture model for random graphs.pdf;/home/polarolouis/Zotero/storage/HVVF5MNY/daudin2007.pdf.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1007/s11222-007-9046-7 + \endverb + \verb{url} + \verb https://doi.org/10.1007/s11222-007-9046-7 + \endverb + \keyw{Mixture models,Random graphs,Variational~method} + \endentry + \entry{desjardins-proulxEcologicalInteractionsNetflix2017}{article}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=e6f2e3608eb78a89f65a1e4632b852d7}{% + family={Desjardins-Proulx}, + familyi={D\bibinithyphendelim P\bibinitperiod}, + given={Philippe}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=e5c9887a52ecb13e307da69a7bd95579}{% + family={Laigle}, + familyi={L\bibinitperiod}, + given={Idaline}, + giveni={I\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=707f55e341a1c9baf6b1c57fc13a6701}{% + family={Poisot}, + familyi={P\bibinitperiod}, + given={Timothée}, + giveni={T\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=63bf0d8e60941c7bd0526fb3208072b5}{% + family={Gravel}, + familyi={G\bibinitperiod}, + given={Dominique}, + giveni={D\bibinitperiod}, + givenun=0}}% + } + \list{publisher}{1}{% + {PeerJ Inc.}% + } + \strng{namehash}{6fdcc4093a18a4d307c5c28c05c369aa} + \strng{fullhash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{fullhashraw}{c3e64892b634eab5a19dfbb1247066bb} + \strng{bibnamehash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{authorbibnamehash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{authornamehash}{6fdcc4093a18a4d307c5c28c05c369aa} + \strng{authorfullhash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{authorfullhashraw}{c3e64892b634eab5a19dfbb1247066bb} + \field{sortinit}{D} + \field{sortinithash}{6f385f66841fb5e82009dc833c761848} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Species interactions are a key component of ecosystems but we generally have an incomplete picture of who-eats-who in a given community. Different techniques have been devised to predict species interactions using theoretical models or abundances. Here, we explore the K nearest neighbour approach, with a special emphasis on recommendation, along with a supervised machine learning technique. Recommenders are algorithms developed for companies like Netflix to predict whether a customer will like a product given the preferences of similar customers. These machine learning techniques are well-suited to study binary ecological interactions since they focus on positive-only data. By removing a prey from a predator, we find that recommenders can guess the missing prey around 50\% of the times on the first try, with up to 881 possibilities. Traits do not improve significantly the results for the K nearest neighbour, although a simple test with a supervised learning approach (random forests) show we can predict interactions with high accuracy using only three traits per species. This result shows that binary interactions can be predicted without regard to the ecological community given only three variables: body mass and two variables for the species’ phylogeny. These techniques are complementary, as recommenders can predict interactions in the absence of traits, using only information about other species’ interactions, while supervised learning algorithms such as random forests base their predictions on traits only but do not exploit other species’ interactions. Further work should focus on developing custom similarity measures specialized for ecology to improve the KNN algorithms and using richer data to capture indirect relationships between species.} + \field{day}{10} + \field{issn}{2167-8359} + \field{journaltitle}{PeerJ} + \field{langid}{english} + \field{month}{8} + \field{shortjournal}{PeerJ} + \field{title}{Ecological Interactions and the {{Netflix}} Problem} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{5} + \field{year}{2017} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{e3644} + \range{pages}{-1} + \verb{doi} + \verb 10.7717/peerj.3644 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/3L7JALP4/Desjardins-Proulx et al. - 2017 - Ecological interactions and the Netflix problem.pdf + \endverb + \verb{urlraw} + \verb https://peerj.com/articles/3644 + \endverb + \verb{url} + \verb https://peerj.com/articles/3644 + \endverb + \endentry + \entry{doreRelativeEffectsAnthropogenic2021}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=5f8486271db5e2981426fd924aa1f23e}{% + family={Doré}, + familyi={D\bibinitperiod}, + given={Maël}, + giveni={M\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=0e7741d31a239c4be11fc31138a136c1}{% + family={Fontaine}, + familyi={F\bibinitperiod}, + given={Colin}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=ced1f9b5102addb42e37cc32bb0822c2}{% + family={Thébault}, + familyi={T\bibinitperiod}, + given={Elisa}, + giveni={E\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{c9a7cb75b065abd1e803419ba2751185} + \strng{fullhash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{fullhashraw}{a13d5d8e849820e44f068077f3aef7c1} + \strng{bibnamehash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{authorbibnamehash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{authornamehash}{c9a7cb75b065abd1e803419ba2751185} + \strng{authorfullhash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{authorfullhashraw}{a13d5d8e849820e44f068077f3aef7c1} + \field{sortinit}{D} + \field{sortinithash}{6f385f66841fb5e82009dc833c761848} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Pollinators provide crucial ecosystem services that underpin to wild plant reproduction and yields of insect-pollinated crops. Understanding the relative impacts of anthropogenic pressures and climate on the structure of plant–pollinator interaction networks is vital considering ongoing global change and pollinator decline. Our ability to predict the consequences of global change for pollinator assemblages worldwide requires global syntheses, but these analytical approaches may be hindered by variable methods among studies that either invalidate comparisons or mask biological phenomena. Here we conducted a synthetic analysis that assesses the relative impact of anthropogenic pressures and climatic variability, and accounts for heterogeneity in sampling methodology to reveal network responses at the global scale. We analyzed an extensive dataset, comprising 295 networks over 123 locations all over the world, and reporting over 50,000 interactions between flowering plant species and their insect visitors. Our study revealed that anthropogenic pressures correlate with an increase in generalism in pollination networks while pollinator richness and taxonomic composition are more related to climatic variables with an increase in dipteran pollinator richness associated with cooler temperatures. The contrasting response of species richness and generalism of the plant–pollinator networks stresses the importance of considering interaction network structure alongside diversity in ecological monitoring. In addition, differences in sampling design explained more variation than anthropogenic pressures or climate on both pollination networks richness and generalism, highlighting the crucial need to report and incorporate sampling design in macroecological comparative studies of pollination networks. As a whole, our study reveals a potential human impact on pollination networks at a global scale. However, further research is needed to evaluate potential consequences of loss of specialist species and their unique ecological interactions and evolutionary pathways on the ecosystem pollination function at a global scale.} + \field{issn}{1365-2486} + \field{journaltitle}{Global Change Biology} + \field{langid}{english} + \field{number}{6} + \field{title}{Relative Effects of Anthropogenic Pressures, Climate, and Sampling Design on the Structure of Pollination Networks at the Global Scale} + \field{urlday}{21} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{27} + \field{year}{2021} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{1266\bibrangedash 1280} + \range{pages}{15} + \verb{doi} + \verb 10.1111/gcb.15474 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/89ZXBJQP/10.1111@gcb.15474.pdf.pdf;/home/polarolouis/Zotero/storage/IVR6RGG7/Doré et al. - 2021 - Relative effects of anthropogenic pressures, clima.pdf;/home/polarolouis/Zotero/storage/WSJ4DV98/gcb.html + \endverb + \verb{urlraw} + \verb https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.15474 + \endverb + \verb{url} + \verb https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.15474 + \endverb + \keyw{anthropogenic pressures,climate,connectance,data,generalism,human impacts,plant-pollinator,pollination networks,richness,sampling effects,specialization} + \endentry + \entry{govaertEMAlgorithmBlock2005}{article}{}{} + \name{author}{2}{}{% + {{un=2,uniquepart=given,hash=e362e82efc56e96877c249de27098dd7}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=2}}% + {{un=2,uniquepart=given,hash=5554bf45de9d6150691084d7cde5594c}{% + family={Nadif}, + familyi={N\bibinitperiod}, + given={M.}, + giveni={M\bibinitperiod}, + givenun=2}}% + } + \strng{namehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{bibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorbibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authornamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \field{sortinit}{G} + \field{sortinithash}{32d67eca0634bf53703493fb1090a2e8} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.} + \field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}} + \field{issn}{1939-3539} + \field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence} + \field{month}{4} + \field{number}{4} + \field{title}{An {{EM}} Algorithm for the Block Mixture Model} + \field{volume}{27} + \field{year}{2005} + \field{dateera}{ce} + \field{pages}{643\bibrangedash 647} + \range{pages}{5} + \verb{doi} + \verb 10.1109/TPAMI.2005.69 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/6IG45HH2/govaert2005.pdf.pdf;/home/polarolouis/Zotero/storage/TL8M3XRF/Govaert et Nadif - 2005 - An EM algorithm for the block mixture model.pdf;/home/polarolouis/Zotero/storage/2Y48IB26/1401917.html + \endverb + \keyw{Approximation algorithms,Classification algorithms,Clustering algorithms,Clustering methods,Data mining,EM algorithm,Index Terms- Block mixture model,Maximum likelihood estimation,Parameter estimation,Partitioning algorithms,Self organizing feature maps,Sparse matrices,variational approximation.} + \endentry + \entry{govaertLatentBlockModel2010}{article}{}{} + \name{author}{2}{}{% + {{un=2,uniquepart=given,hash=5dbd99c49ebc046dee294b4d416a1850}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={Gérard}, + giveni={G\bibinitperiod}, + givenun=2}}% + {{un=2,uniquepart=given,hash=a6bc7c3c64d6c8adfb8e4a1479f69e37}{% + family={Nadif}, + familyi={N\bibinitperiod}, + given={Mohamed}, + giveni={M\bibinitperiod}, + givenun=2}}% + } + \list{publisher}{1}{% + {Taylor \& Francis}% + } + \strng{namehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{fullhash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{fullhashraw}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{bibnamehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authorbibnamehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authornamehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authorfullhash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authorfullhashraw}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \field{sortinit}{G} + \field{sortinithash}{32d67eca0634bf53703493fb1090a2e8} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, variables, there are other methods, called block clustering methods, which simultaneously consider the two sets and organize the data into homogeneous blocks. This kind of method has practical importance in a wide variety of applications such as text and market basket data analysis. Typically, the data that arise in these applications are arranged as a two-way contingency table. Using Poisson distributions, a latent block model for these data is proposed and, setting it under the maximum likelihood approach and the classification maximum likelihood approach, various algorithms are provided. Their performances are evaluated and compared to a simple use of EM or CEM applied separately on the rows and columns of the contingency table.} + \field{day}{13} + \field{issn}{0361-0926} + \field{journaltitle}{Communications in Statistics - Theory and Methods} + \field{month}{1} + \field{number}{3} + \field{title}{Latent {{Block Model}} for {{Contingency Table}}} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{39} + \field{year}{2010} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{416\bibrangedash 425} + \range{pages}{10} + \verb{doi} + \verb 10.1080/03610920903140197 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/PPHP33Z9/Govaert et Nadif - 2010 - Latent Block Model for Contingency Table.pdf;/home/polarolouis/Zotero/storage/UT8TARCX/govaert2010.pdf.