diff --git a/presentation.tex b/presentation.tex index 36c897f..7b1363c 100644 --- a/presentation.tex +++ b/presentation.tex @@ -33,7 +33,7 @@ %% 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} +\usetikzlibrary{decorations.pathreplacing,calligraphy,external,petri, shapes.geometric} %% Tikz sets \tikzset{ diff --git a/principal.tex b/principal.tex index 5d8dc49..76f55af 100644 --- a/principal.tex +++ b/principal.tex @@ -27,7 +27,7 @@ \end{pmatrix} \end{align*} \footnotesize - Associated adjacency matrix + Associated bi-adjacency matrix \end{column} \end{columns} \begin{figure}[ht] @@ -40,23 +40,23 @@ \end{column} \begin{column}{0.5\textwidth} \begin{itemize} + \item Increasingly available \item Modeling of various interactions, here ecosystems \item Structure necessary for: biodiversity monitoring, robustness, risk of collapse - \item Increasingly available \end{itemize} \end{column} \end{columns} \end{frame} \begin{frame}{Analysis methods for a network} - TODO (Supprimable) Several methods~: + Several methods~: \begin{itemize} \item Metrics at \begin{itemize} \item node level: degree, centrality\dots \item network level: density, nestedness\dots \end{itemize} \item \textbf<2>{Node embedding and/or clustering with latent variable models} - \\\cite{hoffLatentSpaceApproaches2002,snijdersEstimationPredictionStochastic1997} + \\\cite{snijdersEstimationPredictionStochastic1997,hoffLatentSpaceApproaches2002} \item Node or network embedding with Graph Convolutional Networks \\\cite{kipfVariationalGraphAutoEncoders2016a} \end{itemize} @@ -153,42 +153,43 @@ \node[city, pin={[pin edge={<-,thick}, pin distance = 20mm]0:Reading}] (reading) at (0.5,-1.82) {}; \end{tikzpicture} - \caption{Map of the 4 cities} + \caption{Map of the four cities} \end{figure}} \end{frame} \section[Bipartite collection models]{Bipartite network collection models} \label{sec:extension-of-colsbm-to-bipartite-networks} \begin{frame} - \frametitle{Bipartite collections separate BiSBM} - \[ - \forall m \in \{1\dots M\}, Y^m \overset{ind}{\sim} \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1^m, Q_2^m, \pi^m, \rho^m, \alpha^m) - \] - \onslide<2>{ + \frametitle{Model 0: sep-BiSBM} + \footnotesize + $ + \forall m \in \{1\dots M\}, Y^m \overset{ind}{\sim} \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1\alert<2>{^m}, Q_2\alert<2>{^m}, \pi\alert<2>{^m}, \rho\alert<2>{^m}, \alpha\alert<2>{^m}) + $ + \onslide<3>{ \begin{figure}[ht] \centering - \begin{subfigure}[ht]{0.35\textwidth} + \begin{subfigure}[ht]{0.42\textwidth} \centering \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Bristol.pdf} \caption{Bristol} \end{subfigure} - \begin{subfigure}[ht]{0.35\textwidth} + \begin{subfigure}[ht]{0.42\textwidth} \centering \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Edinburgh.pdf} \caption{Edinburgh} \end{subfigure} \hfill - \begin{subfigure}[ht]{0.35\textwidth} + \begin{subfigure}[ht]{0.42\textwidth} \centering \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds.pdf} \caption{Leeds} \end{subfigure} - \begin{subfigure}[ht]{0.35\textwidth} + \begin{subfigure}[ht]{0.42\textwidth} \centering \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Reading.pdf} \caption{Reading} \end{subfigure} - \caption{Reordered adjacency matrices, using LBM} + \caption{Reordered adjacency matrices, using BiSBM for each