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presentation.tex
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@ -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{

124
principal.tex
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@ -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}

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tikz/applications/baldock/shared-iid.pdf
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