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1080/03610920903140197 + \endverb + \verb{url} + \verb https://doi.org/10.1080/03610920903140197 + \endverb + \keyw{62H17,62H30,Block clustering,Block Poisson mixture model,CEM algorithm,Contingency table,EM algorithm} + \endentry + \entry{hollandStochasticBlockmodelsFirst1983}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=f77d8823946c674172702e2a9422f960}{% + family={Holland}, + familyi={H\bibinitperiod}, + given={Paul\bibnamedelima W.}, + giveni={P\bibinitperiod\bibinitdelim W\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=366a6f6fd90063590430fc87699ad172}{% + family={Laskey}, + familyi={L\bibinitperiod}, + given={Kathryn\bibnamedelima Blackmond}, + giveni={K\bibinitperiod\bibinitdelim B\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=68cccf1e7640862e35f66adb8b8df15e}{% + family={Leinhardt}, + familyi={L\bibinitperiod}, + given={Samuel}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{aeaf35c76a5d4569ad7665b4c4d75533} + \strng{fullhash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{fullhashraw}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{bibnamehash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{authorbibnamehash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{authornamehash}{aeaf35c76a5d4569ad7665b4c4d75533} + \strng{authorfullhash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{authorfullhashraw}{2589c0d43c44e4c1eb0c89a68a5510a3} + \field{sortinit}{H} + \field{sortinithash}{23a3aa7c24e56cfa16945d55545109b5} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{shorttitle} + \field{abstract}{A stochastic model is proposed for social networks in which the actors in a network are partitioned into subgroups called blocks. The model provides a stochastic generalization of the blockmodel. Estimation techniques are developed for the special case of a single relation social network, with blocks specified a priori. An extension of the model allows for tendencies toward reciprocation of ties beyond those explained by the partition. The extended model provides a one degree-of-freedom test of the model. A numerical example from the social network literature is used to illustrate the methods.} + \field{day}{1} + \field{issn}{0378-8733} + \field{journaltitle}{Social Networks} + \field{langid}{english} + \field{month}{6} + \field{number}{2} + \field{shortjournal}{Social Networks} + \field{shorttitle}{Stochastic Blockmodels} + \field{title}{Stochastic Blockmodels: {{First}} Steps} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{5} + \field{year}{1983} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{109\bibrangedash 137} + \range{pages}{29} + \verb{doi} + \verb 10.1016/0378-8733(83)90021-7 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/6F8YT8AD/holland1983.pdf.pdf;/home/polarolouis/Zotero/storage/7DSZ3KD9/Holland et al. - 1983 - Stochastic blockmodels First steps.pdf;/home/polarolouis/Zotero/storage/DUL2RV8Q/holland1983.pdf.pdf;/home/polarolouis/Zotero/storage/G9KZBG9W/0378873383900217.html + \endverb + \verb{urlraw} + \verb https://www.sciencedirect.com/science/article/pii/0378873383900217 + \endverb + \verb{url} + \verb https://www.sciencedirect.com/science/article/pii/0378873383900217 + \endverb + \endentry + \entry{hubertComparingPartitions1985}{article}{}{} + \name{author}{2}{}{% + {{un=0,uniquepart=base,hash=d5d1d02dd8d174f83c61ea441c89cba6}{% + family={Hubert}, + familyi={H\bibinitperiod}, + given={Lawrence}, + giveni={L\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=baebbb2356b9e79fc400b332e197f628}{% + family={Arabie}, + familyi={A\bibinitperiod}, + given={Phipps}, + giveni={P\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{fa62d725515e6d56c25bb670992fc030} + \strng{fullhash}{fa62d725515e6d56c25bb670992fc030} + \strng{fullhashraw}{fa62d725515e6d56c25bb670992fc030} + \strng{bibnamehash}{fa62d725515e6d56c25bb670992fc030} + \strng{authorbibnamehash}{fa62d725515e6d56c25bb670992fc030} + \strng{authornamehash}{fa62d725515e6d56c25bb670992fc030} + \strng{authorfullhash}{fa62d725515e6d56c25bb670992fc030} + \strng{authorfullhashraw}{fa62d725515e6d56c25bb670992fc030} + \field{sortinit}{H} + \field{sortinithash}{23a3aa7c24e56cfa16945d55545109b5} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The problem of comparing two different partitions of a finite set of objects reappears continually in the clustering literature. We begin by reviewing a well-known measure of partition correspondence often attributed to Rand (1971), discuss the issue of correcting this index for chance, and note that a recent normalization strategy developed by Morey and Agresti (1984) and adopted by others (e.g., Miligan and Cooper 1985) is based on an incorrect assumption. Then, the general problem of comparing partitions is approached indirectly by assessing the congruence of two proximity matrices using a simple cross-product measure. They are generated from corresponding partitions using various scoring rules. Special cases derivable include traditionally familiar statistics and/or ones tailored to weight certain object pairs differentially. Finally, we propose a measure based on the comparison of object triples having the advantage of a probabilistic interpretation in addition to being corrected for chance (i.e., assuming a constant value under a reasonable null hypothesis) and bounded between ±1.} + \field{day}{1} + \field{issn}{1432-1343} + \field{journaltitle}{Journal of Classification} + \field{langid}{english} + \field{month}{12} + \field{number}{1} + \field{shortjournal}{Journal of Classification} + \field{title}{Comparing Partitions} + \field{urlday}{4} + \field{urlmonth}{7} + \field{urlyear}{2023} + \field{volume}{2} + \field{year}{1985} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{193\bibrangedash 218} + \range{pages}{26} + \verb{doi} + \verb 10.1007/BF01908075 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/7TKW7HEM/Hubert et Arabie - 1985 - Comparing partitions.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1007/BF01908075 + \endverb + \verb{url} + \verb https://doi.org/10.1007/BF01908075 + \endverb + \keyw{Consensus indices,Measures of agreement,Measures of association} + \endentry + \entry{kaszewska-gilasGlobalStudiesHostParasite2021}{article}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=1060144f6bf089ddb39c0a773fa82781}{% + family={Kaszewska-Gilas}, + familyi={K\bibinithyphendelim G\bibinitperiod}, + given={Katarzyna}, + giveni={K\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=8f601d5f526bf7c56a62c351a97a6fc0}{% + family={Kosicki}, + familyi={K\bibinitperiod}, + given={Jakub\bibnamedelima Ziemowit}, + giveni={J\bibinitperiod\bibinitdelim Z\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7ee4c3605774e1066f3346ae7e22994a}{% + family={Hromada}, + familyi={H\bibinitperiod}, + given={Martin}, + giveni={M\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=43ca2b485ec7de4873e6148b934bffc2}{% + family={Skoracki}, + familyi={S\bibinitperiod}, + given={Maciej}, + giveni={M\bibinitperiod}, + givenun=0}}% + } + \list{publisher}{1}{% + {Multidisciplinary Digital Publishing Institute}% + } + \strng{namehash}{60e665ce10e70d3c88ec91570e0391a7} + \strng{fullhash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{fullhashraw}{db3017d0681dc7614f83d067f3cd7c90} + \strng{bibnamehash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{authorbibnamehash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{authornamehash}{60e665ce10e70d3c88ec91570e0391a7} + \strng{authorfullhash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{authorfullhashraw}{db3017d0681dc7614f83d067f3cd7c90} + \field{sortinit}{K} + \field{sortinithash}{c02bf6bff1c488450c352b40f5d853ab} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The quill mites belonging to the family Syringophilidae (Acari: Prostigmata: Cheyletoidea) are obligate ectoparasites of birds. They inhabit different types of the quills, where they spend their whole life cycle. In this paper, we conducted a global study of syringophilid mites associated with columbiform birds. We examined 772 pigeon and dove individuals belonging to 112 species (35\% world fauna) from all zoogeographical regions (except Madagascan) where Columbiformes occur. We measured the prevalence (IP) and the confidence interval (CI) for all infested host species. IP ranges between 4.2 and 66.7 (CI 0.2–100). We applied a bipartite analysis to determine host–parasite interaction, network indices, and host specificity on species and whole network levels. The Syringophilidae–Columbiformes network was composed of 25 mite species and 65 host species. The bipartite network was characterized by a high network level specialization H2′ = 0.93, high nestedness N = 0.908, connectance C = 0.90, and high modularity Q = 0.83, with 20 modules. Moreover, we reconstructed the phylogeny of the quill mites associated with columbiform birds on the generic level. Analysis shows two distinct clades: Meitingsunes + Psittaciphilus, and Peristerophila + Terratosyringophilus.} + \field{issn}{2076-2615} + \field{issue}{12} + \field{journaltitle}{Animals} + \field{langid}{english} + \field{month}{12} + \field{number}{12} + \field{title}{Global {{Studies}} of the {{Host-Parasite Relationships}} between {{Ectoparasitic Mites}} of the {{Family Syringophilidae}} and {{Birds}} of the {{Order Columbiformes}}} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{11} + \field{year}{2021} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{3392} + \range{pages}{1} + \verb{doi} + \verb 10.3390/ani11123392 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/VXVQ5CPH/Kaszewska-Gilas et al. - 2021 - Global Studies of the Host-Parasite Relationships .pdf + \endverb + \verb{urlraw} + \verb https://www.mdpi.com/2076-2615/11/12/3392 + \endverb + \verb{url} + \verb https://www.mdpi.com/2076-2615/11/12/3392 + \endverb + \keyw{Acari,biodiversity,bipartite-example,network,pigeons and doves,quill mites} + \endentry + \entry{pavlopoulosBipartiteGraphsSystems2018}{article}{}{} + \name{author}{6}{}{% + {{un=0,uniquepart=base,hash=0087d9b97de9555720996d74b66fb60b}{% + family={Pavlopoulos}, + familyi={P\bibinitperiod}, + given={Georgios\bibnamedelima A}, + giveni={G\bibinitperiod\bibinitdelim A\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=de4d8713289b9979d359a94af773ab6f}{% + family={Kontou}, + familyi={K\bibinitperiod}, + given={Panagiota\bibnamedelima I}, + giveni={P\bibinitperiod\bibinitdelim I\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=5d39579ad04e92dcee3f5a529b61a11b}{% + family={Pavlopoulou}, + familyi={P\bibinitperiod}, + given={Athanasia}, + giveni={A\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=3a5b31e03e2db8e3ba92112430418c25}{% + family={Bouyioukos}, + familyi={B\bibinitperiod}, + given={Costas}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=27ff66ab47061f7893ae1e468a3fc8ed}{% + family={Markou}, + familyi={M\bibinitperiod}, + given={Evripides}, + giveni={E\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=036f1add5806722fd7b16f47997a3e07}{% + family={Bagos}, + familyi={B\bibinitperiod}, + given={Pantelis\bibnamedelima G}, + giveni={P\bibinitperiod\bibinitdelim G\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{61dfdac1d3d191fffa9416199c8908da} + \strng{fullhash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{fullhashraw}{41e76bcdb009bfb21b1f1062699bb740} + \strng{bibnamehash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{authorbibnamehash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{authornamehash}{61dfdac1d3d191fffa9416199c8908da} + \strng{authorfullhash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{authorfullhashraw}{41e76bcdb009bfb21b1f1062699bb740} + \field{sortinit}{P} + \field{sortinithash}{ff3bcf24f47321b42cb156c2cc8a8422} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{shorttitle} + \field{abstract}{The latest advances in high-throughput techniques during the past decade allowed the systems biology field to expand significantly. Today, the focus of biologists has shifted from the study of individual biological components to the study of complex biological systems and their dynamics at a larger scale. Through the discovery of novel bioentity relationships, researchers reveal new information about biological functions and processes. Graphs are widely used to represent bioentities such as proteins, genes, small molecules, ligands, and others such as nodes and their connections as edges within a network. In this review, special focus is given to the usability of bipartite graphs and their impact on the field of network biology and medicine. Furthermore, their topological properties and how these can be applied to certain biological case studies are discussed. Finally, available methodologies and software are presented, and useful insights on how bipartite graphs can shape the path toward the solution of challenging biological problems are provided.