commit 9d4a30e8cf62b83915eaf85985e5820ac23de52d Author: Louis Lacoste Date: Wed May 15 08:02:02 2024 +0200 Premier commit diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e964244 --- /dev/null +++ b/.gitignore @@ -0,0 +1,301 @@ +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc +*.fmt +*.fot +*.cb +*.cb2 +.*.lb + +## Intermediate documents: +*.dvi +*.xdv +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Generated if empty string is given at "Please type another file name for output:" +.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex(busy) +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync + +## Build tool directories for auxiliary files +# latexrun +latex.out/ + +## Auxiliary and intermediate files from other packages: +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.pre +*.snm +*.vrb + +# changes +*.soc + +# comment +*.cut + +# cprotect +*.cpt + +# elsarticle (documentclass of Elsevier journals) +*.spl + +# endnotes +*.ent + +# fixme +*.lox + +# feynmf/feynmp +*.mf +*.mp +*.t[1-9] +*.t[1-9][0-9] +*.tfm + +#(r)(e)ledmac/(r)(e)ledpar +*.end +*.?end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls +*.glsdefs +*.lzo +*.lzs +*.slg +*.slo +*.sls + +# uncomment this for glossaries-extra (will ignore makeindex's style files!) +# *.ist + +# gnuplot +*.gnuplot +*.table + +# gnuplottex +*-gnuplottex-* + +# gregoriotex +*.gaux +*.glog +*.gtex + +# htlatex +*.4ct +*.4tc +*.idv +*.lg +*.trc +*.xref + +# hyperref +*.brf + +# knitr +*-concordance.tex +# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files +# *.tikz +*-tikzDictionary + +# listings +*.lol + +# luatexja-ruby +*.ltjruby + +# makeidx +*.idx +*.ilg +*.ind + +# minitoc +*.maf +*.mlf +*.mlt +*.mtc[0-9]* +*.slf[0-9]* +*.slt[0-9]* +*.stc[0-9]* + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# newpax +*.newpax + +# nomencl +*.nlg +*.nlo +*.nls + +# pax +*.pax + +# pdfpcnotes +*.pdfpc + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# scrwfile +*.wrt + +# svg +svg-inkscape/ + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# pdfcomment +*.upa +*.upb + +# pythontex +*.pytxcode +pythontex-files-*/ + +# tcolorbox +*.listing + +# thmtools +*.loe + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# titletoc +*.ptc + +# todonotes +*.tdo + +# vhistory +*.hst +*.ver + +# easy-todo +*.lod + +# xcolor +*.xcp + +# xmpincl +*.xmpi + +# xindy +*.xdy + +# xypic precompiled matrices and outlines +*.xyc +*.xyd + +# endfloat +*.ttt +*.fff + +# Latexian +TSWLatexianTemp* + +## Editors: +# WinEdt +*.bak +*.sav + +# Texpad +.texpadtmp + +# LyX +*.lyx~ + +# Kile +*.backup + +# gummi +.*.swp + +# KBibTeX +*~[0-9]* + +# TeXnicCenter +*.tps + +# auto folder when using emacs and auctex +./auto/* +*.el + +# expex forward references with \gathertags +*-tags.tex + +# standalone packages +*.sta + +# Makeindex log files +*.lpz + +# xwatermark package +*.xwm + +# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib +# option is specified. Footnotes are the stored in a file with suffix Notes.bib. +# Uncomment the next line to have this generated file ignored. +#*Notes.bib diff --git a/Annexe/GCN_Barbillon_Rochebrune.pdf b/Annexe/GCN_Barbillon_Rochebrune.pdf new file mode 100644 index 0000000..134273b Binary files /dev/null and b/Annexe/GCN_Barbillon_Rochebrune.pdf differ diff --git a/Annexe/GNNcode.zip b/Annexe/GNNcode.zip new file mode 100644 index 0000000..beca32a Binary files /dev/null and b/Annexe/GNNcode.zip differ diff --git a/img/Organigramme_MIA-Paris-Saclay.png b/img/Organigramme_MIA-Paris-Saclay.png new file mode 100644 index 0000000..5807eb6 Binary files /dev/null and b/img/Organigramme_MIA-Paris-Saclay.png differ diff --git a/img/Organigramme_MIA-Paris-Saclay.svg b/img/Organigramme_MIA-Paris-Saclay.svg new file mode 100644 index 0000000..b148aa7 --- /dev/null +++ b/img/Organigramme_MIA-Paris-Saclay.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/img/annual_time_span_vs_iid.png 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0000000..35dda05 Binary files /dev/null and b/img/moving_window.png differ diff --git a/img/plot_model_function_eps.png b/img/plot_model_function_eps.png new file mode 100644 index 0000000..b11b813 Binary files /dev/null and b/img/plot_model_function_eps.png differ diff --git a/presentation.pdf b/presentation.pdf new file mode 100644 index 0000000..4c9cc35 Binary files /dev/null and b/presentation.pdf differ diff --git a/presentation.tex b/presentation.tex new file mode 100644 index 0000000..5e17691 --- /dev/null +++ b/presentation.tex @@ -0,0 +1,1370 @@ +\documentclass{beamer} +\usetheme{Boadilla} +\usecolortheme{seahorse} + +% importations +\usepackage[french]{babel} % pour dire que le texte est en francais +\usepackage{nth} +\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, stmaryrd} % 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{graphicx} +\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 +\usepackage{adjustbox} % To resize tikzpictures +\usepackage{fontawesome5} +\usepackage{makecell} +\usepackage{appendixnumberbeamer} % Pour cacher la numérotation des backups slides +\usepackage{chronosys} % Frise chronologique + +\renewcommand\theadfont{\tiny} + + +% Beamer +\setbeamertemplate{headline}{% + \begin{beamercolorbox}[ht=2.25ex,dp=3.75ex]{section in head/foot} + \insertnavigation{\paperwidth} + \end{beamercolorbox}% +}% + +%\beamertemplatenavigationsymbolsempty % Pas de bar de navigation +\setbeamerfont{caption}{size=\scriptsize} % Petit titre de figures +\AtBeginSection[]{ + \begin{frame}[noframenumbering] + \vfill + \centering + \begin{beamercolorbox}[sep=8pt,center,shadow=true,rounded=true]{title} + \usebeamerfont{title}\secname\par% + \end{beamercolorbox} + \vfill + \end{frame} +} + +% bibliographie +\usepackage[style=apa,sorting=none]{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} +\usetikzlibrary{decorations.pathreplacing,calligraphy} + +\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}{255,255,0} + +\definecolor{gray}{RGB}{128,128,128} + +% Footnote +\makeatletter +\newcommand\blfootnote[1]{% + \begingroup + \renewcommand{\@makefntext}[1]{\noindent\makebox[1.8em][r]#1} + \renewcommand\thefootnote{}\footnote{#1}% + \addtocounter{footnote}{-1}% + \endgroup +} +\makeatother + +\subtitle{Audition candidature de thèse à l'EDMH} +\title[Comparaison de structures de