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presentation.tex
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@ -33,7 +33,7 @@
%% Tikz Related %% Tikz Related
\usetikzlibrary{calc,shapes,backgrounds,arrows,automata,shadows,positioning} \usetikzlibrary{calc,shapes,backgrounds,arrows,automata,shadows,positioning}
\usetikzlibrary{arrows,shapes,positioning,shadows,trees,calc,backgrounds,automata,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 %% Tikz sets
\tikzset{ \tikzset{

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principal.tex
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@ -27,7 +27,7 @@
\end{pmatrix} \end{pmatrix}
\end{align*} \end{align*}
\footnotesize \footnotesize
Associated adjacency matrix Associated bi-adjacency matrix
\end{column} \end{column}
\end{columns} \end{columns}
\begin{figure}[ht] \begin{figure}[ht]
@ -40,23 +40,23 @@
\end{column} \end{column}
\begin{column}{0.5\textwidth} \begin{column}{0.5\textwidth}
\begin{itemize} \begin{itemize}
\item Increasingly available
\item Modeling of various interactions, here ecosystems \item Modeling of various interactions, here ecosystems
\item Structure necessary for: biodiversity monitoring, robustness, risk of collapse \item Structure necessary for: biodiversity monitoring, robustness, risk of collapse
\item Increasingly available
\end{itemize} \end{itemize}
\end{column} \end{column}
\end{columns} \end{columns}
\end{frame} \end{frame}
\begin{frame}{Analysis methods for a network} \begin{frame}{Analysis methods for a network}
TODO (Supprimable) Several methods~: Several methods~:
\begin{itemize} \begin{itemize}
\item Metrics at \begin{itemize} \item Metrics at \begin{itemize}
\item node level: degree, centrality\dots \item node level: degree, centrality\dots
\item network level: density, nestedness\dots \item network level: density, nestedness\dots
\end{itemize} \end{itemize}
\item \textbf<2>{Node embedding and/or clustering with latent variable models} \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 \item Node or network embedding with Graph Convolutional Networks
\\\cite{kipfVariationalGraphAutoEncoders2016a} \\\cite{kipfVariationalGraphAutoEncoders2016a}
\end{itemize} \end{itemize}
@ -153,42 +153,43 @@
\node[city, pin={[pin edge={<-,thick}, pin distance = 20mm]0:Reading}] (reading) at (0.5,-1.82) {}; \node[city, pin={[pin edge={<-,thick}, pin distance = 20mm]0:Reading}] (reading) at (0.5,-1.82) {};
\end{tikzpicture} \end{tikzpicture}
\caption{Map of the 4 cities} \caption{Map of the four cities}
\end{figure}} \end{figure}}
\end{frame} \end{frame}
\section[Bipartite collection models]{Bipartite network collection models} \section[Bipartite collection models]{Bipartite network collection models}
\label{sec:extension-of-colsbm-to-bipartite-networks} \label{sec:extension-of-colsbm-to-bipartite-networks}
\begin{frame} \begin{frame}
\frametitle{Bipartite collections separate BiSBM} \frametitle{Model 0: sep-BiSBM}
\[ \footnotesize
\forall m \in \{1\dots M\}, Y^m \overset{ind}{\sim} \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1^m, Q_2^m, \pi^m, \rho^m, \alpha^m) $
\] \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<2>{ $
\onslide<3>{
\begin{figure}[ht] \begin{figure}[ht]
\centering \centering
\begin{subfigure}[ht]{0.35\textwidth} \begin{subfigure}[ht]{0.42\textwidth}
\centering \centering
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Bristol.pdf} \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Bristol.pdf}
\caption{Bristol} \caption{Bristol}
\end{subfigure} \end{subfigure}
\begin{subfigure}[ht]{0.35\textwidth} \begin{subfigure}[ht]{0.42\textwidth}
\centering \centering
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Edinburgh.pdf} \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Edinburgh.pdf}
\caption{Edinburgh} \caption{Edinburgh}
\end{subfigure} \end{subfigure}
\hfill \hfill
\begin{subfigure}[ht]{0.35\textwidth} \begin{subfigure}[ht]{0.42\textwidth}
\centering \centering
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds.pdf} \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds.pdf}
\caption{Leeds} \caption{Leeds}
\end{subfigure} \end{subfigure}
\begin{subfigure}[ht]{0.35\textwidth} \begin{subfigure}[ht]{0.42\textwidth}
\centering \centering
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Reading.pdf} \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Reading.pdf}
\caption{Reading} \caption{Reading}
\end{subfigure} \end{subfigure}
\caption{Reordered adjacency matrices, using LBM} \caption{Reordered adjacency matrices, using BiSBM for each network}
\label{fig:adj-reord} \label{fig:adj-reord}
\end{figure} \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) \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} \end{block}
And intermediate models freeing $\pi$ or $\rho$. And intermediate models freeing $\pi$ or $\rho$.