} + \field{day}{1} + \field{issn}{2047-217X} + \field{journaltitle}{GigaScience} + \field{month}{4} + \field{number}{4} + \field{shortjournal}{GigaScience} + \field{shorttitle}{Bipartite Graphs in Systems Biology and Medicine} + \field{title}{Bipartite Graphs in Systems Biology and Medicine: A Survey of Methods and Applications} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{7} + \field{year}{2018} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{giy014} + \range{pages}{-1} + \verb{doi} + \verb 10.1093/gigascience/giy014 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/2KJFL3SB/Pavlopoulos et al. - 2018 - Bipartite graphs in systems biology and medicine .pdf;/home/polarolouis/Zotero/storage/A2Y2EGPA/pavlopoulos2018.pdf.pdf;/home/polarolouis/Zotero/storage/UK2MK5FW/pavlopoulos2018.pdf.pdf;/home/polarolouis/Zotero/storage/XP7G4PZF/4875933.html + \endverb + \verb{urlraw} + \verb https://doi.org/10.1093/gigascience/giy014 + \endverb + \verb{url} + \verb https://doi.org/10.1093/gigascience/giy014 + \endverb + \endentry + \entry{ramos-jilibertoTopologicalChangeAndean2010}{article}{}{} + \name{author}{7}{}{% + {{un=0,uniquepart=base,hash=37fbaca87cb5258d071137c06f72ec3a}{% + family={Ramos-Jiliberto}, + familyi={R\bibinithyphendelim J\bibinitperiod}, + given={Rodrigo}, + giveni={R\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=2d74d5e68b4441c4d1e274b81e99b7f0}{% + family={Domínguez}, + familyi={D\bibinitperiod}, + given={Daniela}, + giveni={D\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=701a68384704ff87a16386e41a3079b4}{% + family={Espinoza}, + familyi={E\bibinitperiod}, + given={Claudia}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=f91190d571d0252b243c971d0946fbc3}{% + family={López}, + familyi={L\bibinitperiod}, + given={Gioconda}, + giveni={G\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=68347c10bd8b1373ccc0f3acb313593c}{% + family={Valdovinos}, + familyi={V\bibinitperiod}, + given={Fernanda\bibnamedelima S.}, + giveni={F\bibinitperiod\bibinitdelim S\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=024ba0c16a22b2b4cfde442e15f60ed0}{% + family={Bustamante}, + familyi={B\bibinitperiod}, + given={Ramiro\bibnamedelima O.}, + giveni={R\bibinitperiod\bibinitdelim O\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=a3fddc49d4fa3ce834de5373d007e93c}{% + family={Medel}, + familyi={M\bibinitperiod}, + given={Rodrigo}, + giveni={R\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{45e8c0ed18af0c101e1debf3e8f02bd9} + \strng{fullhash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{fullhashraw}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{bibnamehash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{authorbibnamehash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{authornamehash}{45e8c0ed18af0c101e1debf3e8f02bd9} + \strng{authorfullhash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{authorfullhashraw}{c39d20192b3c813ebfe16e20eef0ce57} + \field{sortinit}{R} + \field{sortinithash}{5e1c39a9d46ffb6bebd8f801023a9486} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Pollination interaction networks exhibit structural regularities across a wide range of natural environments. Long-tailed degree distribution, nestedness, and modularity are the most prevalent topological patterns found in most bipartite networks analyzed up to day. In this work we evaluate the variation of these topological properties along an altitudinal gradient. To this end, we examined four plant–pollinator networks from the Chilean Andes at 33°S, in range from 1800 to 3600m elevation. Our results indicate that network topology is strongly and systematically affected by elevation. At increasing altitude, the number of potential visitors per plant decreased, and species’ degree distributions are closer to random expectations. On the other hand, the nested structure of mutualistic interactions systematically decreased with elevation, and network modularity was significantly higher than random expectations over the entire altitudinal range. In addition, at increasing elevations the pollination networks were organized in fewer and more strongly connected modules. Our results suggest that the severe abiotic conditions found at increased elevations translate into less organized pollination networks.} + \field{day}{1} + \field{issn}{1476-945X} + \field{journaltitle}{Ecological Complexity} + \field{langid}{english} + \field{month}{3} + \field{number}{1} + \field{shortjournal}{Ecological Complexity} + \field{title}{Topological Change of {{Andean}} Plant–Pollinator Networks along an Altitudinal Gradient} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{7} + \field{year}{2010} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{86\bibrangedash 90} + \range{pages}{5} + \verb{doi} + \verb 10.1016/j.ecocom.2009.06.001 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/ATY3ZP2X/Ramos-Jiliberto et al. - 2010 - Topological change of Andean plant–pollinator netw.pdf;/home/polarolouis/Zotero/storage/HPBGUP65/ramos-jiliberto2010.pdf.pdf;/home/polarolouis/Zotero/storage/I33MZQQ7/ramos-jiliberto2010.pdf.pdf;/home/polarolouis/Zotero/storage/YJX8XBNW/S1476945X09000622.html + \endverb + \verb{urlraw} + \verb https://www.sciencedirect.com/science/article/pii/S1476945X09000622 + \endverb + \verb{url} + \verb https://www.sciencedirect.com/science/article/pii/S1476945X09000622 + \endverb + \keyw{bipartite-example,Chile,Complexity,Degree distribution,Modularity,Mutualistic networks,Nestedness,Power law} + \endentry + \entry{snijdersEstimationPredictionStochastic1997}{article}{}{} + \name{author}{2}{}{% + {{un=0,uniquepart=base,hash=e25df3941d6ce13c09ad2d002f03a434}{% + family={Snijders}, + familyi={S\bibinitperiod}, + given={Tom\bibnamedelima A.B.}, + giveni={T\bibinitperiod\bibinitdelim A\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=3cfab6ac25c3507c0676ebdd926a01b1}{% + family={Nowicki}, + familyi={N\bibinitperiod}, + given={Krzysztof}, + giveni={K\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{0737c596a5f3986cabea3811efc31eae} + \strng{fullhash}{0737c596a5f3986cabea3811efc31eae} + \strng{fullhashraw}{0737c596a5f3986cabea3811efc31eae} + \strng{bibnamehash}{0737c596a5f3986cabea3811efc31eae} + \strng{authorbibnamehash}{0737c596a5f3986cabea3811efc31eae} + \strng{authornamehash}{0737c596a5f3986cabea3811efc31eae} + \strng{authorfullhash}{0737c596a5f3986cabea3811efc31eae} + \strng{authorfullhashraw}{0737c596a5f3986cabea3811efc31eae} + \field{sortinit}{S} + \field{sortinithash}{b164b07b29984b41daf1e85279fbc5ab} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{blockmodeling for graphs is proposed. The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong. Statistical procedures are derived for estimating the probabilities of edges and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this strategy is practical only for small graphs. A Bayesian estimator, based on the Gibbs sampling, is proposed. This estimator is practical also for large graphs. When ML estimators are used, the block structure can be predicted based on predictive likelihood. When Gibbs sampling is used, the block structure can be predicted from posterior predictive probabilities. A side result is that when the number of vertices tends to infinity while the probabilities remain constant, the block structure can be recovered correctly with probability tending to 1.} + \field{day}{1} + \field{issn}{1432-1343} + \field{journaltitle}{Journal of Classification} + \field{langid}{english} + \field{month}{1} + \field{number}{1} + \field{shortjournal}{J. of Classification} + \field{title}{Estimation and {{Prediction}} for {{Stochastic Blockmodels}} for {{Graphs}} with {{Latent Block Structure}}} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{14} + \field{year}{1997} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{75\bibrangedash 100} + \range{pages}{26} + \verb{doi} + \verb 10.1007/s003579900004 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/2GYRASW5/snijders1997.pdf.pdf;/home/polarolouis/Zotero/storage/JJNQV32Y/Snijders et Nowicki - 1997 - Estimation and Prediction for Stochastic Blockmode.pdf;/home/polarolouis/Zotero/storage/LXGG9SRP/snijders1997.pdf.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1007/s003579900004 + \endverb + \verb{url} + \verb https://doi.org/10.1007/s003579900004 + \endverb + \keyw{Bayesian Estimator,Block Structure,Gibbs Sampling,Large Graph,Statistical Procedure} + \endentry + \enddatalist + \datalist[entry]{apa/global//global/global/global} + \entry{AccueilMIAParisSaclay}{online}{}{} + \field{sortinit}{A} + \field{sortinithash}{2f401846e2029bad6b3ecc16d50031e2} + \field{labeldatesource}{nodate} + \field{labeltitlesource}{title} + \field{title}{Accueil | {{MIA Paris-Saclay}}} + \field{urlday}{3} + \field{urlmonth}{7} + \field{urlyear}{2023} + \field{urldateera}{ce} + \verb{file} + \verb /home/polarolouis/Zotero/storage/I7FWTZC3/mia-ps.inrae.fr.html + \endverb + \verb{urlraw} + \verb https://mia-ps.inrae.fr/ + \endverb + \verb{url} + \verb https://mia-ps.inrae.fr/ + \endverb + \endentry + \entry{anakokDisentanglingStructureEcological2022}{online}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=fe9e51991c906363fdb9789340eb02b8}{% + family={Anakok}, + familyi={A\bibinitperiod}, + given={Emre}, + giveni={E\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=0e7741d31a239c4be11fc31138a136c1}{% + family={Fontaine}, + familyi={F\bibinitperiod}, + given={Colin}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=f23dbf986aa073f9022baede42ef0479}{% + family={Thebault}, + familyi={T\bibinitperiod}, + given={Elisa}, + giveni={E\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{fullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{fullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \strng{bibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorbibnamehash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authornamehash}{91ac6a753125108a3ce0782cad59a3d8} + \strng{authorfullhash}{1f785414b676cf3eff4e0a7230f1c933} + \strng{authorfullhashraw}{1f785414b676cf3eff4e0a7230f1c933} + \field{sortinit}{A} + \field{sortinithash}{2f401846e2029bad6b3ecc16d50031e2} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated in simulation studies. The practical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.} + \field{day}{29} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{langid}{english} + \field{month}{11} + \field{title}{Disentangling the Structure of Ecological Bipartite Networks from Observation Processes} + \field{urlday}{14} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{year}{2022} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{eprint} + \verb 2211.16364 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/LQ3FINZG/Anakok et al. - 2022 - Disentangling the structure of ecological bipartit.pdf + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2211.16364 + \endverb + \keyw{Statistics - Methodology} + \endentry + \entry{biernackiAssessingMixtureModel2000}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=255c9c519676be165266b81a64bfee7e}{% + family={Biernacki}, + familyi={B\bibinitperiod}, + given={C.}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=d4c385b68696de3eb64ee9e356c030b6}{% + family={Celeux}, + familyi={C\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=e362e82efc56e96877c249de27098dd7}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{b7345cdc8a5fd7a8ac9f253a305026a2} + \strng{fullhash}{4f27942f3e82511621b18e076e78f9a9} + \strng{fullhashraw}{4f27942f3e82511621b18e076e78f9a9} + \strng{bibnamehash}{4f27942f3e82511621b18e076e78f9a9} + \strng{authorbibnamehash}{4f27942f3e82511621b18e076e78f9a9} + \strng{authornamehash}{b7345cdc8a5fd7a8ac9f253a305026a2} + \strng{authorfullhash}{4f27942f3e82511621b18e076e78f9a9} + \strng{authorfullhashraw}{4f27942f3e82511621b18e076e78f9a9} + \field{sortinit}{B} + \field{sortinithash}{d7095fff47cda75ca2589920aae98399} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{We propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood. For this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. Then, the integrated completed likelihood (ICL) is approximated using the Bayesian information criterion (BIC). Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data.} + \field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}} + \field{issn}{1939-3539} + \field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence} + \field{month}{7} + \field{number}{7} + \field{title}{Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood} + \field{volume}{22} + \field{year}{2000} + \field{dateera}{ce} + \field{pages}{719\bibrangedash 725} + \range{pages}{7} + \verb{doi} + \verb 10.1109/34.865189 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/MK9H446U/Biernacki et al. - 2000 - Assessing a mixture model for clustering with the .pdf + \endverb + \keyw{Bayesian methods,Context modeling,Gaussian distribution,Numerical simulation,Probability distribution,Robustness} + \endentry + \entry{chabert-liddellLearningCommonStructures2023}{online}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=b2590d483a7fe284c2cdda3920206a4e}{% + family={Chabert-Liddell}, + familyi={C\bibinithyphendelim L\bibinitperiod}, + given={Saint-Clair}, + giveni={S\bibinithyphendelim C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7fecb6ce38c5ec9d4555962d959d2379}{% + family={Barbillon}, + familyi={B\bibinitperiod}, + given={Pierre}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=06c8f96f3a1aba5140a38275380f781f}{% + family={Donnet}, + familyi={D\bibinitperiod}, + given={Sophie}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{fullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{fullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{bibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorbibnamehash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authornamehash}{3101a173d5bb9ee9e4417e1b9abc0d4b} + \strng{authorfullhash}{8aa3fbe7fb498627f8f349ffc9943f6f} + \strng{authorfullhashraw}{8aa3fbe7fb498627f8f349ffc9943f6f} + \field{sortinit}{C} + \field{sortinithash}{4d103a86280481745c9c897c925753c0} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.