network} \label{fig:adj-reord} \end{figure} } @@ -210,7 +211,8 @@ \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1, Q_2, \pi^m, \rho^m, \alpha) \] - with $\theta = ((\pi^m)_{m=1,\dots, M}, (\rho^m)_{m=1,\dots, M}, \alpha)$. + with $\theta = ((\pi\alert{^m})_{m=1,\dots, M}, (\rho\alert{^m})_{m=1,\dots, + M}, \alpha)$. \end{block} And intermediate models freeing $\pi$ or $\rho$. } @@ -276,16 +278,16 @@ \section{Model selection} \begin{frame} \frametitle{Problem of choosing $(Q_1, Q_2)$} - Need to select $Q_1$ and $Q_2$. BIC-Like criterion\footnote{ICL + Entropy + penalty} + Need to select $Q_1$ and $Q_2$. BIC-Like criterion\footnote{ICL + entropy - penalty} \begin{align*} - \text{BIC-L}(\bm{Y}, Q_1, Q_2) & = \max_{\theta} \mathbb{E}_{\mathcal{R}_{\mathbf{Y},\hat{\tau}}} [\ell_c(\bm{Y,Z,W};\theta)] + \mathcal{H(\mathcal{R}_{\mathbf{Y},\hat{\tau}})} - \frac{1}{2}\text{pen}(\theta, Q_1, Q_2) \\ - & = \max_{\theta} \mathcal{J(\mathcal{R}_{\mathbf{Y},\hat{\tau}}, \theta)} - \frac{1}{2}\text{pen}(\theta, Q_1, Q_2) + \text{BIC-L}(\bm{Y}, Q_1, Q_2) & = \mathbb{E}_{\mathcal{R}_{\mathbf{Y},\hat{\tau}}} [\ell_c(\bm{Y,Z,W};\hat{\theta}^{\text{var}})] + \mathcal{H(\mathcal{R}_{\mathbf{Y},\hat{\tau}})} - \frac{1}{2}\text{pen}(Q_1, Q_2) \\ + & = \mathcal{J(\mathcal{R}_{\mathbf{Y},\hat{\tau}}, \hat{\theta}^{\text{var}})} - \frac{1}{2}\text{pen}(Q_1, Q_2) \end{align*} \begin{alertblock}{Exploration problems} \begin{itemize} - \item Exploration of $\mathbb{N}^2$ costly. \uncover<2->{$\rightarrow$ \textbf{Greedy + \item Exploration of a 2D grid is costly. \uncover<2->{$\rightarrow$ \textbf{Greedy approach} and \textbf{sliding window}} \item Sensitivity to initializations. \uncover<3->{$\rightarrow$ \textbf{Spectral clustering} and \textbf{reuse of previous inits}} @@ -325,6 +327,24 @@ \end{figure} \end{frame} +\begin{frame} + \frametitle{Results~\cite{baldockSystemsApproachReveals2019} focus on Leeds} + \begin{figure}[ht] + \centering + \begin{subfigure}[t]{0.5\textwidth} + \centering + \includegraphics[width=1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds.pdf} + \caption{Separate model} + \end{subfigure}\hfill + \begin{subfigure}[t]{0.5\textwidth} + \centering + \includegraphics[width=1\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Leeds.pdf} + \caption{Joint model} + \end{subfigure} + \caption{Reordered adjacency matrix by sep-BiSBM (left) and by \emph{iid}-colBiSBM (right),~\cite{baldockSystemsApproachReveals2019}} + \end{figure} +\end{frame} + \begin{frame}{\emph{Bombus}} \only<1>{ \begin{figure} @@ -343,50 +363,56 @@ \only<2->{ \begin{columns} - \begin{column}{0.35\textwidth} + \begin{column}{0.2\textwidth} \begin{figure} \onslide<3>{ - \begin{subfigure}[t]{0.5\textwidth} + \begin{subfigure}[t]{0.7\textwidth} \centering - \includegraphics[width=0.75\textwidth]{img/baldock/bombus-hortorum.jpeg} + \includegraphics[width=1\textwidth]{img/baldock/bombus-hortorum.jpeg} \caption{\emph{Bombus Hortorum} or garden bumblebee} \end{subfigure} } \onslide<4>{ - \begin{subfigure}[t]{0.5\textwidth} + \begin{subfigure}[t]{0.7\textwidth} \centering - \includegraphics[width=0.75\textwidth]{img/baldock/bombus-lapidarius.jpeg} + \includegraphics[width=1\textwidth]{img/baldock/bombus-lapidarius.jpeg} \caption{\emph{Bombus Lapidarius} or red-tailed