} }
@ -276,16 +278,16 @@
\section{Model selection} \section{Model selection}
\begin{frame} \begin{frame}
\frametitle{Problem of choosing $(Q_1, Q_2)$} \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*} \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) \\ \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) \\
& = \max_{\theta} \mathcal{J(\mathcal{R}_{\mathbf{Y},\hat{\tau}}, \theta)} - \frac{1}{2}\text{pen}(\theta, 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*} \end{align*}
\begin{alertblock}{Exploration problems} \begin{alertblock}{Exploration problems}
\begin{itemize} \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}} approach} and \textbf{sliding window}}
\item Sensitivity to initializations. \uncover<3->{$\rightarrow$ \textbf{Spectral \item Sensitivity to initializations. \uncover<3->{$\rightarrow$ \textbf{Spectral
clustering} and \textbf{reuse of previous inits}} clustering} and \textbf{reuse of previous inits}}
@ -325,6 +327,24 @@
\end{figure} \end{figure}
\end{frame} \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}} \begin{frame}{\emph{Bombus}}
\only<1>{ \only<1>{
\begin{figure} \begin{figure}
@ -343,50 +363,56 @@
\only<2->{ \only<2->{
\begin{columns} \begin{columns}
\begin{column}{0.35\textwidth} \begin{column}{0.2\textwidth}
\begin{figure} \begin{figure}
\onslide<3>{ \onslide<3>{
\begin{subfigure}[t]{0.5\textwidth} \begin{subfigure}[t]{0.7\textwidth}
\centering \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} \caption{\emph{Bombus Hortorum} or garden bumblebee}
\end{subfigure} \end{subfigure}
} }
\onslide<4>{ \onslide<4>{
\begin{subfigure}[t]{0.5\textwidth} \begin{subfigure}[t]{0.7\textwidth}
\centering \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} \caption{\emph{Bombus Lapidarius} or red-tailed bumblebee}
\end{subfigure} \end{subfigure}
} }
\end{figure} \end{figure}
\end{column} \end{column}
\begin{column}{0.6\textwidth} \begin{column}{0.7\textwidth}
\begin{figure} \begin{figure}
\centering \centering
\begin{tikzpicture}[every every node/.style={anchor=south west, inner sep=0pt}, x=1mm, y=1mm] \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 (struct) at (0,0) {\includegraphics[width=0.8\textwidth]{tikz/applications/baldock/shared-iid.pdf}};
\node (gen) at (-25,11) {}; \node (gen) at (-29,14.8) {};
\node (interm) at (-25,2) {}; \node (interm) at (-29,2.5) {};
\node (spe) at (-25,-7) {}; \node (spe) at (-29,-9.8) {};
\node (gen_label) at (18, 11) {}; \node[left = 3mm of spe] (@aux) {\phantom{B, E, R}};
\node (spe_label) at (18, -7) {};
\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>{ \only<3>{
\node[left = 3mm of gen] (towns_gen_garden) {B, L}; \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_gen_garden) edge[->,thick] (gen);
\path (towns_spe_garden) edge[->,thick] (spe); \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} \end{tikzpicture}
\caption{Shared structure of the 4 networks}\label{fig:shared} \caption{Shared structure of the 4 networks}\label{fig:shared}
\end{figure} \end{figure}
@ -413,7 +439,7 @@
\includegraphics[scale=0.1]{backup-app-iid-struct1.png} \includegraphics[scale=0.1]{backup-app-iid-struct1.png}
\includegraphics[scale=0.2]{backup-app-iid-struct2.png} \includegraphics[scale=0.2]{backup-app-iid-struct2.png}
\caption{Model $iid$,\\ \caption{Model $iid$,\\
separate African network and English networks} separate African (left) and English (right) networks}
\end{subfigure}% \end{subfigure}%
~ ~
\begin{subfigure}{0.5\textwidth} \begin{subfigure}{0.5\textwidth}
@ -466,23 +492,21 @@
\end{frame} \end{frame}
\begin{frame}{Perspectives} \begin{frame}{Perspectives}
\begin{itemize}
\item Investigate stability against randomness and local \emph{optima}. \begin{block}{Future work}
\end{itemize} \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{block}{Package and applications}
\begin{itemize} \begin{itemize}
\item Integration into the \texttt{colSBM} package, improvement of user interface and
addition of ecologists' feedback
\item CRAN submission \item CRAN submission
\item Integrate the possibility of an additional criterion for clustering (e.g. \item Integrate the possibility of an additional criterion for clustering (e.g.
urbanization gradient~\cite{fisogniSeasonalTrajectoriesPlantpollinator2022}) urbanization gradient~\cite{fisogniSeasonalTrajectoriesPlantpollinator2022})
\item Apply clustering to data from \item Apply clustering to data from
\cite{pichonTellingMutualisticAntagonistic2024,doreRelativeEffectsAnthropogenic2021} \cite{pichonTellingMutualisticAntagonistic2024,doreRelativeEffectsAnthropogenic2021}
\end{itemize} \end{itemize}
\end{block} \end{block}
\bigskip
\centering
Thank you for your attention~!
\end{frame} \end{frame}

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