} + \field{day}{27} + \field{eprintclass}{stat} + \field{eprinttype}{arxiv} + \field{month}{3} + \field{title}{Learning Common Structures in a Collection of Networks. {{An}} Application to Food Webs} + \field{type}{article} + \field{urlday}{22} + \field{urlmonth}{5} + \field{urlyear}{2023} + \field{year}{2023} + \field{dateera}{ce} + \field{urldateera}{ce} + \verb{doi} + \verb 10.48550/arXiv.2206.00560 + \endverb + \verb{eprint} + \verb 2206.00560 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/M74TXGCF/Chabert-Liddell et al. - 2023 - Learning common structures in a collection of netw.pdf;/home/polarolouis/Zotero/storage/A35M8KNP/2206.html + \endverb + \verb{urlraw} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \verb{url} + \verb http://arxiv.org/abs/2206.00560 + \endverb + \keyw{Statistics - Applications,Statistics - Methodology} + \endentry + \entry{daudinMixtureModelRandom2008}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=de4bdd0bb56d35c0db284d95b0eae35f}{% + family={Daudin}, + familyi={D\bibinitperiod}, + given={J.-J.}, + giveni={J\bibinithyphendelim J\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7099f7ae5fb227f549cc71bbc6d525ab}{% + family={Picard}, + familyi={P\bibinitperiod}, + given={F.}, + giveni={F\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=9f772e002ea2fcde759c25cd69c5299c}{% + family={Robin}, + familyi={R\bibinitperiod}, + given={S.}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{8db2758afbcd0c9a4aff2a9e81bcccaf} + \strng{fullhash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{fullhashraw}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{bibnamehash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{authorbibnamehash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{authornamehash}{8db2758afbcd0c9a4aff2a9e81bcccaf} + \strng{authorfullhash}{1ca792ce8b7d10d284e9b70bf8d15647} + \strng{authorfullhashraw}{1ca792ce8b7d10d284e9b70bf8d15647} + \field{sortinit}{D} + \field{sortinithash}{6f385f66841fb5e82009dc833c761848} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The Erdös–Rényi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it does not fit well to real-world networks. The vertices of those networks are often structured in unknown classes (functionally related proteins or social communities) with different connectivity properties. The stochastic block structures model was proposed for this purpose in the context of social sciences, using a Bayesian approach. We consider the same model in a frequentest statistical framework. We give the degree distribution and the clustering coefficient associated with this model, a variational method to estimate its parameters and a model selection criterion to select the number of classes. This estimation procedure allows us to deal with large networks containing thousands of vertices. The method is used to uncover the modular structure of a network of enzymatic reactions.} + \field{day}{1} + \field{issn}{1573-1375} + \field{journaltitle}{Statistics and Computing} + \field{langid}{english} + \field{month}{6} + \field{number}{2} + \field{shortjournal}{Stat Comput} + \field{title}{A Mixture Model for Random Graphs} + \field{urlday}{16} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{18} + \field{year}{2008} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{173\bibrangedash 183} + \range{pages}{11} + \verb{doi} + \verb 10.1007/s11222-007-9046-7 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/439HK27B/Daudin et al. - 2008 - A mixture model for random graphs.pdf;/home/polarolouis/Zotero/storage/HVVF5MNY/daudin2007.pdf.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1007/s11222-007-9046-7 + \endverb + \verb{url} + \verb https://doi.org/10.1007/s11222-007-9046-7 + \endverb + \keyw{Mixture models,Random graphs,Variational~method} + \endentry + \entry{desjardins-proulxEcologicalInteractionsNetflix2017}{article}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=e6f2e3608eb78a89f65a1e4632b852d7}{% + family={Desjardins-Proulx}, + familyi={D\bibinithyphendelim P\bibinitperiod}, + given={Philippe}, + giveni={P\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=e5c9887a52ecb13e307da69a7bd95579}{% + family={Laigle}, + familyi={L\bibinitperiod}, + given={Idaline}, + giveni={I\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=707f55e341a1c9baf6b1c57fc13a6701}{% + family={Poisot}, + familyi={P\bibinitperiod}, + given={Timothée}, + giveni={T\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=63bf0d8e60941c7bd0526fb3208072b5}{% + family={Gravel}, + familyi={G\bibinitperiod}, + given={Dominique}, + giveni={D\bibinitperiod}, + givenun=0}}% + } + \list{publisher}{1}{% + {PeerJ Inc.}% + } + \strng{namehash}{6fdcc4093a18a4d307c5c28c05c369aa} + \strng{fullhash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{fullhashraw}{c3e64892b634eab5a19dfbb1247066bb} + \strng{bibnamehash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{authorbibnamehash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{authornamehash}{6fdcc4093a18a4d307c5c28c05c369aa} + \strng{authorfullhash}{c3e64892b634eab5a19dfbb1247066bb} + \strng{authorfullhashraw}{c3e64892b634eab5a19dfbb1247066bb} + \field{sortinit}{D} + \field{sortinithash}{6f385f66841fb5e82009dc833c761848} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Species interactions are a key component of ecosystems but we generally have an incomplete picture of who-eats-who in a given community. Different techniques have been devised to predict species interactions using theoretical models or abundances. Here, we explore the K nearest neighbour approach, with a special emphasis on recommendation, along with a supervised machine learning technique. Recommenders are algorithms developed for companies like Netflix to predict whether a customer will like a product given the preferences of similar customers. These machine learning techniques are well-suited to study binary ecological interactions since they focus on positive-only data. By removing a prey from a predator, we find that recommenders can guess the missing prey around 50\% of the times on the first try, with up to 881 possibilities. Traits do not improve significantly the results for the K nearest neighbour, although a simple test with a supervised learning approach (random forests) show we can predict interactions with high accuracy using only three traits per species. This result shows that binary interactions can be predicted without regard to the ecological community given only three variables: body mass and two variables for the species’ phylogeny. These techniques are complementary, as recommenders can predict interactions in the absence of traits, using only information about other species’ interactions, while supervised learning algorithms such as random forests base their predictions on traits only but do not exploit other species’ interactions. Further work should focus on developing custom similarity measures specialized for ecology to improve the KNN algorithms and using richer data to capture indirect relationships between species.} + \field{day}{10} + \field{issn}{2167-8359} + \field{journaltitle}{PeerJ} + \field{langid}{english} + \field{month}{8} + \field{shortjournal}{PeerJ} + \field{title}{Ecological Interactions and the {{Netflix}} Problem} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{5} + \field{year}{2017} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{e3644} + \range{pages}{-1} + \verb{doi} + \verb 10.7717/peerj.3644 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/3L7JALP4/Desjardins-Proulx et al. - 2017 - Ecological interactions and the Netflix problem.pdf + \endverb + \verb{urlraw} + \verb https://peerj.com/articles/3644 + \endverb + \verb{url} + \verb https://peerj.com/articles/3644 + \endverb + \endentry + \entry{doreRelativeEffectsAnthropogenic2021}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=5f8486271db5e2981426fd924aa1f23e}{% + family={Doré}, + familyi={D\bibinitperiod}, + given={Maël}, + giveni={M\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=0e7741d31a239c4be11fc31138a136c1}{% + family={Fontaine}, + familyi={F\bibinitperiod}, + given={Colin}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=ced1f9b5102addb42e37cc32bb0822c2}{% + family={Thébault}, + familyi={T\bibinitperiod}, + given={Elisa}, + giveni={E\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{c9a7cb75b065abd1e803419ba2751185} + \strng{fullhash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{fullhashraw}{a13d5d8e849820e44f068077f3aef7c1} + \strng{bibnamehash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{authorbibnamehash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{authornamehash}{c9a7cb75b065abd1e803419ba2751185} + \strng{authorfullhash}{a13d5d8e849820e44f068077f3aef7c1} + \strng{authorfullhashraw}{a13d5d8e849820e44f068077f3aef7c1} + \field{sortinit}{D} + \field{sortinithash}{6f385f66841fb5e82009dc833c761848} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Pollinators provide crucial ecosystem services that underpin to wild plant reproduction and yields of insect-pollinated crops. Understanding the relative impacts of anthropogenic pressures and climate on the structure of plant–pollinator interaction networks is vital considering ongoing global change and pollinator decline. Our ability to predict the consequences of global change for pollinator assemblages worldwide requires global syntheses, but these analytical approaches may be hindered by variable methods among studies that either invalidate comparisons or mask biological phenomena. Here we conducted a synthetic analysis that assesses the relative impact of anthropogenic pressures and climatic variability, and accounts for heterogeneity in sampling methodology to reveal network responses at the global scale. We analyzed an extensive dataset, comprising 295 networks over 123 locations all over the world, and reporting over 50,000 interactions between flowering plant species and their insect visitors. Our study revealed that anthropogenic pressures correlate with an increase in generalism in pollination networks while pollinator richness and taxonomic composition are more related to climatic variables with an increase in dipteran pollinator richness associated with cooler temperatures. The contrasting response of species richness and generalism of the plant–pollinator networks stresses the importance of considering interaction network structure alongside diversity in ecological monitoring. In addition, differences in sampling design explained more variation than anthropogenic pressures or climate on both pollination networks richness and generalism, highlighting the crucial need to report and incorporate sampling design in macroecological comparative studies of pollination networks. As a whole, our study reveals a potential human impact on pollination networks at a global scale. However, further research is needed to evaluate potential consequences of loss of specialist species and their unique ecological interactions and evolutionary pathways on the ecosystem pollination function at a global scale.} + \field{issn}{1365-2486} + \field{journaltitle}{Global Change Biology} + \field{langid}{english} + \field{number}{6} + \field{title}{Relative Effects of Anthropogenic Pressures, Climate, and Sampling Design on the Structure of Pollination Networks at the Global Scale} + \field{urlday}{21} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{27} + \field{year}{2021} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{1266\bibrangedash 1280} + \range{pages}{15} + \verb{doi} + \verb 10.1111/gcb.15474 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/89ZXBJQP/10.1111@gcb.15474.pdf.pdf;/home/polarolouis/Zotero/storage/IVR6RGG7/Doré et al. - 2021 - Relative effects of anthropogenic pressures, clima.pdf;/home/polarolouis/Zotero/storage/WSJ4DV98/gcb.html + \endverb + \verb{urlraw} + \verb https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.15474 + \endverb + \verb{url} + \verb https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.15474 + \endverb + \keyw{anthropogenic pressures,climate,connectance,data,generalism,human impacts,plant-pollinator,pollination networks,richness,sampling effects,specialization} + \endentry + \entry{govaertEMAlgorithmBlock2005}{article}{}{} + \name{author}{2}{}{% + {{un=2,uniquepart=given,hash=e362e82efc56e96877c249de27098dd7}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={G.}, + giveni={G\bibinitperiod}, + givenun=2}}% + {{un=2,uniquepart=given,hash=5554bf45de9d6150691084d7cde5594c}{% + family={Nadif}, + familyi={N\bibinitperiod}, + given={M.