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\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}

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@ -13,12 +13,12 @@
\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[colorlinks,citecolor=blueind,urlcolor=blue,bookmarks=false,hypertexnames=true]{hyperref} % pour les hyperliens dans le document
\usepackage{tocbibind} % Pour avoir des index pour table des matières, biblio
\usepackage{tikz} % For graph plots
%% Bibliography
\usepackage[style=authoryear]{biblatex}
\usepackage[style=apa,citestyle=authoryear-comp]{biblatex}
\addbibresource{references.bib}
@ -82,7 +82,7 @@ $V$ vertices.
\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=electricblue]
\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}};
@ -143,7 +143,7 @@ networks, biomolecular networks or epidemiological
networks. \parencite{pavlopoulosBipartiteGraphsSystems2018}
Some interesting results can arise when using a tool widely used on a particular
Some interesting results can arise when applying a tool widely used on a particular
kind of interactions is used on another kind of interactions. Companies like
Netflix use recommender system, to recommend another product to consumers based
on their previous interactions.

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references.bib
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@ -158,6 +158,17 @@
file = {/home/polarolouis/Zotero/storage/VXVQ5CPH/Kaszewska-Gilas et al. - 2021 - Global Studies of the Host-Parasite Relationships .pdf}
}
@misc{larousseDefinitionsBipartiBipartite,
title = {{D\'efinitions : biparti, bipartite - Dictionnaire de fran\c{c}ais Larousse}},
shorttitle = {{D\'efinitions}},
author = {Larousse, {\'E}ditions},
urldate = {2023-06-17},
abstract = {biparti, bipartite - D\'efinitions Fran\c{c}ais : Retrouvez la d\'efinition de biparti, bipartite, ainsi que les difficult\'es... - synonymes, homonymes, difficult\'es, citations.},
howpublished = {https://www.larousse.fr/dictionnaires/francais/biparti/9503},
langid = {french},
file = {/home/polarolouis/Zotero/storage/MA2VH6NX/9503.html}
}
@article{pavlopoulosBipartiteGraphsSystems2018,
title = {Bipartite Graphs in Systems Biology and Medicine: A Survey of Methods and Applications},
shorttitle = {Bipartite Graphs in Systems Biology and Medicine},
@ -210,3 +221,11 @@
keywords = {Bayesian Estimator,Block Structure,Gibbs Sampling,Large Graph,Statistical Procedure},
file = {/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}
}
@misc{WebLifeEcological,
title = {Web of {{Life}}: Ecological Networks Database},
urldate = {2023-06-17},
howpublished = {https://www.web-of-life.es/map.php},
keywords = {networks,site},
file = {/home/polarolouis/Zotero/storage/9WZE8QLQ/map.html}
}