réseaux]{Comparaison de structures de + réseaux. + Applications à des réseaux écologiques} +\author[L. Lacoste]{Louis \textsc{Lacoste}} % Sous la supervision de Pierre +\date{23 mai 2024} + +\begin{document} + +% titre +\begin{frame}[noframenumbering,plain] + \maketitle +\end{frame} + +\begin{frame} + \tableofcontents +\end{frame} + +\section{Parcours} +\label{sec:parcours} +\begin{frame}{Formations} + + \begin{itemize} + \item 2023--2024, M2 Mathématiques pour les Sciences du Vivant, + Université Paris-Saclay\\ + {\small UC à choix \nth{2} semestre : modèles à variables + latentes, statistiques spatiales et méthodes de stats en grande dimensions} + \item 2022--2023, Année de césure + \item 2020--2022, 1ère et 2ème année en formation Ingénieur + AgroParisTech\\ + {\small Cours optionnels suivis : statistiques spatiales, + mathématiques pour la santé, ingénierie par la simulation informatique \dots} + \item 2018--2020, Classe Préparatoire BCPST + \end{itemize} + +\end{frame} +\begin{frame}{Expériences professionnelles} + + \begin{itemize} + \item 2024 Avril--Sept., Détection de structures et clustering de réseaux + écologiques. Stage dans l’UMR MIA Paris-Saclay, supervisé par Pierre Barbillon. + \item 2023 Janv.--Juillet, Détection de structures dans des collections de + réseaux bipartites et écriture du package implémentant la méthode. + Stage dans l’UMR MIA Paris-Saclay, supervisé par Pierre Barbillon. + \item 2022 Mai--Déc., Stage assistant ingénieur en Qualité chez + Eurofins Food France + \end{itemize} + +\end{frame} + + +\section[Axes de recherche]{Axes de recherche} + +\begin{frame} + \frametitle{Contexte écologique} + \begin{itemize} + \item Faire de la détection de structure sur un réseau (SBM, LBM) mais + intérêt à le faire sur plusieurs + \item De nombreux réseaux disponibles \parencite{WebLifeEcological} et + décrivant des interactions similaires. Par exemple des + interactions proies-prédateurs, plantes-pollinisateurs \dots + \item Re-grouper les réseaux selon leur similarité (\emph{clustering} + de réseaux) + \item Transférer de l'information grâce à la collection (par exemple + reconstitution de données manquantes) + \item Déterminer des structures d'interactions fines de manière + agnostique % Pas d'idee preco + %\item Vérifier si le regroupement est lié à des co-variables + \end{itemize} +\end{frame} + +\begin{frame}{Contexte mathématiques} + +\end{frame} + +\subsection[Axe 1]{Axe 1 : Modèles à variables + latentes pour une collection de réseaux bipartites} +\label{sec:axe-1} + +% TODO Demander si suppression car plus techniques qu'important +% \begin{frame} +% \frametitle{Réseaux bipartites} +% \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=black,scale=0.95, transform +% shape] +% \tikzstyle{every state}=[draw=none,text=black,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=black,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 +% $X=\left( +% \begin{array}{rrrrr} +% 1 & 1 & 1 & 1 & 0 \\ +% 0 & 0 & 1 & 1 & 1 \\ +% 0 & 0 & 0 & 0 & 1 \\ +% \end{array}\right) +% $\\ +% \end{column} +% \end{columns} +% \smallskip +% Permet de décrire des interactions impliquant deux agents dont les rôles +% sont de natures différentes.\\ +% Par exemple : hôtes-parasites, plantes-pollinisateurs, graines-disperseurs +% \dots +% \end{frame} + +\begin{frame} + \frametitle{Collections bipartites} + \begin{center} + \begin{adjustbox}{trim=0 0 1 1.5cm} + \begin{tikzpicture}[scale=.33] + \begin{scope}[xshift=18cm, yshift=2cm] + \tikzstyle{every state}=[draw=none, text=black,scale=0.75, + transform shape] + \tikzset{edge_proba/.style={draw=white, fill=none, + text=black}} + + \tikzstyle{every node}=[fill=blueind] + \node[edge_proba] (pi1) at (1,5.7) + {\textbf{$\pi_{{\color{blueind}\bullet}}$}}; + \node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}}; + \node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}}; + \node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}}; + + \tikzstyle{every node}=[fill=cyanind] + \node[edge_proba] (pi2) at (6.75,5.7) + {\textbf{$\pi_{{\color{cyanind}\bullet}}$}}; + \node[state, draw=black!50] (R21) at (6.25,5) + {\textbf{R21}}; + \node[state, draw=black!50] (R22) at (7.25,5) + {\textbf{R22}}; + + \tikzstyle{every node}=[fill=electricblue] + \node[edge_proba] (pi3) at (10,5.7) + {\textbf{$\pi_{{\color{electricblue}\bullet}}$}}; + \node[state, draw=black!50] (R31) at (10,5) {\textbf{R31}}; + + \tikzstyle{every node}=[fill=burntorange, shape=rectangle] + \node[edge_proba] (rho1) at (0.5,-1) + {\textbf{$\rho_{{\color{burntorange}\bullet}}$}}; + \tikzstyle{every state}=[draw=none,text=black,scale=0.75, + transform shape, shape=rectangle] + \node[state, draw=black!50] (B1) at (0,0) {\textbf{C11}}; + \node[state, draw=black!50] (B2) at (1,0) {\textbf{C12}}; + \tikzstyle{every node}=[fill=goldenyellow, shape=rectangle] + \node[edge_proba] (rho2) at (4,-1) + {\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}}; + \node[state, draw=black!50] (B3) at (3.5,0) {\textbf{C21}}; + \node[state, draw=black!50] (B4) at (4.5,0) {\textbf{C22}}; + \tikzstyle{every node}=[fill=peach, shape=rectangle] + \node[edge_proba] (rho3) at (10,-1) + {\textbf{$\rho_{{\color{peach}\bullet}}$}}; + \node[state, draw=black!50] (B5) at (10,0) {\textbf{C31}}; + + \node[font=\small, text justified,draw=none, fill=none, + below = 0.05cm of rho2] {LBM}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1.5pt,draw opacity=0.2] + + \path (R11) edge (B2); + \path (R11) edge (B3); + \path (R11) edge (B4); + + \path (R12) edge [] (B1); + \path (R12) edge (B2); + \path (R12) edge (B3); + \path (R12) edge (B4); + + \path (R13) edge [] (B1); + \path (R13) edge (B2); + \path (R13) edge (B3); + + \path (R21) edge (B4); + \path (R21) edge (B5); + + \path (R22) edge (B3); + \path (R22) edge (B4); + + \path (R11) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[left, + fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$} + (B1); + \path (R13) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, + fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{goldenyellow}\bullet}}$} + (B4); + \path (R21) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + anchor=center, fill=none] + {$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$} (B3); + \path (R22) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, + fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{peach}\bullet}}$} (B5); + \path (R31) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + right, fill=none] + {$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$} (B5); + \end{scope} + + \begin{scope}[xshift=3cm, yshift = 1cm] + \node[text justified, fill=none] at (10, 3.5) + {$\overset{iid}{\sim}$}; + \begin{scope}[yshift = 6cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,1.25) + {\textbf{1}}; + \node[state, draw=black!50] (R12) at (1,1.25) + {\textbf{2}}; + \node[state, draw=black!50] (R13) at (2,1.25) + {\textbf{3}}; + \node[state, draw=black!50] (R21) at (3,1.25) + {\textbf{4}}; + \node[state, draw=black!50] (R31) at (5,1.25) + {\textbf{6}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + \node[state, draw=black!50] (B1) at (0.5,-1) + {\textbf{1}}; + + \node[state, draw=black!50] (B31) at (2.5,-1) + {\textbf{3}}; + \node[state, draw=black!50] (B4) at (3.5,-1) + {\textbf{4}}; + + \node[state, draw=black!50] (B5) at (4.5,-1) + {\textbf{5}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (B1); + \path (R11) edge (B31); + \path (R11) edge (B4); + + \path (R12) edge [] (B1); + \path (R12) edge (B31); + \path (R12) edge (B4); + + \path (R13) edge [] (B1); + \path (R13) edge (B31); + \path (R13) edge (B4); + + \path (R21) edge (B31); + \path (R21) edge (B4); + \path (R21) edge (B5); + + \path (R31) edge (B5); + \end{scope} + \node[text width=3cm,font=\small, text justified, + rotate=90, fill=none] (dots) at (2.5, 7.5){\dots}; + + \begin{scope}[yshift = 0cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,2.25) + {\textbf{4}}; + \node[state, draw=black!50] (R13) at (2,2.25) + {\textbf{6}}; + \node[state, draw=black!50] (R21) at (3,2.25) + {\textbf{3}}; + \node[state, draw=black!50] (R22) at (4,2.25) + {\textbf{5}}; + \node[state, draw=black!50] (R31) at (5,2.25) + {\textbf{2}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + \node[state, draw=black!50] (B1) at (0.5,0) + {\textbf{5}}; + \node[state, draw=black!50] (B2) at (1.5,0) + {\textbf{1}}; + + \node[state, draw=black!50] (B4) at (3.5,0) + {\textbf{2}}; + + \node[state, draw=black!50] (B5) at (4.5,0) + {\textbf{4}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (B1); + \path (R11) edge (B2); + \path (R11) edge (B4); + + \path (R13) edge [] (B1); + \path (R13) edge (B2); + \path (R13) edge (B4); + + \path (R21) edge (B4); + \path (R21) edge (B5); + + \path (R22) edge (B4); + \path (R22) edge (B5); + + \path (R31) edge (B5); + \end{scope} + \end{scope} + \end{tikzpicture} + \end{adjustbox} + \end{center} + + Pour + \begin{itemize} + \item $Q_1 = + |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ + blocs fixés en ligne + \item $Q_2 = + |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ + blocs fixés en colonne + \end{itemize} + \begin{block}{Paramètres} + \begin{itemize} + \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ en ligne et + $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne + \item + $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = + \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = + {\color{burntorange}\bullet})$ + \end{itemize} + \end{block} +\end{frame} + + +\begin{frame} + \frametitle{Application, données plantes pollinisateurs} + \small + Voici des résultats du modèle \emph{iid-colBiSBM} sur des données + plantes-pollinisateurs (\cite{doreRelativeEffectsAnthropogenic2021} + et~\cite{thebaultDatabasePlantpollinatorNetworks2020}) + % DONE Ajouter un tableau avec le nombre de réseaux dans chaque sous-collection + \begin{columns} + \begin{column}{0.49\linewidth} + \includegraphics[scale=0.30]{img/annual_time_span_vs_iid.png} + + \begin{center} + \begin{table} + \tiny + \begin{tabular}{ |c|c|c|c|c|c| } + \hline + \thead{N°de \\collection} & 1 & 2 & 3 & 4 & 5 \\ + \hline + \thead{Nombre de \\réseaux} & 38 & 45 & 1 & 20 & 19 \\ + \hline + \end{tabular} + \end{table} + + \end{center} + \end{column} + \begin{column}{0.49\linewidth} + \begin{figure}[H] + \includegraphics[width=0.30\textwidth]{img/iid-meso-1.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-2.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-3.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-4.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-5.png} + \caption{Connectivités de la partition} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\subsection[Axe 2]{Axe 2 : Embedding de n\oe uds par + apprentissage profond pour comparaison des topologies de réseaux} +\label{sec:axe-2} + +\subsection[Axe 3]{Axe 3 : Inférence jointe de réseaux} +\label{sec:axe-3} + +\section{Organisation de la thèse} +\label{sec:organisation-these} + +\begin{frame} + \begin{block}{Planning prévisionnel de la thèse} + TODO Ici une timeline + \end{block} + \begin{block}{Financement} + L'INRAE, par le département MathNum donne 50\% des financements de la + thèse. + \end{block} +\end{frame} + +\section*{Remerciements} +\begin{frame}[noframenumbering] + \vfill + \centering + \huge Merci pour votre attention. + \vfill +\end{frame} + +\renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}} +\begin{frame}[noframenumbering,plain,allowframebreaks] + \frametitle{Bibliographie} + \printbibliography +\end{frame} + +\appendix + +\section{Modèles à variables latentes pour collection de réseaux bipartites} +\begin{frame} + \frametitle{Latent Block Model (LBM\footnotemark[2])} + %DONE remplacer i \in bullet par Zi = \bullet + Proposé par~\cite{govaertEMAlgorithmBlock2005}. + \begin{columns} + \begin{column}{0.40\linewidth} + \begin{figure}[H] + \center + \begin{tikzpicture}[scale=0.35] + \tikzstyle{every state}=[draw, text=black,scale=0.95, + transform shape] + \tikzstyle{every state}=[draw=none,text=black,scale=0.75, + transform shape] + \tikzset{edge_proba/.style={draw=white, fill=none, + text=black}} + + \tikzstyle{every node}=[fill=blueind] + \node[edge_proba] (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[edge_proba] (pi2) at (6.75,5.7) + {\textbf{$\pi_{{\color{cyanind}\bullet}}$}}; + \node[state, draw=black!50] (R21) at (6.25,5) + {\textbf{R21}}; + \node[state, draw=black!50] (R22) at (7.25,5) + {\textbf{R22}}; + + \tikzstyle{every node}=[fill=electricblue] + \node[edge_proba] (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[edge_proba] (pi3) at (0.5,-0.7) + {\textbf{$\rho_{{\color{burntorange}\bullet}}$}}; + \tikzstyle{every