}, + giveni={M\bibinitperiod}, + givenun=2}}% + } + \strng{namehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{fullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{bibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorbibnamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authornamehash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhash}{cf148152bf4f33b329bfd7d07cf74c02} + \strng{authorfullhashraw}{cf148152bf4f33b329bfd7d07cf74c02} + \field{sortinit}{G} + \field{sortinithash}{32d67eca0634bf53703493fb1090a2e8} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.} + \field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}} + \field{issn}{1939-3539} + \field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence} + \field{month}{4} + \field{number}{4} + \field{title}{An {{EM}} Algorithm for the Block Mixture Model} + \field{volume}{27} + \field{year}{2005} + \field{dateera}{ce} + \field{pages}{643\bibrangedash 647} + \range{pages}{5} + \verb{doi} + \verb 10.1109/TPAMI.2005.69 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/6IG45HH2/govaert2005.pdf.pdf;/home/polarolouis/Zotero/storage/TL8M3XRF/Govaert et Nadif - 2005 - An EM algorithm for the block mixture model.pdf;/home/polarolouis/Zotero/storage/2Y48IB26/1401917.html + \endverb + \keyw{Approximation algorithms,Classification algorithms,Clustering algorithms,Clustering methods,Data mining,EM algorithm,Index Terms- Block mixture model,Maximum likelihood estimation,Parameter estimation,Partitioning algorithms,Self organizing feature maps,Sparse matrices,variational approximation.} + \endentry + \entry{govaertLatentBlockModel2010}{article}{}{} + \name{author}{2}{}{% + {{un=2,uniquepart=given,hash=5dbd99c49ebc046dee294b4d416a1850}{% + family={Govaert}, + familyi={G\bibinitperiod}, + given={Gérard}, + giveni={G\bibinitperiod}, + givenun=2}}% + {{un=2,uniquepart=given,hash=a6bc7c3c64d6c8adfb8e4a1479f69e37}{% + family={Nadif}, + familyi={N\bibinitperiod}, + given={Mohamed}, + giveni={M\bibinitperiod}, + givenun=2}}% + } + \list{publisher}{1}{% + {Taylor \& Francis}% + } + \strng{namehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{fullhash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{fullhashraw}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{bibnamehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authorbibnamehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authornamehash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authorfullhash}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \strng{authorfullhashraw}{8c07dc45270c2c9b55f2b3ebf5a87cf7} + \field{sortinit}{G} + \field{sortinithash}{32d67eca0634bf53703493fb1090a2e8} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, variables, there are other methods, called block clustering methods, which simultaneously consider the two sets and organize the data into homogeneous blocks. This kind of method has practical importance in a wide variety of applications such as text and market basket data analysis. Typically, the data that arise in these applications are arranged as a two-way contingency table. Using Poisson distributions, a latent block model for these data is proposed and, setting it under the maximum likelihood approach and the classification maximum likelihood approach, various algorithms are provided. Their performances are evaluated and compared to a simple use of EM or CEM applied separately on the rows and columns of the contingency table.} + \field{day}{13} + \field{issn}{0361-0926} + \field{journaltitle}{Communications in Statistics - Theory and Methods} + \field{month}{1} + \field{number}{3} + \field{title}{Latent {{Block Model}} for {{Contingency Table}}} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{39} + \field{year}{2010} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{416\bibrangedash 425} + \range{pages}{10} + \verb{doi} + \verb 10.1080/03610920903140197 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/PPHP33Z9/Govaert et Nadif - 2010 - Latent Block Model for Contingency Table.pdf;/home/polarolouis/Zotero/storage/UT8TARCX/govaert2010.pdf.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1080/03610920903140197 + \endverb + \verb{url} + \verb https://doi.org/10.1080/03610920903140197 + \endverb + \keyw{62H17,62H30,Block clustering,Block Poisson mixture model,CEM algorithm,Contingency table,EM algorithm} + \endentry + \entry{hollandStochasticBlockmodelsFirst1983}{article}{}{} + \name{author}{3}{}{% + {{un=0,uniquepart=base,hash=f77d8823946c674172702e2a9422f960}{% + family={Holland}, + familyi={H\bibinitperiod}, + given={Paul\bibnamedelima W.}, + giveni={P\bibinitperiod\bibinitdelim W\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=366a6f6fd90063590430fc87699ad172}{% + family={Laskey}, + familyi={L\bibinitperiod}, + given={Kathryn\bibnamedelima Blackmond}, + giveni={K\bibinitperiod\bibinitdelim B\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=68cccf1e7640862e35f66adb8b8df15e}{% + family={Leinhardt}, + familyi={L\bibinitperiod}, + given={Samuel}, + giveni={S\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{aeaf35c76a5d4569ad7665b4c4d75533} + \strng{fullhash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{fullhashraw}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{bibnamehash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{authorbibnamehash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{authornamehash}{aeaf35c76a5d4569ad7665b4c4d75533} + \strng{authorfullhash}{2589c0d43c44e4c1eb0c89a68a5510a3} + \strng{authorfullhashraw}{2589c0d43c44e4c1eb0c89a68a5510a3} + \field{sortinit}{H} + \field{sortinithash}{23a3aa7c24e56cfa16945d55545109b5} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{shorttitle} + \field{abstract}{A stochastic model is proposed for social networks in which the actors in a network are partitioned into subgroups called blocks. The model provides a stochastic generalization of the blockmodel. Estimation techniques are developed for the special case of a single relation social network, with blocks specified a priori. An extension of the model allows for tendencies toward reciprocation of ties beyond those explained by the partition. The extended model provides a one degree-of-freedom test of the model. A numerical example from the social network literature is used to illustrate the methods.} + \field{day}{1} + \field{issn}{0378-8733} + \field{journaltitle}{Social Networks} + \field{langid}{english} + \field{month}{6} + \field{number}{2} + \field{shortjournal}{Social Networks} + \field{shorttitle}{Stochastic Blockmodels} + \field{title}{Stochastic Blockmodels: {{First}} Steps} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{5} + \field{year}{1983} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{109\bibrangedash 137} + \range{pages}{29} + \verb{doi} + \verb 10.1016/0378-8733(83)90021-7 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/6F8YT8AD/holland1983.pdf.pdf;/home/polarolouis/Zotero/storage/7DSZ3KD9/Holland et al. - 1983 - Stochastic blockmodels First steps.pdf;/home/polarolouis/Zotero/storage/DUL2RV8Q/holland1983.pdf.pdf;/home/polarolouis/Zotero/storage/G9KZBG9W/0378873383900217.html + \endverb + \verb{urlraw} + \verb https://www.sciencedirect.com/science/article/pii/0378873383900217 + \endverb + \verb{url} + \verb https://www.sciencedirect.com/science/article/pii/0378873383900217 + \endverb + \endentry + \entry{hubertComparingPartitions1985}{article}{}{} + \name{author}{2}{}{% + {{un=0,uniquepart=base,hash=d5d1d02dd8d174f83c61ea441c89cba6}{% + family={Hubert}, + familyi={H\bibinitperiod}, + given={Lawrence}, + giveni={L\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=baebbb2356b9e79fc400b332e197f628}{% + family={Arabie}, + familyi={A\bibinitperiod}, + given={Phipps}, + giveni={P\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{fa62d725515e6d56c25bb670992fc030} + \strng{fullhash}{fa62d725515e6d56c25bb670992fc030} + \strng{fullhashraw}{fa62d725515e6d56c25bb670992fc030} + \strng{bibnamehash}{fa62d725515e6d56c25bb670992fc030} + \strng{authorbibnamehash}{fa62d725515e6d56c25bb670992fc030} + \strng{authornamehash}{fa62d725515e6d56c25bb670992fc030} + \strng{authorfullhash}{fa62d725515e6d56c25bb670992fc030} + \strng{authorfullhashraw}{fa62d725515e6d56c25bb670992fc030} + \field{sortinit}{H} + \field{sortinithash}{23a3aa7c24e56cfa16945d55545109b5} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The problem of comparing two different partitions of a finite set of objects reappears continually in the clustering literature. We begin by reviewing a well-known measure of partition correspondence often attributed to Rand (1971), discuss the issue of correcting this index for chance, and note that a recent normalization strategy developed by Morey and Agresti (1984) and adopted by others (e.g., Miligan and Cooper 1985) is based on an incorrect assumption. Then, the general problem of comparing partitions is approached indirectly by assessing the congruence of two proximity matrices using a simple cross-product measure. They are generated from corresponding partitions using various scoring rules. Special cases derivable include traditionally familiar statistics and/or ones tailored to weight certain object pairs differentially. Finally, we propose a measure based on the comparison of object triples having the advantage of a probabilistic interpretation in addition to being corrected for chance (i.e., assuming a constant value under a reasonable null hypothesis) and bounded between ±1.} + \field{day}{1} + \field{issn}{1432-1343} + \field{journaltitle}{Journal of Classification} + \field{langid}{english} + \field{month}{12} + \field{number}{1} + \field{shortjournal}{Journal of Classification} + \field{title}{Comparing Partitions} + \field{urlday}{4} + \field{urlmonth}{7} + \field{urlyear}{2023} + \field{volume}{2} + \field{year}{1985} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{193\bibrangedash 218} + \range{pages}{26} + \verb{doi} + \verb 10.1007/BF01908075 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/7TKW7HEM/Hubert et Arabie - 1985 - Comparing partitions.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1007/BF01908075 + \endverb + \verb{url} + \verb https://doi.org/10.1007/BF01908075 + \endverb + \keyw{Consensus indices,Measures of agreement,Measures of association} + \endentry + \entry{kaszewska-gilasGlobalStudiesHostParasite2021}{article}{}{} + \name{author}{4}{}{% + {{un=0,uniquepart=base,hash=1060144f6bf089ddb39c0a773fa82781}{% + family={Kaszewska-Gilas}, + familyi={K\bibinithyphendelim G\bibinitperiod}, + given={Katarzyna}, + giveni={K\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=8f601d5f526bf7c56a62c351a97a6fc0}{% + family={Kosicki}, + familyi={K\bibinitperiod}, + given={Jakub\bibnamedelima Ziemowit}, + giveni={J\bibinitperiod\bibinitdelim Z\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=7ee4c3605774e1066f3346ae7e22994a}{% + family={Hromada}, + familyi={H\bibinitperiod}, + given={Martin}, + giveni={M\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=43ca2b485ec7de4873e6148b934bffc2}{% + family={Skoracki}, + familyi={S\bibinitperiod}, + given={Maciej}, + giveni={M\bibinitperiod}, + givenun=0}}% + } + \list{publisher}{1}{% + {Multidisciplinary Digital Publishing Institute}% + } + \strng{namehash}{60e665ce10e70d3c88ec91570e0391a7} + \strng{fullhash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{fullhashraw}{db3017d0681dc7614f83d067f3cd7c90} + \strng{bibnamehash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{authorbibnamehash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{authornamehash}{60e665ce10e70d3c88ec91570e0391a7} + \strng{authorfullhash}{db3017d0681dc7614f83d067f3cd7c90} + \strng{authorfullhashraw}{db3017d0681dc7614f83d067f3cd7c90} + \field{sortinit}{K} + \field{sortinithash}{c02bf6bff1c488450c352b40f5d853ab} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{The quill mites belonging to the family Syringophilidae (Acari: Prostigmata: Cheyletoidea) are obligate ectoparasites of birds. They inhabit different types of the quills, where they spend their whole life cycle. In this paper, we conducted a global study of syringophilid mites associated with columbiform birds. We examined 772 pigeon and dove individuals belonging to 112 species (35\% world fauna) from all zoogeographical regions (except Madagascan) where Columbiformes occur. We measured the prevalence (IP) and the confidence interval (CI) for all infested host species. IP ranges between 4.2 and 66.7 (CI 0.2–100). We applied a bipartite analysis to determine host–parasite interaction, network indices, and host specificity on species and whole network levels. The Syringophilidae–Columbiformes network was composed of 25 mite species and 65 host species. The bipartite network was characterized by a high network level specialization H2′ = 0.93, high nestedness N = 0.908, connectance C = 0.90, and high modularity Q = 0.83, with 20 modules. Moreover, we reconstructed the phylogeny of the quill mites associated with columbiform birds on the generic level. Analysis shows two distinct clades: Meitingsunes + Psittaciphilus, and Peristerophila + Terratosyringophilus.