bumblebee} \end{subfigure} } \end{figure} \end{column} - \begin{column}{0.6\textwidth} + \begin{column}{0.7\textwidth} \begin{figure} \centering \begin{tikzpicture}[every every node/.style={anchor=south west, inner sep=0pt}, x=1mm, y=1mm] \node (struct) at (0,0) {\includegraphics[width=0.8\textwidth]{tikz/applications/baldock/shared-iid.pdf}}; - \node (gen) at (-25,11) {}; - \node (interm) at (-25,2) {}; - \node (spe) at (-25,-7) {}; + \node (gen) at (-29,14.8) {}; + \node (interm) at (-29,2.5) {}; + \node (spe) at (-29,-9.8) {}; - \node (gen_label) at (18, 11) {}; - \node (spe_label) at (18, -7) {}; + \node[left = 3mm of spe] (@aux) {\phantom{B, E, R}}; + + \node[isosceles triangle, + isosceles triangle apex angle=10, + draw, + rotate=270, + shading = axis, + top color=blue!50, + bottom color=blue!1!white, + anchor=right corner, minimum height=42mm, label={[label distance = 2mm]207:Generalists}, label={[label distance = 12mm]357:Specialists}] (T) at ($(struct.north east)+(-1,-2.5)$) {}; - \node (for_label) at (struct.west) {}; - \onslide<3->{ - \node[right = 3mm of gen_label] (generalist) {Gen.}; - \node[right = 3mm of spe_label] (specialist) {Spe.}; - \path (generalist) edge[->,thick] (gen_label); - \path (specialist) edge[->,thick] (spe_label); - } \only<3>{ \node[left = 3mm of gen] (towns_gen_garden) {B, L}; - \node[left = 3mm of spe] (towns_spe_garden) {E, R}; + \node[left = 3mm of spe] (towns_spe_garden) {\phantom{B, }E, R}; \path (towns_gen_garden) edge[->,thick] (gen); \path (towns_spe_garden) edge[->,thick] (spe); } - % \only<4>{} + \only<4>{ + \node[left = 3mm of interm] (towns_interm_red) {L}; + \node[left = 3mm of spe] (towns_spe_red) {B, E, R}; + \path (towns_interm_red) edge[->,thick] (interm); + \path (towns_spe_red) edge[->,thick] (spe); + } \end{tikzpicture} \caption{Shared structure of the 4 networks}\label{fig:shared} \end{figure} @@ -413,7 +439,7 @@ \includegraphics[scale=0.1]{backup-app-iid-struct1.png} \includegraphics[scale=0.2]{backup-app-iid-struct2.png} \caption{Model $iid$,\\ - separate African network and English networks} + separate African (left) and English (right) networks} \end{subfigure}% ~ \begin{subfigure}{0.5\textwidth} @@ -466,23 +492,21 @@ \end{frame} \begin{frame}{Perspectives} - \begin{itemize} - \item Investigate stability against randomness and local \emph{optima}. - \end{itemize} + + \begin{block}{Future work} + \begin{itemize} + \item Multi-layer networks (account for sampling bias, presence/absence) + \item Graph Convolutional Network to allow for scalability + \end{itemize} + \end{block} \begin{block}{Package and applications} \begin{itemize} - \item Integration into the \texttt{colSBM} package, improvement of user interface and - addition of ecologists' feedback \item CRAN submission \item Integrate the possibility of an additional criterion for clustering (e.g. urbanization gradient~\cite{fisogniSeasonalTrajectoriesPlantpollinator2022}) \item Apply clustering to data from \cite{pichonTellingMutualisticAntagonistic2024,doreRelativeEffectsAnthropogenic2021} \end{itemize} - \end{block} - \bigskip - \centering - Thank you for your attention~! \end{frame} \ No newline at end of file diff --git a/tikz/applications/baldock/shared-iid.pdf b/tikz/applications/baldock/shared-iid.pdf index b903407..bd4349b 100644 Binary files a/tikz/applications/baldock/shared-iid.pdf and b/tikz/applications/baldock/shared-iid.pdf differ