state}=[draw=none,text=black,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[edge_proba] (pi3) at (4,-0.7) + {\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}}; + \node[state, draw=black!50] (B3) at (3.5,0) {\textbf{C21}}; + \node[state, draw=black!50] (B4) at (4.5,0) {\textbf{C22}}; + \tikzstyle{every node}=[fill=peach, shape=rectangle] + \node[edge_proba] (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[left, + 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[midway, left, + 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[midway, + right, 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[midway, left, + 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[midway, + right, fill=none] + {$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$} (B5); + + \end{tikzpicture} + \caption{Exemple de LBM\footnotemark} + \label{fig:LBMvisu} + \end{figure} + \end{column} + \begin{column}{0.51\linewidth} + Pour \begin{itemize} + \item $Q_1 = + |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ + blocs fixés en ligne + \item $Q_2 = + |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ + blocs fixés en colonne + \end{itemize} + \begin{block}{Paramètres} + \begin{itemize} + \item $\pi_{\bullet} = \mathbb{P}(Z_i = \bullet)$ en ligne + et $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne + \item + $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = + \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = + {\color{burntorange}\bullet})$ + \end{itemize} + \end{block} + \end{column} + \end{columns} + + \footnotetext{Que j'appellerai par la suite BiSBM} + +\end{frame} +\begin{frame} + \frametitle{\emph{colSBM}} + Le modèle \emph{colSBM} + \parencite{chabert-liddellLearningCommonStructures2023}.\\ + % Difficulté estimer les parametres + + % DONE Modifier les realisations pour variabilite, mettre iid au dessus du sim et inverser modele et realisations + \smallskip + \definecolor{yellow}{RGB}{255,190,60} + \begin{center} + \begin{adjustbox}{trim=0 0 0 1cm} + \begin{tikzpicture}[scale=.32] + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=.5pt, bend left] + \tikzstyle{every state}=[draw, text=black,scale=0.95, transform + shape] + \tikzset{edge_proba/.style={draw=white, fill=none, text=black}} + + \tikzstyle{every node}=[fill=yellow] + \node[state, draw=black!50] (A1) at (0,2) {\textbf{A1}}; + \node[state, draw=black!50] (A2) at (1.5, 2) {\textbf{A2}}; + \node[state, draw=black!50] (A3) at (0.75,3.25) {\textbf{A3}}; + + \tikzstyle{every node}=[fill=blueind] + \node[state, draw=black!50] (B1) at (4.5,3) {\textbf{B1}}; + \node[state, draw=black!50] (B2) at (4,4.75) {\textbf{B2}}; + \node[state, draw=black!50] (B3) at (5.5,6) {\textbf{B3}}; + \node[state, draw=black!50] (B4) at (7,4.75) {\textbf{B4}}; + \node[state, draw=black!50] (B5) at (6.5,3) {\textbf{B5}}; + + \tikzstyle{every node}=[fill=greenind] + \node[state, draw=black!50] (C1) at (5,0) {\textbf{C1}}; + \node[state, draw=black!50] (C2) at (7,1) {\textbf{C2}}; + + \path (A1) edge[bend right] (A2); + \path (A1) edge node[midway, left, fill=none] + {$\alpha_{{\color{yellow}\bullet}{\color{yellow}\bullet}}$} (A3); + \path (A3) edge (A2); + + \path (A3) edge node[midway, above, fill=none] + {$\alpha_{{\color{yellow}\bullet}{\color{blueind}\bullet}}$} (B3); + + \path (B1) edge (B2); + \path (B2) edge (B3); + \path (B3) edge (B4); + \path (B4) edge (B5); + \path (B5) edge (B1); + + \path (B1) edge[bend left=0] (B4); + \path (B5) edge[bend left=0] (B2); + + \path (A2) edge[bend right] node[midway, below, fill=none] + {$\alpha_{{\color{yellow}\bullet}{\color{greenind}\bullet}}$} (C1); + \path (C1) edge[bend right] node[midway, below, fill=none] + {$\alpha_{{\color{greenind}\bullet}{\color{greenind}\bullet}}$} (C2); + \path (C2) edge[bend right] node[midway, right, fill=none] + {$\alpha_{{\color{greenind}\bullet}{\color{blueind}\bullet}}$} (B4); + + \node[font=\small, text justified,draw=none, fill=none] at + (4.5,-1.5) {SBM}; + + % Sampled network + \begin{scope}[xshift=-16cm,yshift=4cm] + \node[font=\small, text justified, fill=none] at (10, -2.5) + {$\overset{iid}{\sim}$}; + \tikzstyle{every node}=[fill=gray, scale=0.95] + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=.5pt, bend left] + \tikzstyle{every state}=[draw, text=black,scale=0.95, + transform shape] + + \node[state, draw=black!50] (A1) at (0,0) {\textbf{10}}; + \node[state, draw=black!50] (A2) at (1, 0) {\textbf{2}}; + \node[state, draw=black!50] (A3) at (0.5,1) {\textbf{5}}; + + \node[state, draw=black!50] (B2) at (2,2.75) {\textbf{9}}; + \node[state, draw=black!50] (B3) at (3.5,4) {\textbf{6}}; + \node[state, draw=black!50] (B4) at (5,2.75) {\textbf{3}}; + \node[state, draw=black!50] (B5) at (4.5,1) {\textbf{7}}; + + \node[state, draw=black!50] (C1) at (3,-0.5) {\textbf{4}}; + + \path (A1) edge[bend right] (A2); + \path (A1) edge (A3); + \path (A3) edge (A2); + + \path (A3) edge (B3); + + \path (B2) edge (B3); + \path (B3) edge (B4); + \path (B4) edge (B5); + + \path (B5) edge[bend left=0] (B2); + + \path (A2) edge[bend right] (C1); + + \node[text width=3cm,font=\small, text justified, + rotate=90, fill=none, below = -0.8cm of C1] (dots) {\dots}; + + \end{scope} + \begin{scope}[xshift=-16cm,yshift=-4cm] + \tikzstyle{every node}=[fill=gray, scale=0.95] + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=.5pt, bend left] + \tikzstyle{every state}=[draw, text=black,scale=0.95, + transform shape] + + \node[state, draw=black!50] (A2) at (1, 0) {\textbf{2}}; + \node[state, draw=black!50] (A3) at (0.5,1) {\textbf{1}}; + + \node[state, draw=black!50] (B1) at (2.5,1) {\textbf{5}}; + \node[state, draw=black!50] (B2) at (2,2.75) {\textbf{10}}; + \node[state, draw=black!50] (B4) at (5,2.75) {\textbf{8}}; + \node[state, draw=black!50] (B5) at (4.5,1) {\textbf{7}}; + + \node[state, draw=black!50] (C2) at (5,0) {\textbf{3}}; + + \path (A3) edge (A2); + + \path (B1) edge (B2); + \path (B4) edge (B5); + \path (B5) edge (B1); + + \path (B1) edge[bend left=0] (B4); + \path (B5) edge[bend left=0] (B2); + + \path (C2) edge[bend right] (B4); + \end{scope} + \end{tikzpicture} + \end{adjustbox} + \end{center} + Pour $Q = + |\{{\color{yellow}\bullet},{\color{blueind}\bullet},{\color{greenind}\bullet}\}|$ + blocs fixés : + \begin{block}{Paramètres} + \begin{itemize} + \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ + \item $\alpha_{{\color{greenind}\bullet}{\color{blueind}\bullet}} = + \mathbb{P}(X_{ij} = 1 | Z_i = {\color{greenind}\bullet}, Z_j = + {\color{blueind}\bullet})$ + \end{itemize} + \end{block} +\end{frame} + +\begin{frame} + \frametitle{Collections bipartites} + \begin{center} + \begin{adjustbox}{trim=0 0 1 1.5cm} + \begin{tikzpicture}[scale=.33] + \begin{scope}[xshift=18cm, yshift=2cm] + \tikzstyle{every state}=[draw=none, text=black,scale=0.75, + transform shape] + \tikzset{edge_proba/.style={draw=white, fill=none, + text=black}} + + \tikzstyle{every node}=[fill=blueind] + \node[edge_proba] (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[edge_proba] (pi2) at (6.75,5.7) + {\textbf{$\pi_{{\color{cyanind}\bullet}}$}}; + \node[state, draw=black!50] (R21) at (6.25,5) + {\textbf{R21}}; + \node[state, draw=black!50] (R22) at (7.25,5) + {\textbf{R22}}; + + \tikzstyle{every node}=[fill=electricblue] + \node[edge_proba] (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[edge_proba] (rho1) at (0.5,-1) + {\textbf{$\rho_{{\color{burntorange}\bullet}}$}}; + \tikzstyle{every state}=[draw=none,text=black,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[edge_proba] (rho2) at (4,-1) + {\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}}; + \node[state, draw=black!50] (B3) at (3.5,0) {\textbf{C21}}; + \node[state, draw=black!50] (B4) at (4.5,0) {\textbf{C22}}; + \tikzstyle{every node}=[fill=peach, shape=rectangle] + \node[edge_proba] (rho3) at (10,-1) + {\textbf{$\rho_{{\color{peach}\bullet}}$}}; + \node[state, draw=black!50] (B5) at (10,0) {\textbf{C31}}; + + \node[font=\small, text justified,draw=none, fill=none, + below = 0.05cm of rho2] {BiSBM}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1.5pt,draw opacity=0.2] + + \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 (R21) edge (B4); + \path (R21) edge (B5); + + \path (R22) edge (B3); + \path (R22) edge (B4); + + \path (R11) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[left, + fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$} + (B1); + \path (R13) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, + 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[midway, + anchor=center, fill=none] + {$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$} (B3); + \path (R22) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, + 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[midway, + right, fill=none] + {$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$} (B5); + \end{scope} + + \begin{scope}[xshift=3cm, yshift = 1cm] + \node[text justified, fill=none] at (10, 3.5) + {$\overset{iid}{\sim}$}; + \begin{scope}[yshift = 6cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,1.25) + {\textbf{1}}; + \node[state, draw=black!50] (R12) at (1,1.25) + {\textbf{2}}; + \node[state, draw=black!50] (R13) at (2,1.25) + {\textbf{3}}; + \node[state, draw=black!50] (R21) at (3,1.25) + {\textbf{4}}; + \node[state, draw=black!50] (R31) at (5,1.25) + {\textbf{6}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + \node[state, draw=black!50] (B1) at (0.5,-1) + {\textbf{1}}; + + \node[state, draw=black!50] (B31) at (2.5,-1) + {\textbf{3}}; + \node[state, draw=black!50] (B4) at (3.5,-1) + {\textbf{4}}; + + \node[state, draw=black!50] (B5) at (4.5,-1) + {\textbf{5}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (B1); + \path (R11) edge (B31); + \path (R11) edge (B4); + + \path (R12) edge [] (B1); + \path (R12) edge (B31); + \path (R12) edge (B4); + + \path (R13) edge [] (B1); + \path (R13) edge (B31); + \path (R13) edge (B4); + + \path (R21) edge (B31); + \path (R21) edge (B4); + \path (R21) edge (B5); + + \path (R31) edge (B5); + \end{scope} + \node[text width=3cm,font=\small, text justified, + rotate=90, fill=none] (dots) at (2.5, 7.5){\dots}; + + \begin{scope}[yshift = 0cm] + \tikzstyle{every state}=[draw, text=black,scale=0.75, + transform shape] + + \tikzstyle{every node}=[fill=gray] + \node[state, draw=black!50] (R11) at (0,2.25) + {\textbf{4}}; + \node[state, draw=black!50] (R13) at (2,2.25) + {\textbf{6}}; + \node[state, draw=black!50] (R21) at (3,2.25) + {\textbf{3}}; + \node[state, draw=black!50] (R22) at (4,2.25) + {\textbf{5}}; + \node[state, draw=black!50] (R31) at (5,2.25) + {\textbf{2}}; + + \tikzstyle{every + state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + \node[state, draw=black!50] (B1) at (0.5,0) + {\textbf{5}}; + \node[state, draw=black!50] (B2) at (1.5,0) + {\textbf{1}}; + + \node[state, draw=black!50] (B4) at (3.5,0) + {\textbf{2}}; + + \node[state, draw=black!50] (B5) at (4.5,0) + {\textbf{4}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1pt, draw=gray, fill=gray] + \path (R11) edge (B1); + \path (R11) edge (B2); + \path (R11) edge (B4); + + \path (R13) edge [] (B1); + \path (R13) edge (B2); + \path (R13) edge (B4); + + \path (R21) edge (B4); + \path (R21) edge (B5); + + \path (R22) edge (B4); + \path (R22) edge (B5); + + \path (R31) edge (B5); + \end{scope} + \end{scope} + \end{tikzpicture} + \end{adjustbox} + \end{center} + + Pour + \begin{itemize} + \item $Q_1 = + |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ + blocs fixés en ligne + \item $Q_2 = + |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ + blocs fixés en colonne + \end{itemize} + \begin{block}{Paramètres} + \begin{itemize} + \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ en ligne et + $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne + \item + $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = + \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = + {\color{burntorange}\bullet})$ + \end{itemize} + \end{block} +\end{frame} + +\begin{frame} + \frametitle{Différents modèles} + \begin{block}{\emph{iid-colBiSBM}} + $\bm{\pi} = (\pi_1, \dots \pi_{Q_1})$ et $\bm{\rho} = (\rho_1, \dots + \rho_{Q_2})$ %{$\forall q \in \llbracket 1, Q_1 - 1\rrbracket, \pi_q > 0$ et $\forall r \in \llbracket 1, Q_2 - 1\rrbracket, \rho_r > 0$} + , tous les réseaux partagent les mêmes paramètres\footnotemark + \end{block} + + \begin{block}{\emph{$\pi\rho$-colBiSBM}} + $\bm{\pi} = ((\pi_{\color{black}1}^{\color{red}m}, \dots + \pi_{\color{black}Q_1}^{\color{red}m}))_{m=1,\dots M}$ et $\bm{\rho} = + ((\rho_{\color{black}1}^{\color{red}m}, \dots + \rho_{\color{black}Q_2}^{\color{red}m}))_{m=1,\dots M}$ + %{$\forall q \in \llbracket 1, Q_1 - 1\rrbracket, \pi_q > 0$ et $\forall r \in \llbracket 1, Q_2 - 1\rrbracket, \rho_r > 0$} + \small \\ + avec $\forall q,m \in \llbracket 1, Q_1 \rrbracket \times \llbracket 1, + M \rrbracket, \pi_q^m \in \left[ 0,1 \right]$ + et $\forall r,m \in \llbracket 1, Q_2 \rrbracket \times \llbracket 1, M + \rrbracket, \rho_r^m \in \left[ 0,1 \right]$ + \end{block} + Et également deux autres modèles ($\pi$-colBiSBM et $\rho$-colBiSBM) où + seulement une des deux dimensions est libre. + \footnotetext{Dans tous les modèles la structure de connectivité est + supposée identique au sein de la collection.