223 lines
No EOL
9.2 KiB
TeX
223 lines
No EOL
9.2 KiB
TeX
\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} % 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{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
|
|
% bibliographie
|
|
\usepackage[style=apa]{biblatex}
|
|
\addbibresource{references.bib}
|
|
|
|
|
|
% Tikz
|
|
%% Tikz Related
|
|
\usetikzlibrary{calc,shapes,backgrounds,arrows,automata,shadows,positioning}
|
|
\usetikzlibrary{arrows,shapes,positioning,shadows,trees,calc,backgrounds,automata,positioning}
|
|
|
|
|
|
|
|
\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{redorg}{RGB}{215,48,39}
|
|
\definecolor{orangeorg}{RGB}{253,174,97}
|
|
|
|
\definecolor{blueind}{RGB}{69,117,233}
|
|
\definecolor{cyanind}{RGB}{116,173,209}
|
|
\definecolor{electricblue}{RGB}{125, 249, 255}
|
|
|
|
\definecolor{greenind}{RGB}{112,130,56}
|
|
|
|
\definecolor{burntorange}{RGB}{204, 85, 0}
|
|
\definecolor{goldenyellow}{RGB}{255, 192, 0}
|
|
\definecolor{peach}{RGB}{255, 229, 180}
|
|
|
|
\definecolor{gray}{RGB}{128,128,128}
|
|
|
|
|
|
\title{Séminaire des stagiaires}
|
|
\subtitle{Adaptation de colSBM aux réseaux bipartites}
|
|
\author[L. Lacoste]{Louis \textsc{Lacoste}}
|
|
\date{29 juin 2023}
|
|
|
|
\begin{document}
|
|
|
|
% titre
|
|
\begin{frame}
|
|
\maketitle
|
|
\end{frame}
|
|
|
|
\section{Contexte du modèle}
|
|
\begin{frame}
|
|
\frametitle{Contexte écologique}
|
|
\begin{itemize}
|
|
\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 Déterminer des structures d'interactions fines de manière agnostique
|
|
\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=white,scale=0.95, transform shape]
|
|
\tikzstyle{every state}=[draw=none,text=white,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=white,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
|
|
$B=\left(
|
|
\begin{array}{rrrrr}
|
|
1 & 1 & 1 & 1 & 0 \\
|
|
0 & 0 & 1 & 1 & 1 \\
|
|
0 & 0 & 0 & 0 & 1 \\
|
|
\end{array}\right)
|
|
$\\
|
|
\end{column}
|
|
\end{columns}
|
|
\smallskip
|
|
Permet de décrire toute interaction impliquant deux agents dont les rôles
|
|
sont de natures différentes.\\
|
|
Par exemple : hôtes-parasites, plantes-pollinisateurs, graines-disperseurs \dots
|
|
\end{frame}
|
|
\begin{frame}
|
|
\frametitle{Latent Block Model (LBM)}
|
|
Proposé par \cite{govaertEMAlgorithmBlock2005}.