} + \field{issn}{2076-2615} + \field{issue}{12} + \field{journaltitle}{Animals} + \field{langid}{english} + \field{month}{12} + \field{number}{12} + \field{title}{Global {{Studies}} of the {{Host-Parasite Relationships}} between {{Ectoparasitic Mites}} of the {{Family Syringophilidae}} and {{Birds}} of the {{Order Columbiformes}}} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{11} + \field{year}{2021} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{3392} + \range{pages}{1} + \verb{doi} + \verb 10.3390/ani11123392 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/VXVQ5CPH/Kaszewska-Gilas et al. - 2021 - Global Studies of the Host-Parasite Relationships .pdf + \endverb + \verb{urlraw} + \verb https://www.mdpi.com/2076-2615/11/12/3392 + \endverb + \verb{url} + \verb https://www.mdpi.com/2076-2615/11/12/3392 + \endverb + \keyw{Acari,biodiversity,bipartite-example,network,pigeons and doves,quill mites} + \endentry + \entry{pavlopoulosBipartiteGraphsSystems2018}{article}{}{} + \name{author}{6}{}{% + {{un=0,uniquepart=base,hash=0087d9b97de9555720996d74b66fb60b}{% + family={Pavlopoulos}, + familyi={P\bibinitperiod}, + given={Georgios\bibnamedelima A}, + giveni={G\bibinitperiod\bibinitdelim A\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=de4d8713289b9979d359a94af773ab6f}{% + family={Kontou}, + familyi={K\bibinitperiod}, + given={Panagiota\bibnamedelima I}, + giveni={P\bibinitperiod\bibinitdelim I\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=5d39579ad04e92dcee3f5a529b61a11b}{% + family={Pavlopoulou}, + familyi={P\bibinitperiod}, + given={Athanasia}, + giveni={A\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=3a5b31e03e2db8e3ba92112430418c25}{% + family={Bouyioukos}, + familyi={B\bibinitperiod}, + given={Costas}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=27ff66ab47061f7893ae1e468a3fc8ed}{% + family={Markou}, + familyi={M\bibinitperiod}, + given={Evripides}, + giveni={E\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=036f1add5806722fd7b16f47997a3e07}{% + family={Bagos}, + familyi={B\bibinitperiod}, + given={Pantelis\bibnamedelima G}, + giveni={P\bibinitperiod\bibinitdelim G\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{61dfdac1d3d191fffa9416199c8908da} + \strng{fullhash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{fullhashraw}{41e76bcdb009bfb21b1f1062699bb740} + \strng{bibnamehash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{authorbibnamehash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{authornamehash}{61dfdac1d3d191fffa9416199c8908da} + \strng{authorfullhash}{41e76bcdb009bfb21b1f1062699bb740} + \strng{authorfullhashraw}{41e76bcdb009bfb21b1f1062699bb740} + \field{sortinit}{P} + \field{sortinithash}{ff3bcf24f47321b42cb156c2cc8a8422} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{shorttitle} + \field{abstract}{The latest advances in high-throughput techniques during the past decade allowed the systems biology field to expand significantly. Today, the focus of biologists has shifted from the study of individual biological components to the study of complex biological systems and their dynamics at a larger scale. Through the discovery of novel bioentity relationships, researchers reveal new information about biological functions and processes. Graphs are widely used to represent bioentities such as proteins, genes, small molecules, ligands, and others such as nodes and their connections as edges within a network. In this review, special focus is given to the usability of bipartite graphs and their impact on the field of network biology and medicine. Furthermore, their topological properties and how these can be applied to certain biological case studies are discussed. Finally, available methodologies and software are presented, and useful insights on how bipartite graphs can shape the path toward the solution of challenging biological problems are provided.} + \field{day}{1} + \field{issn}{2047-217X} + \field{journaltitle}{GigaScience} + \field{month}{4} + \field{number}{4} + \field{shortjournal}{GigaScience} + \field{shorttitle}{Bipartite Graphs in Systems Biology and Medicine} + \field{title}{Bipartite Graphs in Systems Biology and Medicine: A Survey of Methods and Applications} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{7} + \field{year}{2018} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{giy014} + \range{pages}{-1} + \verb{doi} + \verb 10.1093/gigascience/giy014 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/2KJFL3SB/Pavlopoulos et al. - 2018 - Bipartite graphs in systems biology and medicine .pdf;/home/polarolouis/Zotero/storage/A2Y2EGPA/pavlopoulos2018.pdf.pdf;/home/polarolouis/Zotero/storage/UK2MK5FW/pavlopoulos2018.pdf.pdf;/home/polarolouis/Zotero/storage/XP7G4PZF/4875933.html + \endverb + \verb{urlraw} + \verb https://doi.org/10.1093/gigascience/giy014 + \endverb + \verb{url} + \verb https://doi.org/10.1093/gigascience/giy014 + \endverb + \endentry + \entry{ramos-jilibertoTopologicalChangeAndean2010}{article}{}{} + \name{author}{7}{}{% + {{un=0,uniquepart=base,hash=37fbaca87cb5258d071137c06f72ec3a}{% + family={Ramos-Jiliberto}, + familyi={R\bibinithyphendelim J\bibinitperiod}, + given={Rodrigo}, + giveni={R\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=2d74d5e68b4441c4d1e274b81e99b7f0}{% + family={Domínguez}, + familyi={D\bibinitperiod}, + given={Daniela}, + giveni={D\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=701a68384704ff87a16386e41a3079b4}{% + family={Espinoza}, + familyi={E\bibinitperiod}, + given={Claudia}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=f91190d571d0252b243c971d0946fbc3}{% + family={López}, + familyi={L\bibinitperiod}, + given={Gioconda}, + giveni={G\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=68347c10bd8b1373ccc0f3acb313593c}{% + family={Valdovinos}, + familyi={V\bibinitperiod}, + given={Fernanda\bibnamedelima S.}, + giveni={F\bibinitperiod\bibinitdelim S\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=024ba0c16a22b2b4cfde442e15f60ed0}{% + family={Bustamante}, + familyi={B\bibinitperiod}, + given={Ramiro\bibnamedelima O.}, + giveni={R\bibinitperiod\bibinitdelim O\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=a3fddc49d4fa3ce834de5373d007e93c}{% + family={Medel}, + familyi={M\bibinitperiod}, + given={Rodrigo}, + giveni={R\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{45e8c0ed18af0c101e1debf3e8f02bd9} + \strng{fullhash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{fullhashraw}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{bibnamehash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{authorbibnamehash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{authornamehash}{45e8c0ed18af0c101e1debf3e8f02bd9} + \strng{authorfullhash}{c39d20192b3c813ebfe16e20eef0ce57} + \strng{authorfullhashraw}{c39d20192b3c813ebfe16e20eef0ce57} + \field{sortinit}{R} + \field{sortinithash}{5e1c39a9d46ffb6bebd8f801023a9486} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{Pollination interaction networks exhibit structural regularities across a wide range of natural environments. Long-tailed degree distribution, nestedness, and modularity are the most prevalent topological patterns found in most bipartite networks analyzed up to day. In this work we evaluate the variation of these topological properties along an altitudinal gradient. To this end, we examined four plant–pollinator networks from the Chilean Andes at 33°S, in range from 1800 to 3600m elevation. Our results indicate that network topology is strongly and systematically affected by elevation. At increasing altitude, the number of potential visitors per plant decreased, and species’ degree distributions are closer to random expectations. On the other hand, the nested structure of mutualistic interactions systematically decreased with elevation, and network modularity was significantly higher than random expectations over the entire altitudinal range. In addition, at increasing elevations the pollination networks were organized in fewer and more strongly connected modules. Our results suggest that the severe abiotic conditions found at increased elevations translate into less organized pollination networks.} + \field{day}{1} + \field{issn}{1476-945X} + \field{journaltitle}{Ecological Complexity} + \field{langid}{english} + \field{month}{3} + \field{number}{1} + \field{shortjournal}{Ecological Complexity} + \field{title}{Topological Change of {{Andean}} Plant–Pollinator Networks along an Altitudinal Gradient} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{7} + \field{year}{2010} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{86\bibrangedash 90} + \range{pages}{5} + \verb{doi} + \verb 10.1016/j.ecocom.2009.06.001 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/ATY3ZP2X/Ramos-Jiliberto et al. - 2010 - Topological change of Andean plant–pollinator netw.pdf;/home/polarolouis/Zotero/storage/HPBGUP65/ramos-jiliberto2010.pdf.pdf;/home/polarolouis/Zotero/storage/I33MZQQ7/ramos-jiliberto2010.pdf.pdf;/home/polarolouis/Zotero/storage/YJX8XBNW/S1476945X09000622.html + \endverb + \verb{urlraw} + \verb https://www.sciencedirect.com/science/article/pii/S1476945X09000622 + \endverb + \verb{url} + \verb https://www.sciencedirect.com/science/article/pii/S1476945X09000622 + \endverb + \keyw{bipartite-example,Chile,Complexity,Degree distribution,Modularity,Mutualistic networks,Nestedness,Power law} + \endentry + \entry{snijdersEstimationPredictionStochastic1997}{article}{}{} + \name{author}{2}{}{% + {{un=0,uniquepart=base,hash=e25df3941d6ce13c09ad2d002f03a434}{% + family={Snijders}, + familyi={S\bibinitperiod}, + given={Tom\bibnamedelima A.B.}, + giveni={T\bibinitperiod\bibinitdelim A\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=3cfab6ac25c3507c0676ebdd926a01b1}{% + family={Nowicki}, + familyi={N\bibinitperiod}, + given={Krzysztof}, + giveni={K\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{0737c596a5f3986cabea3811efc31eae} + \strng{fullhash}{0737c596a5f3986cabea3811efc31eae} + \strng{fullhashraw}{0737c596a5f3986cabea3811efc31eae} + \strng{bibnamehash}{0737c596a5f3986cabea3811efc31eae} + \strng{authorbibnamehash}{0737c596a5f3986cabea3811efc31eae} + \strng{authornamehash}{0737c596a5f3986cabea3811efc31eae} + \strng{authorfullhash}{0737c596a5f3986cabea3811efc31eae} + \strng{authorfullhashraw}{0737c596a5f3986cabea3811efc31eae} + \field{sortinit}{S} + \field{sortinithash}{b164b07b29984b41daf1e85279fbc5ab} + \field{extradatescope}{labelyear} + \field{labeldatesource}{} + \true{uniqueprimaryauthor} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{abstract}{blockmodeling for graphs is proposed. The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong. Statistical procedures are derived for estimating the probabilities of edges and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this strategy is practical only for small graphs. A Bayesian estimator, based on the Gibbs sampling, is proposed. This estimator is practical also for large graphs. When ML estimators are used, the block structure can be predicted based on predictive likelihood. When Gibbs sampling is used, the block structure can be predicted from posterior predictive probabilities. A side result is that when the number of vertices tends to infinity while the probabilities remain constant, the block structure can be recovered correctly with probability tending to 1.} + \field{day}{1} + \field{issn}{1432-1343} + \field{journaltitle}{Journal of Classification} + \field{langid}{english} + \field{month}{1} + \field{number}{1} + \field{shortjournal}{J. of Classification} + \field{title}{Estimation and {{Prediction}} for {{Stochastic Blockmodels}} for {{Graphs}} with {{Latent Block Structure}}} + \field{urlday}{15} + \field{urlmonth}{6} + \field{urlyear}{2023} + \field{volume}{14} + \field{year}{1997} + \field{dateera}{ce} + \field{urldateera}{ce} + \field{pages}{75\bibrangedash 100} + \range{pages}{26} + \verb{doi} + \verb 10.1007/s003579900004 + \endverb + \verb{file} + \verb /home/polarolouis/Zotero/storage/2GYRASW5/snijders1997.pdf.pdf;/home/polarolouis/Zotero/storage/JJNQV32Y/Snijders et Nowicki - 1997 - Estimation and Prediction for Stochastic Blockmode.pdf;/home/polarolouis/Zotero/storage/LXGG9SRP/snijders1997.pdf.pdf + \endverb + \verb{urlraw} + \verb https://doi.org/10.1007/s003579900004 + \endverb + \verb{url} + \verb https://doi.org/10.1007/s003579900004 + \endverb + \keyw{Bayesian Estimator,Block Structure,Gibbs Sampling,Large Graph,Statistical Procedure} + \endentry + \enddatalist +\endrefsection +\endinput + diff --git a/rapport/rapport.bcf-SAVE-ERROR b/rapport/rapport.bcf-SAVE-ERROR new file mode 100644 index 0000000..4815b19 --- /dev/null +++ b/rapport/rapport.bcf-SAVE-ERROR @@ -0,0 +1,3089 @@ + + + + + + output_encoding + utf8 + + + input_encoding + utf8 + + + debug + 0 + + + mincrossrefs + 999 + + + minxrefs + 2 + + + sortcase + 1 + + + sortupper + 1 + + + + + + + alphaothers + + + + + extradatecontext + labelname + labeltitle + + + labelalpha + 0 + + + labelnamespec + shortauthor + author + shorteditor + editor + + + labeltitle + 0 + + + labeltitlespec + shorttitle + title + maintitle + + + labeltitleyear + 0 + 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+ + + jurisdiction + organization citation + + + legmaterial + source + + + legadminmaterial + citation + source + + + constitution + article + section + amendment + + + software + appentry + + + report + addendum + author + authortype + chapter + doi + eprint + eprintclass + eprinttype + institution + isrn + language + location + note + number + pages + pagetotal + pubstate + subtitle + title + titleaddon + type + version + + + presentation + addendum + author + booksubtitle + booktitle + booktitleaddon + chapter + doi + editor + editortype + eprint + eprintclass + eprinttype + eventday + eventendday + eventendhour + eventendminute + eventendmonth + eventendseason + eventendsecond + eventendtimezone + eventendyear + eventhour + eventminute + eventmonth + eventseason + eventsecond + eventtimezone + eventyear + eventtitle + eventtitleaddon + isbn + language + location + mainsubtitle + maintitle + maintitleaddon + note + number + organization + pages + part + publisher + pubstate + series + subtitle + title + titleaddon + venue + volume + volumes + + + abstract + addendum + afterword + annotator + author + bookauthor + booksubtitle + booktitle + booktitleaddon + chapter + commentator + editor + editora + editorb + editorc + foreword + holder + institution + introduction + issuesubtitle + issuetitle + issuetitleaddon + journalsubtitle + journaltitle + journaltitleaddon + location + mainsubtitle + maintitle + maintitleaddon + nameaddon + note + organization + origlanguage + origlocation + origpublisher + origtitle + part + publisher + relatedstring + series + shortauthor + shorteditor + shorthand + shortjournal + shortseries + shorttitle + sortname + sortshorthand + sorttitle + subtitle + title + titleaddon + translator + venue + + + article + book + inbook + bookinbook + suppbook + booklet + collection + incollection + suppcollection + manual + misc + mvbook + mvcollection + online + patent + periodical + suppperiodical + proceedings + inproceedings + reference + inreference + report + set + thesis + unpublished + + + date + year + + + + + set + + entryset + + + + article + + author + journaltitle + title + + + + book + mvbook + + author + title + + + + inbook + bookinbook + suppbook + + author + title + booktitle + + + + booklet + + + author + editor + + title + + + + collection + reference + mvcollection + mvreference + + editor + title + + + + incollection + suppcollection + inreference + + author + editor + title + booktitle + + + + dataset + + title + + + + manual + + title + + + + misc + software + + title + + + + online + + title + + url + doi + eprint + + + + + patent + + author + title + number + + + + periodical + + editor + title + + + + proceedings + mvproceedings + + title + + + + inproceedings + + author + title + booktitle + + + + report + + author + title + type + institution + + + + thesis + + author + title + type + institution + + + + unpublished + + author + title + + + + + isbn + + + issn + + + ismn + + + gender + + + + book + inbook + article + report + + author + title + + + + + + + ../references.bib + + + AccueilMIAParisSaclay + ramos-jilibertoTopologicalChangeAndean2010 + kaszewska-gilasGlobalStudiesHostParasite2021 + pavlopoulosBipartiteGraphsSystems2018 + desjardins-proulxEcologicalInteractionsNetflix2017 + govaertLatentBlockModel2010 + hollandStochasticBlockmodelsFirst1983 + snijdersEstimationPredictionStochastic1997 + daudinMixtureModelRandom2008 + govaertEMAlgorithmBlock2005 + chabert-liddellLearningCommonStructures2023 + chabert-liddellLearningCommonStructures2023 + daudinMixtureModelRandom2008 + chabert-liddellLearningCommonStructures2023 + biernackiAssessingMixtureModel2000 + daudinMixtureModelRandom2008 + chabert-liddellLearningCommonStructures2023 diff --git a/rapport.tex b/rapport/rapport.tex similarity index 99% rename from rapport.tex rename to rapport/rapport.tex index 3fa4cf9..c040dd5 100644 --- a/rapport.tex +++ b/rapport/rapport.tex @@ -26,13 +26,16 @@ %% Bibliography \usepackage[style=apa,citestyle=authoryear-comp]{biblatex} -\addbibresource{references.bib} +\addbibresource{../references.bib} %% For good md to tex conversion \providecommand{\tightlist}{% \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} \usepackage{booktabs} +% Images + + % Figure placement \floatplacement{figure}{H} diff --git a/tikz/collbm-iid.tex b/tikz/collbm-iid.tex new file mode 100644 index 0000000..8940aa8 --- /dev/null +++ b/tikz/collbm-iid.tex @@ -0,0 +1,117 @@ +\begin{scope}[xshift=18cm, yshift=2cm] + \input{../tikz/lbm.tex} +\end{scope} + +\begin{scope}[xshift=3cm, yshift = 1cm] + \node[text justified, fill=none] at (10, 3.5) + {$\overset{iid}{\sim}$}; + \begin{scope}[yshift = 6cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,1.25) + {\textbf{1}}; + \node[state, draw=black!50] (R12) at (1,1.25) + {\textbf{2}}; + \node[state, draw=black!50] (R13) at (2,1.25) + {\textbf{3}}; + \node[state, draw=black!50] (R21) at (3,1.25) + {\textbf{4}}; + \node[state, draw=black!50] (R31) at (5,1.25) + {\textbf{6}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + + % Label réseau + \node[font=\small, text justified,draw=none, fill=none, + below left = 0.04cm of R11] {$Y^1 = $}; + + + \node[state, draw=black!50] (C11) at (0.5,-1) + {\textbf{1}}; + + \node[state, draw=black!50] (C211) at (2.5,-1) + {\textbf{3}}; + \node[state, draw=black!50] (C22) at (3.5,-1) + {\textbf{4}}; + + \node[state, draw=black!50] (C31) at (4.5,-1) + {\textbf{5}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (C11); + \path (R11) edge (C211); + \path (R11) edge (C22); + + \path (R12) edge [] (C11); + \path (R12) edge (C211); + \path (R12) edge (C22); + + \path (R13) edge [] (C11); + \path (R13) edge (C211); + \path (R13) edge (C22); + + \path (R21) edge (C211); + \path (R21) edge (C22); + \path (R21) edge (C31); + + \path (R31) edge (C31); + \end{scope} + \node[text width=3cm,font=\small, text justified, + rotate=90, fill=none] (dots) at (2.5, 7.5){\dots}; + + \begin{scope}[yshift = 0cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,2.25) + {\textbf{4}}; + \node[state, draw=black!50] (R13) at (2,2.25) + {\textbf{6}}; + \node[state, draw=black!50] (R21) at (3,2.25) + {\textbf{3}}; + \node[state, draw=black!50] (R22) at (4,2.25) + {\textbf{5}}; + \node[state, draw=black!50] (R31) at (5,2.25) + {\textbf{2}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + % Label réseau + \node[font=\small, text justified,draw=none, fill=none, + below left = 0.04cm of R11] {$Y^M = $}; + + \node[state, draw=black!50] (C11) at (0.5,0) + {\textbf{5}}; + \node[state, draw=black!50] (C12) at (1.5,0) + {\textbf{1}}; + + \node[state, draw=black!50] (C22) at (3.5,0) + {\textbf{2}}; + + \node[state, draw=black!50] (C31) at (4.5,0) + {\textbf{4}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (C11); + \path (R11) edge (C12); + \path (R11) edge (C22); + + \path (R13) edge [] (C11); + \path (R13) edge (C12); + \path (R13) edge (C22); + + \path (R21) edge (C22); + \path (R21) edge (C31); + + \path (R22) edge (C22); + \path (R22) edge (C31); + + \path (R31) edge (C31); + \end{scope} +\end{scope} diff --git a/tikz/collbm-pirho.tex b/tikz/collbm-pirho.tex new file mode 100644 index 0000000..48c0781 --- /dev/null +++ b/tikz/collbm-pirho.tex @@ -0,0 +1,117 @@ +\begin{scope}[xshift=18cm, yshift=2cm] + \input{../tikz/lbm-pirho.tex} +\end{scope} + +\begin{scope}[xshift=3cm, yshift = 1cm] + \node[text justified, fill=none] at (10, 3.5) + {$\sim$}; + \begin{scope}[yshift = 6cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,1.25) + {\textbf{1}}; + \node[state, draw=black!50] (R12) at (1,1.25) + {\textbf{2}}; + \node[state, draw=black!50] (R13) at (2,1.25) + {\textbf{3}}; + \node[state, draw=black!50] (R21) at (3,1.25) + {\textbf{4}}; + \node[state, draw=black!50] (R31) at (5,1.25) + {\textbf{6}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + + % Label réseau + \node[font=\small, text justified,draw=none, fill=none, + below left = 0.04cm of R11] {$Y^1 = $}; + + + \node[state, draw=black!50] (C11) at (0.5,-1) + {\textbf{1}}; + + \node[state, draw=black!50] (C211) at (2.5,-1) + {\textbf{3}}; + \node[state, draw=black!50] (C22) at (3.5,-1) + {\textbf{4}}; + + \node[state, draw=black!50] (C31) at (4.5,-1) + {\textbf{5}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (C11); + \path (R11) edge (C211); + \path (R11) edge (C22); + + \path (R12) edge [] (C11); + \path (R12) edge (C211); + \path (R12) edge (C22); + + \path (R13) edge [] (C11); + \path (R13) edge (C211); + \path (R13) edge (C22); + + \path (R21) edge (C211); + \path (R21) edge (C22); + \path (R21) edge (C31); + + \path (R31) edge (C31); + \end{scope} + \node[text width=3cm,font=\small, text justified, + rotate=90, fill=none] (dots) at (2.5, 7.5){\dots}; + + \begin{scope}[yshift = 0cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,2.25) + {\textbf{4}}; + \node[state, draw=black!50] (R13) at (2,2.25) + {\textbf{6}}; + \node[state, draw=black!50] (R21) at (3,2.25) + {\textbf{3}}; + \node[state, draw=black!50] (R22) at (4,2.25) + {\textbf{5}}; + \node[state, draw=black!50] (R31) at (5,2.25) + {\textbf{2}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + % Label réseau + \node[font=\small, text justified,draw=none, fill=none, + below left = 0.04cm of R11] {$Y^M = $}; + + \node[state, draw=black!50] (C11) at (0.5,0) + {\textbf{5}}; + \node[state, draw=black!50] (C12) at (1.5,0) + {\textbf{1}}; + + \node[state, draw=black!50] (C22) at (3.5,0) + {\textbf{2}}; + + \node[state, draw=black!50] (C31) at (4.5,0) + {\textbf{4}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (C11); + \path (R11) edge (C12); + \path (R11) edge (C22); + + \path (R13) edge [] (C11); + \path (R13) edge (C12); + \path (R13) edge (C22); + + \path (R21) edge (C22); + \path (R21) edge (C31); + + \path (R22) edge (C22); + \path (R22) edge (C31); + + \path (R31) edge (C31); + \end{scope} +\end{scope} diff --git a/tikz/greedy-exploration.tex b/tikz/greedy-exploration.tex new file mode 100644 index 0000000..3da6b30 --- /dev/null +++ b/tikz/greedy-exploration.tex @@ -0,0 +1,26 @@ +\draw[step=1cm, help lines] (-2,-2) grid (2,2); +\foreach \x in {1,...,5} \draw (\x-3,-2 + .1)--(\x-3,-2 -.3) node[below] {\footnotesize $\x$}; +\foreach \y in {1,...,5} \draw (-2 + .1, \y-3)--(-2 -.3,\y-3) node[below] {\footnotesize $\y$}; +\draw[fill=gray, draw=gray] (0,0) circle [radius=0.225cm]; +\draw[fill=blueind, draw=blueind] (1,0) circle [radius=0.225cm]; +\draw[fill=blueind, draw=blueind] (0,1) circle [radius=0.225cm]; +\draw[fill=red, draw=red] (-1,0) circle [radius=0.225cm]; +\draw[fill=red, draw=red] (0,-1) circle [radius=0.225cm]; + +% Légende +\node[font=\tiny, text justified,fill=none, rotate=-45] (Splits) at (0.5,0.5){{\color{blueind} Splits}}; +\node[font=\tiny, text justified,fill=none, rotate=-45] (Merges) at (-0.5,-0.5){{\color{red} Merges}}; + +% Splitting +\draw[>=stealth,->,thick, draw=blueind] (0.225,0) -- +(0.55,0); +\draw[>=stealth,->,thick, draw=blueind] (0,0.225) -- +(0,0.55); + +% Merging +\draw[>=stealth,->,thick, draw=red] (-0.225,0) -- +(-0.55,0); +\draw[>=stealth,->,thick, draw=red] (0,-0.225) -- +(0,-0.55); + +% Axes +\draw[>=to,->,thick] (-2,-2) -- +(4.3,0); +\node[font=\small, fill=none] (Q_1) at (2.6,-2) {$Q_1$}; +\draw[>=to,->,thick] (-2,-2) -- +(0,4.3); +\node[font=\small, fill=none] (Q_2) at (-2, 2.6) {$Q_2$}; diff --git a/tikz/lbm-pirho.tex b/tikz/lbm-pirho.tex new file mode 100644 index 0000000..dffa685 --- /dev/null +++ b/tikz/lbm-pirho.tex @@ -0,0 +1,106 @@ +% Couleurs personnalisées +\definecolor{ao(english)}{rgb}{0.0, 0.5, 0.0} +\definecolor{redorg}{RGB}{215, 48, 39} +\definecolor{orangeorg}{RGB}{253, 174, 97} + +\definecolor{blueind}{RGB}{016, 101, 171} +\definecolor{cyanind}{RGB}{058, 147, 195} +\definecolor{electricblue}{RGB}{142, 196, 222} + +\definecolor{greenind}{RGB}{112, 130, 56} + +\definecolor{burntorange}{RGB}{179, 021, 041} +\definecolor{goldenyellow}{RGB}{215, 095, 076} +\definecolor{peach}{RGB}{246, 164, 130} + +\definecolor{gray}{RGB}{128, 128, 128} + +\tikzstyle{every state}=[draw, text=black,scale=0.95, +transform shape] +\tikzstyle{every state}=[draw=none,text=black,scale=0.75, +transform shape] +\tikzset{edge_proba/.style={draw=none, fill=none, + text=black}} + +\tikzstyle{every node}=[fill=blueind] +\node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}}; +\node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}}; +\node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}}; +\node[edge_proba] (pi1) at (1,5.7) {\contour{white}{\textbf{$\pi_{{\color{blueind}\bullet}}^{\color{red}m}$}}}; + +\tikzstyle{every node}=[fill=cyanind] +\node[state, draw=black!50] (R21) at (6.25,5) +{\textbf{R21}}; +\node[state, draw=black!50] (R22) at (7.25,5) +{\textbf{R22}}; +\node[edge_proba] (pi2) at (6.75,5.7) {\contour{white}{\textbf{$\pi_{{\color{cyanind}\bullet}}^{\color{red}m}$}}}; + +\node[state, draw=black!50, fill=electricblue] (R31) at (10,5) {\textbf{R31}}; +\node[edge_proba] (pi3) at (10,5.7) {\contour{white}{\textbf{$\pi_{{\color{electricblue}\bullet}}^{\color{red}m}$}}}; + +\tikzstyle{every node}=[fill=burntorange, shape=rectangle] +\tikzstyle{every state}=[draw=none,text=black,scale=0.75, +transform shape, shape=rectangle] +\node[state, draw=black!50] (C11) at (0,0) {\textbf{C11}}; +\node[state, draw=black!50] (C12) at (1,0) {\textbf{C12}}; +\node[edge_proba] (rho1) at (0.5,-0.9) +{\contour{white}{\textbf{$\rho_{{\color{burntorange}\bullet}}^{\color{red}m}$}}}; + +\tikzstyle{every node}=[fill=goldenyellow, shape=rectangle] +\node[state, draw=black!50] (C21) at (3.5,0) {\textbf{C21}}; +\node[state, draw=black!50] (C22) at (4.5,0) {\textbf{C22}}; +\node[edge_proba] (rho2) at (4,-0.9) +{\contour{white}{\textbf{$\rho_{{\color{goldenyellow}\bullet}}^{\color{red}m}$}}}; + +\tikzstyle{every node}=[fill=peach, shape=rectangle] +\node[state, draw=black!50] (C31) at (10,0) {\textbf{C31}}; +\node[edge_proba] (rho3) at (10,-0.9) +{\contour{white}{\textbf{$\rho_{{\color{peach}\bullet}}^{\color{red}m}$}}}; + + +\tikzstyle{every edge}=[-,>=stealth',shorten +>=1pt,auto,draw,line width=1.5pt,draw opacity=0.2] + + +\path (R11) edge (C12); +\path (R11) edge (C21); +\path (R11) edge (C22); + +\path (R12) edge [] (C11); +\path (R12) edge (C12); +\path (R12) edge (C21); +\path (R12) edge (C22); + +\path (R13) edge [] (C11); +\path (R13) edge (C12); +\path (R13) edge (C21); + + +\path (R11) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left = -0.7cm, + fill=none] {\contour{white}{$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$}} +(C11); +\path (R13) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, right = -0.7cm, + fill=none] {\contour{white}{$\alpha_{{\color{blueind}\bullet}{\color{goldenyellow}\bullet}}$}} +(C22); + + +\path (R21) edge (C22); +\path (R21) edge (C31); + +\path (R22) edge (C21); +\path (R22) edge (C22); +\path (R21) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + right = -0.3cm, fill=none] + {\contour{white}{$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$}} (C21); + +\path (R22) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, right = -0.6cm, + fill=none] {\contour{white}{$\alpha_{{\color{cyanind}\bullet}{\color{peach}\bullet}}$}} (C31); + +\path (R31) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + right=-0.4cm, fill=none] + {\contour{white}{$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$}} (C31); \ No newline at end of file diff --git a/tikz/lbm.tex b/tikz/lbm.tex new file mode 100644 index 0000000..c3e42d2 --- /dev/null +++ b/tikz/lbm.tex @@ -0,0 +1,107 @@ +% Couleurs personnalisées +\definecolor{ao(english)}{rgb}{0.0, 0.5, 0.0} +\definecolor{redorg}{RGB}{215, 48, 39} +\definecolor{orangeorg}{RGB}{253, 174, 97} + +\definecolor{blueind}{RGB}{016, 101, 171} +\definecolor{cyanind}{RGB}{058, 147, 195} +\definecolor{electricblue}{RGB}{142, 196, 222} + +\definecolor{greenind}{RGB}{112, 130, 56} + +\definecolor{burntorange}{RGB}{179, 021, 041} +\definecolor{goldenyellow}{RGB}{215, 095, 076} +\definecolor{peach}{RGB}{246, 164, 130} + +\definecolor{gray}{RGB}{128, 128, 128} + +\tikzstyle{every state}=[draw, text=black,scale=0.95, +transform shape] +\tikzstyle{every state}=[draw=none,text=black,scale=0.75, +transform shape] +\tikzset{edge_proba/.style={draw=white, fill=none, + text=black}} + +\tikzstyle{every node}=[fill=blueind] +\node[edge_proba] (pi1) at (1,5.7) +{\textbf{$\pi_{{\color{blueind}\bullet}}$}}; +\node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}}; +\node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}}; +\node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}}; + +\tikzstyle{every node}=[fill=cyanind] +\node[edge_proba] (pi2) at (6.75,5.7) +{\textbf{$\pi_{{\color{cyanind}\bullet}}$}}; +\node[state, draw=black!50] (R21) at (6.25,5) +{\textbf{R21}}; +\node[state, draw=black!50] (R22) at (7.25,5) +{\textbf{R22}}; + +\tikzstyle{every node}=[fill=electricblue] +\node[edge_proba] (pi3) at (10,5.7) +{\textbf{$\pi_{{\color{electricblue}\bullet}}$}}; +\node[state, draw=black!50] (R31) at (10,5) {\textbf{R31}}; + +\tikzstyle{every node}=[fill=burntorange, shape=rectangle] +\node[edge_proba] (rho1) at (0.5,-0.9) +{\textbf{$\rho_{{\color{burntorange}\bullet}}$}}; +\tikzstyle{every state}=[draw=none,text=black,scale=0.75, +transform shape, shape=rectangle] +\node[state, draw=black!50] (C11) at (0,0) {\textbf{C11}}; +\node[state, draw=black!50] (C12) at (1,0) {\textbf{C12}}; +\tikzstyle{every node}=[fill=goldenyellow, shape=rectangle] +\node[edge_proba] (rho2) at (4,-0.9) +{\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}}; +\node[state, draw=black!50] (C21) at (3.5,0) {\textbf{C21}}; +\node[state, draw=black!50] (C22) at (4.5,0) {\textbf{C22}}; +\tikzstyle{every node}=[fill=peach, shape=rectangle] +\node[edge_proba] (rho3) at (10,-0.9) +{\textbf{$\rho_{{\color{peach}\bullet}}$}}; +\node[state, draw=black!50] (C31) at (10,0) {\textbf{C31}}; + +\tikzstyle{every edge}=[-,>=stealth',shorten +>=1pt,auto,draw,line width=1.5pt,draw opacity=0.2] + + +\path (R11) edge (C12); +\path (R11) edge (C21); +\path (R11) edge (C22); + +\path (R12) edge [] (C11); +\path (R12) edge (C12); +\path (R12) edge (C21); +\path (R12) edge (C22); + +\path (R13) edge [] (C11); +\path (R13) edge (C12); +\path (R13) edge (C21); + + +\path (R11) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left = -0.7cm, + fill=none] {\contour{white}{$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$}} +(C11); +\path (R13) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, right = -0.7cm, + fill=none] {\contour{white}{$\alpha_{{\color{blueind}\bullet}{\color{goldenyellow}\bullet}}$}} +(C22); + + +\path (R21) edge (C22); +\path (R21) edge (C31); + +\path (R22) edge (C21); +\path (R22) edge (C22); +\path (R21) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + right = -0.3cm, fill=none] + {\contour{white}{$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$}} (C21); + +\path (R22) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, right = -0.6cm, + fill=none] {\contour{white}{$\alpha_{{\color{cyanind}\bullet}{\color{peach}\bullet}}$}} (C31); + +\path (R31) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + right=-0.4cm, fill=none] + {\contour{white}{$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$}} (C31); \ No newline at end of file diff --git a/tikz/moving-window.tex b/tikz/moving-window.tex new file mode 100644 index 0000000..a0e3984 --- /dev/null +++ b/tikz/moving-window.tex @@ -0,0 +1,127 @@ +\definecolor{mypurple}{RGB}{128,0,128} +\begin{tikzpicture} + \tikzstyle{model}=[circle,draw=none,fill=gray, thick] + \tikzstyle{split}=[>=stealth,->, thick, draw=blueind] + \tikzstyle{merge}=[>=stealth,->,thick, draw=red] + \draw[step=1cm, help lines] (-2,-2) grid (2,2); + \onslide<1-7>{ + \node[model] (mode) at (0,0) {{\color{red}X}}; + } + + % Axes + \draw[>=to,->,thick] (-2,-2) -- +(1,0); + \node[font=\small, fill=none] (Q_1) at (-0.75,-2) {$Q_1$}; + \draw[>=to,->,thick] (-2,-2) -- +(0,1); + \node[font=\small, fill=none] (Q_2) at (-2,-0.75) {$Q_2$}; + + \onslide<2-8>{ + \draw[color=red, line width=1pt] (-1.5,-1.5) rectangle ++(3,3); + } + \onslide<3>{ + \node[model] (bottom_left) at (-1,-1) {}; + \node[model, opacity=0.6] (row_1) at (0,-1) {}; + \node[model, opacity=0.6] (col_1) at (-1,0) {}; + + \draw[split] (bottom_left) -- (col_1); + \draw[split] (-1.75,0) -- (col_1); + \draw[split] (bottom_left) -- (row_1); + \draw[split] (0,-1.75) -- (row_1); + } + \onslide<4-7>{ + \node[model] (bottom_left) at (-1,-1) {}; + \node[model, draw=blueind] (row_1) at (0,-1) {}; + \node[model, draw=blueind] (col_1) at (-1,0) {}; + } + \onslide<4>{ + \node[model, opacity=0.6] (row_2) at (1,-1) {}; + \node[model, opacity=0.6] (col_2) at (-1,1) {}; + + \draw[split] (col_1) -- (col_2); + \draw[split] (-1.75,1) -- (col_2); + \draw[split] (row_1) -- (row_2); + \draw[split] (1,-1.75) -- (row_2); + \draw[split] (row_1) -- (mode); + \draw[split] (col_1) -- (mode); + } + \onslide<5-7>{ + \node[model, draw=blueind] (row_2) at (1,-1) {}; + \node[model, draw=blueind] (col_2) at (-1,1) {}; + \node[model, draw=blueind] (mode) at (0,0) {{\color{red}X}}; + } + \onslide<5>{ + \node[model, opacity=0.6] (row_3) at (1,0) {}; + \node[model, opacity=0.6] (col_3) at (0,1) {}; + + \draw[split] (col_2) -- (col_3); + \draw[split] (row_2) -- (row_3); + \draw[split] (mode) -- (row_3); + \draw[split] (mode) -- (col_3); + } + \onslide<6-7>{ + \node[model, draw=blueind] (row_3) at (1,0) {}; + \node[model, draw=blueind] (col_3) at (0,1) {}; + } + \onslide<6>{ + \node[model, opacity=0.6] (top_right) at (1,1) {}; + \draw[split] (col_3) -- (top_right); + \draw[split] (row_3) -- (top_right); + } + \onslide<7>{ + \node[model, draw=blueind] (top_right) at (1,1) {}; + } + \onslide<8>{ + \node[model, draw=mypurple] (top_right) at (1,1) {}; + \node[model, draw=mypurple] (row_3) at (1,0) {}; + \node[model, draw=mypurple] (col_3) at (0,1) {}; + \node[model, draw=mypurple] (row_2) at (1,-1) {}; + \node[model, draw=mypurple] (col_2) at (-1,1) {}; + \node[model, draw=mypurple] (mode) at (0,0) {{\color{red}X}}; + \node[model, draw=red] (bottom_left) at (-1,-1) {}; + \node[model, draw=mypurple] (row_1) at (0,-1) {}; + \node[model, draw=mypurple] (col_1) at (-1,0) {}; + + \draw[merge] (1,1.75) -- (top_right); + \draw[merge] (1.75,1) -- (top_right); + \draw[merge] (0,1.75) -- (col_3); + \draw[merge] (1.75,0) -- (row_3); + \draw[merge] (1.75,-1) -- (row_2); + \draw[merge] (-1,1.75) -- (col_2); + + \draw[merge] (top_right) -- (col_3); + \draw[merge] (top_right) -- (row_3); + \draw[merge] (col_3) -- (col_2); + \draw[merge] (row_3) -- (row_2) ; + \draw[merge] (row_3) -- (mode); + \draw[merge] (col_3) -- (mode); + \draw[merge] (col_2) --(col_1); + \draw[merge] (row_2) -- (row_1); + \draw[merge] (mode) -- (row_1); + \draw[merge] (mode) -- (col_1); + \draw[merge] (col_1) -- (bottom_left); + \draw[merge] (row_1) -- (bottom_left); + } + \onslide<9>{ + \node[model, draw=mypurple] (top_right) at (1,1) {}; + \node[model, draw=mypurple] (new_mode) at (1,0) {{\color{red}X}}; + \node[model, draw=mypurple] (col_3) at (0,1) {}; + \node[model, draw=mypurple] (row_2) at (1,-1) {}; + \node[model, draw=mypurple] (col_2) at (-1,1) {}; + \node[model, draw=mypurple] (old_mode) at (0,0) {}; + \node[model, draw=red] (bottom_left) at (-1,-1) {}; + \node[model, draw=mypurple] (row_1) at (0,-1) {}; + \node[model, draw=mypurple] (col_1) at (-1,0) {}; + } + \onslide<10>{ + \draw[color=red, line width=1pt] (-0.5,-1.5) rectangle ++(3,3); + + \node[model, draw=mypurple] (top_right) at (1,1) {}; + \node[model, draw=mypurple] (new_mode) at (1,0) {{\color{red}X}}; + \node[model, draw=mypurple] (col_3) at (0,1) {}; + \node[model, draw=mypurple] (row_2) at (1,-1) {}; + \node[model, draw=mypurple] (col_2) at (-1,1) {}; + \node[model, draw=mypurple] (old_mode) at (0,0) {}; + \node[model, draw=red] (bottom_left) at (-1,-1) {}; + \node[model, draw=mypurple] (row_1) at (0,-1) {}; + \node[model, draw=mypurple] (col_1) at (-1,0) {}; + } +\end{tikzpicture} \ No newline at end of file diff --git a/tikz/network.tex b/tikz/network.tex new file mode 100644 index 0000000..43e6548 --- /dev/null +++ b/tikz/network.tex @@ -0,0 +1,7 @@ +\draw[thick] +(-0.5,0) node[vertex] (n1^4) {} +-- (0.25,2.2) node[vertex] (n2^4) {} +-- (2,1.6) node[vertex] (n3^4) {} +-- (-0.7,1.4) node[vertex] (n4^4) {} +-- (-0.9,1.0) node[vertex] (n5^4) {} +-- (0.8,1.2) node[vertex] (n6^4) {} -- cycle; \ No newline at end of file diff --git a/tikz/plantpollinatornetwork.tex b/tikz/plantpollinatornetwork.tex new file mode 100644 index 0000000..ac9958e --- /dev/null +++ b/tikz/plantpollinatornetwork.tex @@ -0,0 +1,38 @@ +\tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,thin,draw] +\tikzstyle{every state}=[draw, text=white,scale=0.70, font=\scriptsize, transform shape] + +% Upper level +\tikzstyle{every state}=[draw=none,text=white,scale=0.55, font=\scriptsize, transform shape] +% premier cluster +\tikzstyle{every node}=[fill=green!50!blue!20!white] +\node[state] (N1) at (1.1,3) {\includegraphics[width=.15\textwidth]{pollen.png}}; +\node[state, right = of N1] (N2) {\includegraphics[width=.15\textwidth]{pollen.png}}; % at (.75,3) +\node[state, right = of N2] (N3) {\includegraphics[width=.15\textwidth]{pollen.png}}; % at (1.5,3) +\node[state, right = of N3] (N4) {\includegraphics[width=.15\textwidth]{pollen.png}}; % at (2.25,3) +% \node[state] (N5) at (3,3) {\includegraphics[width=.1\textwidth]{pollen.png}}; +% \node[state] (N6) at (3.75,3) {\includegraphics[width=.1\textwidth]{pollen.png}}; + +\tikzstyle{every node}=[shape=rectangle,fill=red!50!blue!20!white] +% \node[state, fill = white] (P) at (-1.5, 0) {\includegraphics[width=.08\textwidth]{bee.png}}; +\node[state, tokens=0] (P1) at (-1, 0) {\includegraphics[width=.1\textwidth]{bee.png}}; +\node[state, tokens=0, right = of P1] (P2) {\includegraphics[width=.1\textwidth]{bee.png}}; % at (-.25, 0) +\node[state, tokens=0, right = of P2] (P3) {\includegraphics[width=.1\textwidth]{bee.png}}; %at (.5, 0) +\node[state, tokens=0, right = of P3] (P4) {\includegraphics[width=.1\textwidth]{bee.png}}; % at (1.25, 0) +\node[state, tokens=0, right = of P4] (P5) {\includegraphics[width=.1\textwidth]{bee.png}};% at (2,0) +\node[state, tokens=0, right = of P5] (P6) {\includegraphics[width=.1\textwidth]{bee.png}}; % at (2.75,0) +% \node[state, tokens=0] (P7) at (3.5,0) {\includegraphics[width=.1\textwidth]{bee.png}}; +% \node[state, tokens=0] (P8) at (4.25,0) {\includegraphics[width=.1\textwidth]{bee.png}}; + +\tikzstyle{every edge}=[>=stealth,shorten >=1pt,auto,thin,draw] +\path (P1) edge (N1); +\path (P2) edge (N1); +\path (P3) edge (N1); +\path (P4) edge (N2); +\path (P4) edge (N1); +\path (P6) edge (N2); +\path (P1) edge (N3); +%\path (P7) edge (N4); +%\path (P8) edge (N5); +%\path (P4) edge (N6); +\path (P5) edge (N3); +\path (P5) edge (N4); \ No newline at end of file