} +\end{frame} +\begin{frame} + \frametitle{Estimation des paramètres} + % DONE dire que tau i q m c' est la proba que Zim = q, approximation de la proba variationnelle. Parce qu on impose lindependance + Maximisation d'une borne inférieure de la log-vraisemblance des données + observées. + \begin{multline*} + \ell (\bm{X};\bm{\theta}) \geq \color{red}\sum_{m=1}^{M} \bigg( + \color{black} \sum_{i = 1}^{n_1^m}\sum_{j=1}^{n_2^m}\sum_{q \in + \mathcal{Q}_{1,m}} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{1,m}_{i,q} + \tau^{2,m}_{j,r} \log f(X^{m}_{ij}; \alpha_{qr}) \\ + + \sum_{i=1}^{n_1^m} \sum_{q \in \mathcal{Q}_{1,m}} \tau^{1,m}_{i,q} + \log \pi_{\color{black}q}^{\color{gray}m} + \sum_{j=1}^{n_2^m} \sum_{r \in + \mathcal{Q}_{2,m}} \tau^{2,m}_{j,r} \log \rho_{\color{black}r}^{\color{gray}m} + \\ + - \sum_{i=1}^{n_1} \tau^{1,m}_{i,q} \log \tau^{1,m}_{i,q} - + \sum_{j=1}^{n_2} \tau^{2,m}_{j,r} \log \tau^{2,m}_{j,r} \color{red}\bigg) + \color{black} =: J(\bm{\tau};\bm{\theta}) $$ + \end{multline*} + + \begin{block}{Approximation variationnelle} + $\tau_{i,q}^{1,m} = P(Z_i = q | X^m_{ij})$ et $\tau_{j,r}^{2,m} = P(W_j + = r | X^m_{ij})$ tels que $P(Z_i = q, W_j = r | X^m_{ij}) = + \tau_{i,q}^{1,m}\times\tau_{j,r}^{2,m}$ + \end{block} + +\end{frame} + +\begin{frame} + \frametitle{Sélection de modèle : choix de $(Q_1,Q_2)$ - Approche + gloutonne} + % DONE But maximiser un critere le BICL, deplacer voir St Clair dans la note + % VEM a Q1 Q2 fixer + % Choix de Q1 Q2 par maximisation du BICL + % Itemize dans la box : init, explo voisin, arrets + \underline{Le VEM se fait à $Q_1, Q_2$ fixés}, il faut donc déterminer les + \enquote*{meilleures} coordonnées. + Nous maximisons un BIC-L\footnote{\emph{Bayesian Information Criterion - + Like}, en adaptant les formules + de~\cite{chabert-liddellLearningCommonStructures2023}}. + + Détermination d'un premier mode par approche \emph{gloutonne} \smallskip + \begin{columns} + \begin{column}{0.5\linewidth} + \begin{tikzpicture} + \draw[step=1cm, help lines] (-2,-2) grid (2,2); + \draw[fill=gray, draw=gray] (0,0) circle [radius=0.225cm]; + \draw[fill=blueind, draw=blueind] (1,0) circle + [radius=0.225cm]; + \draw[fill=blueind, draw=blueind] (0,1) circle + [radius=0.225cm]; + \draw[fill=red, draw=red] (-1,0) circle [radius=0.225cm]; + \draw[fill=red, draw=red] (0,-1) circle [radius=0.225cm]; + + % Légende + \node[font=\tiny, text justified,fill=none, rotate=-45] + (Splits) at (0.5,0.5){{\color{blueind} Splits}}; + \node[font=\tiny, text justified,fill=none, rotate=-45] + (Merges) at (-0.5,-0.5){{\color{red} Merges}}; + + % Splitting + \draw[>=stealth,->,thick, draw=blueind] (0.225,0) -- +(0.55,0); + \draw[>=stealth,->,thick, draw=blueind] (0,0.225) -- +(0,0.55); + + % Merging + \draw[>=stealth,->,thick, draw=red] (-0.225,0) -- +(-0.55,0); + \draw[>=stealth,->,thick, draw=red] (0,-0.225) -- +(0,-0.55); + + % Axes + \draw[>=to,->,thick] (-2,-2) -- +(1,0); + \node[font=\small, fill=none] (Q_1) at (-0.75,-2) {$Q_1$}; + \draw[>=to,->,thick] (-2,-2) -- +(0,1); + \node[font=\small, fill=none] (Q_2) at (-2,-0.75) {$Q_2$}; + + \end{tikzpicture} + \end{column} + \begin{column}{0.5\linewidth} + \begin{block}{Exploration gloutonne} + \begin{itemize} + \item Initialisation sur $(1,2)$ et $(2,1)$ + \item Exploration des 4 voisins et déplacement sur le + meilleur des 4 + \item Arrêt après 2 étapes successives sans augmentation du + BIC-L + \end{itemize} + \end{block} + \end{column} + \end{columns} +\end{frame} +\begin{frame} + \frametitle{Sélection de modèle : choix de $(Q_1,Q_2)$ - Fenêtre glissante} + \begin{columns} + \begin{column}{0.60\linewidth} + \begin{figure} + \includegraphics[scale=0.18]{img/moving_window.png} + \caption{Exemple de parcours de fenêtre glissante} + \end{figure} + \end{column} + \begin{column}{0.4\linewidth} + \definecolor{mypurple}{RGB}{128,0,128} + \begin{tikzpicture} + + \tikzstyle{model}=[circle,draw=none,fill=gray] + \tikzstyle{split}=[>=stealth,->,thick, draw=blueind] + \tikzstyle{merge}=[>=stealth,->,thick, draw=red] + \draw[step=1cm, help lines] (-2,-2) grid (2,2); + \node[model] (mode) at (0,0) {{\color{red}X}}; + + \onslide<2->{ + \draw[color=red, line width=1pt] (-1.5,-1.5) rectangle + ++(3,3); + } + \onslide<2-2>{ + + \node[model] (bottom_left) at (-1,-1) {}; + \node[model, opacity=0.6] (row_1) at (0,-1) {}; + \node[model, opacity=0.6] (col_1) at (-1,0) {}; + + \draw[split] (bottom_left) -- (col_1); + \draw[split] (-1.75,0) -- (col_1); + \draw[split] (bottom_left) -- (row_1); + \draw[split] (0,-1.75) -- (row_1); + + \node[model] (bottom_left) at (-1,-1) {}; + \node[model, draw=blue] (row_1) at (0,-1) {}; + \node[model, draw=blue] (col_1) at (-1,0) {}; + + \node[model, opacity=0.6] (row_2) at (1,-1) {}; + \node[model, opacity=0.6] (col_2) at (-1,1) {}; + + \draw[split] (col_1) -- (col_2); + \draw[split] (-1.75,1) -- (col_2); + \draw[split] (row_1) -- (row_2); + \draw[split] (1,-1.75) -- (row_2); + \draw[split] (row_1) -- (mode); + \draw[split] (col_1) -- (mode); + + \node[model, draw=blue] (row_2) at (1,-1) {}; + \node[model, draw=blue] (col_2) at (-1,1) {}; + \node[model, draw=blue] (mode) at (0,0) {{\color{red}X}}; + + \node[model, opacity=0.6] (row_3) at (1,0) {}; + \node[model, opacity=0.6] (col_3) at (0,1) {}; + + \draw[split] (col_2) -- (col_3); + \draw[split] (row_2) -- (row_3); + \draw[split] (mode) -- (row_3); + \draw[split] (mode) -- (col_3); + + \node[model, draw=blue] (row_3) at (1,0) {}; + \node[model, draw=blue] (col_3) at (0,1) {}; + + \node[model, opacity=0.6] (top_right) at (1,1) {}; + \draw[split] (col_3) -- (top_right); + \draw[split] (row_3) -- (top_right); + + \node[model, draw=blue] (top_right) at (1,1) {}; + } + \onslide<3->{ + \node[model, draw=mypurple] (top_right) at (1,1) {}; + \node[model, draw=mypurple] (row_3) at (1,0) {}; + \node[model, draw=mypurple] (col_3) at (0,1) {}; + \node[model, draw=mypurple] (row_2) at (1,-1) {}; + \node[model, draw=mypurple] (col_2) at (-1,1) {}; + \node[model, draw=mypurple] (mode) at (0,0) + {{\color{red}X}}; + \node[model, draw=red] (bottom_left) at (-1,-1) {}; + \node[model, draw=mypurple] (row_1) at (0,-1) {}; + \node[model, draw=mypurple] (col_1) at (-1,0) {}; + + \draw[merge] (1,1.75) -- (top_right); + \draw[merge] (1.75,1) -- (top_right); + \draw[merge] (0,1.75) -- (col_3); + \draw[merge] (1.75,0) -- (row_3); + \draw[merge] (1.75,-1) -- (row_2); + \draw[merge] (-1,1.75) -- (col_2); + + \draw[merge] (top_right) -- (col_3); + \draw[merge] (top_right) -- (row_3); + \draw[merge] (col_3) -- (col_2); + \draw[merge] (row_3) -- (row_2) ; + \draw[merge] (row_3) -- (mode); + \draw[merge] (col_3) -- (mode); + \draw[merge] (col_2) --(col_1); + \draw[merge] (row_2) -- (row_1); + \draw[merge] (mode) -- (row_1); + \draw[merge] (mode) -- (col_1); + \draw[merge] (col_1) -- (bottom_left); + \draw[merge] (row_1) -- (bottom_left); + } + \end{tikzpicture} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Clustering de réseaux} + \begin{columns} + \begin{column}{0.2\linewidth} + \begin{block}{Objectif} + Déterminer une partition qui maximise la somme du BICL de ses + sous-collections. + \end{block} + \end{column} + \begin{column}{0.78\linewidth} + \begin{tikzpicture} + \tikzstyle{instruct}=[font=\small, text justified, + rectangle,draw,fill=yellow!50] + \tikzstyle{first_col}=[rectangle, text justified, + draw,fill=gray!50] + \tikzstyle{second_col}=[scale=0.55, circle, draw,fill=red!50] + \tikzstyle{test}=[font=\small, text justified, diamond, + aspect=2.5,thick, + draw=blue,fill=yellow!50,text=blue] + \tikzstyle{es}=[font=\small, text justified, + rectangle,draw,rounded corners=4pt,fill=cyanind!25] + + \node[es] (liste) at (0,4) {Donner une collection à + partitionner}; + \node[instruct, text width=5cm, below = 0.45cm of liste] + (1-collection) {Ajuster \emph{colBiSBM}}; + \node[first_col, right = 0.5cm of 1-collection] (1-col-obj) {}; + \node[instruct, text width=5cm, below = 0.45cm of 1-collection] + (dissimi) {Calculer une matrice de dissimilarité de la collection}; + \node[instruct, text width=5cm, below = 0.45cm of dissimi] + (2-sous-collection) {Séparer la \emph{collection en 2 sous-collections} et + ajuster les \emph{colBiSBM}}; + \node[second_col, right = 0.25cm of 2-sous-collection] + (1-sec-col-obj) {1}; + \node[second_col, right = 0.25cm of 1-sec-col-obj] + (1-sec-col-obj) {2}; + \node[test,below = 0.45cm of 2-sous-collection, scale=0.5] + (BICL-test) {$\sum_{i=1}^{2} + (\text{BIC-L}(\tikz[baseline=-0.25cm]{\node[second_col] {i};} )) > + \text{BIC-L}(\tikz[baseline=-0.25cm]{\node[first_col] {};})$?}; + \node[es, right = 0.55cm of BICL-test] (sortie) {Renvoyer + \tikz{\node[rectangle, draw, fill=gray!50, rounded corners=0pt] {};}}; + \node[es, left = 0.45cm of dissimi, text width = 2cm] + (recursion) {Recommencer sur \tikz{\node[second_col] {1};} et + \tikz{\node[second_col] {2};} }; + + \tikzstyle{suite}=[->,>=stealth,thick,rounded corners=4pt] + \draw[suite] (liste) -- (1-collection); + \draw[suite] (1-collection) -- (dissimi); + \draw[suite] (dissimi) -- (2-sous-collection); + \draw[suite] (2-sous-collection) -- (BICL-test); + \draw[suite] (BICL-test) -| node[near start, above, fill=none] + {Oui} (recursion); + \draw[suite] (recursion.north) |- (1-collection.west); + \draw[suite] (BICL-test) -- node[near start, above, fill=none] + {Non} (sortie); + + \end{tikzpicture} + \end{column} + \end{columns} + \blfootnote{Même approche + que~\cite{chabert-liddellLearningCommonStructures2023}} +\end{frame} + + +\begin{frame} + \frametitle{Application, données plantes pollinisateurs} + \small + Voici des résultats du modèle \emph{iid-colBiSBM} sur des données + plantes-pollinisateurs (\cite{doreRelativeEffectsAnthropogenic2021} + et~\cite{thebaultDatabasePlantpollinatorNetworks2020}) + % DONE Ajouter un tableau avec le nombre de réseaux dans chaque sous-collection + \begin{columns} + \begin{column}{0.49\linewidth} + \includegraphics[scale=0.30]{img/annual_time_span_vs_iid.png} + + \begin{center} + \begin{table} + \tiny + \begin{tabular}{ |c|c|c|c|c|c| } + \hline + \thead{N°de \\collection} & 1 & 2 & 3 & 4 & 5 \\ + \hline + \thead{Nombre de \\réseaux} & 38 & 45 & 1 & 20 & 19 \\ + \hline + \end{tabular} + \end{table} + + \end{center} + \end{column} + \begin{column}{0.49\linewidth} + \begin{figure}[H] + \includegraphics[width=0.45\textwidth]{img/iid-meso-1.png} + \includegraphics[width=0.45\textwidth]{img/iid-meso-2.png} + \includegraphics[width=0.45\textwidth]{img/iid-meso-3.png} + \includegraphics[width=0.45\textwidth]{img/iid-meso-4.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-5.png} + \caption{Connectivités de la partition} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Perspectives sur \emph{colSBM}} + % DONE Ajouter une slide conclusion perspective + % Rappeler les modeles avec clustering + % Evoquer l'analyse de reseaux corrigés pour l'échantillonnage + % Lien vers le package + + \begin{itemize} + \item 4 modèles dont 3 qui ont une flexibilité sur au moins une des + dimensions (adaptabilité aux données) + \item Partitionner un ensemble de réseaux selon leurs structures + \item Comparer les \emph{clusterings} de réseaux obtenus entre données + brutes et données corrigées (par exemple par la méthode + \emph{CoOPLBM}\footnote{~\cite{anakokDisentanglingStructureEcological2022}}) + \end{itemize} + + \bigskip + \centering + Le package est disponible sur GitHub : \faGithub + \url{https://github.com/Chabert-Liddell/colSBM} + + \bigskip + +\end{frame} + +\end{document} \ No newline at end of file diff --git a/references.bib b/references.bib new file mode 100644 index 0000000..9bf5420 --- /dev/null +++ b/references.bib @@ -0,0 +1,407 @@ +@online{AccueilMIAParisSaclay, + title = {Accueil | {{MIA Paris-Saclay}}}, + url = {https://mia-ps.inrae.fr/}, + urldate = {2023-07-03}, + file = {/home/polarolouis/Zotero/storage/I7FWTZC3/mia-ps.inrae.fr.html} +} + +@online{anakokDisentanglingStructureEcological2022, + title = {Disentangling the Structure of Ecological Bipartite Networks from Observation Processes}, + author = {Anakok, Emre and Barbillon, Pierre and Fontaine, Colin and Thebault, Elisa}, + date = {2022-11-29}, + eprint = {2211.16364}, + eprinttype = {arxiv}, + eprintclass = {stat}, + url = {http://arxiv.org/abs/2211.16364}, + urldate = {2023-06-14}, + abstract = {The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated in simulation studies. The practical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.