|
|
|
|
\begin{figure}[H]
|
|
\center
|
|
\begin{tikzpicture}[scale=.6]
|
|
\tikzstyle{every state}=[draw, text=white,scale=0.95, transform shape]
|
|
\tikzstyle{every state}=[draw=none,text=white,scale=0.75, transform shape]
|
|
|
|
\tikzstyle{every node}=[fill=blueind]
|
|
\node[state, draw=white, fill=none, text=black, scale=2] (pi1) at (1,5.7) {\textbf{$\pi_{{\color{blueind}\bullet}}$}};
|
|
\node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}};
|
|
\node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}};
|
|
\node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}};
|
|
|
|
\tikzstyle{every node}=[fill=cyanind]
|
|
\node[state, draw=white, fill=none, text=black, scale=2] (pi2) at (6.5,5.7) {\textbf{$\pi_{{\color{cyanind}\bullet}}$}};
|
|
\node[state, draw=black!50] (R21) at (6,5) {\textbf{R21}};
|
|
\node[state, draw=black!50] (R22) at (7,5) {\textbf{R22}};
|
|
|
|
\tikzstyle{every node}=[fill=electricblue]
|
|
\node[state, draw=white, fill=none, text=black, scale=2] (pi3) at (10,5.7) {\textbf{$\pi_{{\color{electricblue}\bullet}}$}};
|
|
\node[state, draw=black!50] (R31) at (10,5) {\textbf{R31}};
|
|
|
|
\tikzstyle{every node}=[fill=burntorange, shape=rectangle]
|
|
\node[state, draw=white, fill=none, text=black, scale=2] (pi3) at (0.5,-0.7) {\textbf{$\rho_{{\color{burntorange}\bullet}}$}};
|
|
\tikzstyle{every state}=[draw=none,text=white,scale=0.75, transform shape, shape=rectangle]
|
|
\node[state, draw=black!50] (B1) at (0,0) {\textbf{C11}};
|
|
\node[state, draw=black!50] (B2) at (1,0) {\textbf{C12}};
|
|
\tikzstyle{every node}=[fill=goldenyellow, shape=rectangle]
|
|
\node[state, draw=white, fill=none, text=black, scale=2] (pi3) at (4.5,-0.7) {\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}};
|
|
\node[state, draw=black!50] (B3) at (4,0) {\textbf{C21}};
|
|
\node[state, draw=black!50] (B4) at (5,0) {\textbf{C22}};
|
|
\tikzstyle{every node}=[fill=peach, shape=rectangle]
|
|
\node[state, draw=white, fill=none, text=black, scale=2] (pi3) at (10,-0.7) {\textbf{$\rho_{{\color{peach}\bullet}}$}};
|
|
\node[state, draw=black!50] (B5) at (10,0) {\textbf{C31}};
|
|
|
|
\tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1.5pt,draw opacity=0.2]
|
|
|
|
\path (R11) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[anchor=center, fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$} (B1);
|
|
\path (R11) edge (B2);
|
|
\path (R11) edge (B3);
|
|
\path (R11) edge (B4);
|
|
|
|
\path (R12) edge [] (B1);
|
|
\path (R12) edge (B2);
|
|
\path (R12) edge (B3);
|
|
\path (R12) edge (B4);
|
|
|
|
\path (R13) edge [] (B1);
|
|
\path (R13) edge (B2);
|
|
\path (R13) edge (B3);
|
|
\path (R13) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[anchor=center, fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{goldenyellow}\bullet}}$} (B4);
|
|
|
|
\path (R21) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[anchor=center, fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$} (B3);
|
|
\path (R21) edge (B4);
|
|
\path (R21) edge (B5);
|
|
|
|
\path (R22) edge (B3);
|
|
\path (R22) edge (B4);
|
|
\path (R22) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[anchor=center, fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{peach}\bullet}}$} (B5);
|
|
|
|
\path (R31) edge[-,>=stealth',shorten >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[anchor=center, fill=none] {$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$} (B5);
|
|
|
|
\end{tikzpicture}
|
|
\caption{Exemple de LBM}
|
|
\label{fig:LBMvisu}
|
|
\end{figure}
|
|
|
|
\end{frame}
|
|
\begin{frame}
|
|
\frametitle{Extension de \emph{colSBM} aux réseaux bipartites}
|
|
Le modèle \emph{colSBM} \parencite{chabert-liddellLearningCommonStructures2023}
|
|
|
|
\begin{equation*}
|
|
\overbrace{
|
|
}^\text{Collection}
|
|
\end{equation*}
|
|
|
|
|
|
\end{frame}
|
|
\begin{frame}
|
|
\frametitle{Collections en bipartites}
|
|
|
|
|
|
\end{frame}
|
|
|
|
\section*{Bibliographie}
|
|
\begin{frame}
|
|
\frametitle{Bibliographie}
|
|
\printbibliography
|
|
\end{frame}
|
|
|
|
\end{document} |