}, + langid = {english}, + pubstate = {preprint}, + keywords = {Statistics - Methodology}, + file = {/home/polarolouis/Zotero/storage/LQ3FINZG/Anakok et al. - 2022 - Disentangling the structure of ecological bipartit.pdf} +} + +@article{aubertModelbasedBiclusteringOverdispersed2021, + title = {Model-Based Biclustering for Overdispersed Count Data with Application in Microbial Ecology}, + author = {Aubert, Julie and Schbath, Sophie and Robin, Stéphane}, + date = {2021}, + journaltitle = {Methods in Ecology and Evolution}, + volume = {12}, + number = {6}, + pages = {1050--1061}, + issn = {2041-210X}, + doi = {10.1111/2041-210X.13582}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.13582}, + urldate = {2023-06-22}, + abstract = {Different studies have shown that microbial communities living in animals (humans included), in or around plants have a significant impact on health and disease of their host and on various services, such as adaptation under stressing environment. The basic input data to study microbiomes is a matrix representing abundance data of micro-organisms across different sampling units. Such a matrix typically corresponds to taxonomic profiles derived from the high-throughput sequencing of environmental samples. Biclustering is one way to study the interactions between the structure of micro-organism communities and the environmental samples they come from. We propose a latent block model (LBM) and an associated inference procedure for the biclustering of rows and columns of abundance matrices. The LBM assumes that micro-organisms (rows) and environmental samples (columns) can both be clustered into groups characterizing preferential interaction or avoidance. We use the Poisson–Gamma distribution to model the overdispersion observed in microbial abundance data and introduce row and column effects to account for the sequencing effort in each sample and the mean abundance of each micro-organism. Because the latent variables are not independent conditionally on the observed ones, classical maximum likelihood inference is intractable. We then derive a variational-based inference algorithm and propose a strategy to select the number of biclusters. We illustrate the flexibility and performance of our approach both on a simulation study and on three ecological datasets. The model-based framework allows us to adapt to peculiarities of microbial ecological abundance data and allows us to explore relationships between entities of two different natures. We implemented our method in the cobiclust R package available on the CRAN and built a website with example of usage (https://julieaubert.github.io/cobiclust/cobiclust-example1.html).}, + langid = {english}, + keywords = {count data,latent block model,metabarcoding,microbial interactions,model-based biclustering,Poisson–Gamma distribution,variational EM algorithm}, + file = {/home/polarolouis/Zotero/storage/A4V9MJAF/Aubert et al. - 2021 - Model-based biclustering for overdispersed count d.pdf} +} + +@article{biernackiAssessingMixtureModel2000, + title = {Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood}, + author = {Biernacki, C. and Celeux, G. and Govaert, G.}, + date = {2000-07}, + journaltitle = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, + volume = {22}, + number = {7}, + pages = {719--725}, + issn = {1939-3539}, + doi = {10.1109/34.865189}, + abstract = {We propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood. For this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. Then, the integrated completed likelihood (ICL) is approximated using the Bayesian information criterion (BIC). Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data.}, + eventtitle = {{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}}, + keywords = {Bayesian methods,Context modeling,Gaussian distribution,Numerical simulation,Probability distribution,Robustness}, + file = {/home/polarolouis/Zotero/storage/MK9H446U/Biernacki et al. - 2000 - Assessing a mixture model for clustering with the .pdf} +} + +@article{celisseConsistencyMaximumlikelihoodVariational2012, + title = {Consistency of Maximum-Likelihood and Variational Estimators in the Stochastic Block Model}, + author = {Celisse, Alain and Daudin, Jean-Jacques and Pierre, Laurent}, + date = {2012-01}, + journaltitle = {Electronic Journal of Statistics}, + volume = {6}, + pages = {1847--1899}, + publisher = {{Institute of Mathematical Statistics and Bernoulli Society}}, + issn = {1935-7524, 1935-7524}, + doi = {10.1214/12-EJS729}, + url = {https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-6/issue-none/Consistency-of-maximum-likelihood-and-variational-estimators-in-the-stochastic/10.1214/12-EJS729.full}, + urldate = {2023-06-06}, + abstract = {The stochastic block model (SBM) is a probabilistic model designed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference in SBM by use of maximum-likelihood and variational approaches. The identifiability of SBM is proved while asymptotic properties of maximum-likelihood and variational estimators are derived. In particular, the consistency of these estimators is settled for the probability of an edge between two vertices (and for the group proportions at the price of an additional assumption), which is to the best of our knowledge the first result of this type for variational estimators in random graphs.}, + issue = {none}, + keywords = {62E17,62G05,62G20,62H30,Concentration inequalities,consistency,maximum likelihood estimators,Random graphs,Stochastic block model,variational estimators}, + file = {/home/polarolouis/Zotero/storage/JNWRIYKG/celisse2012.pdf.pdf;/home/polarolouis/Zotero/storage/XG463B5I/Celisse et al. - 2012 - Consistency of maximum-likelihood and variational .pdf} +} + +@online{chabert-liddellLearningCommonStructures2023, + type = {article}, + title = {Learning Common Structures in a Collection of Networks. {{An}} Application to Food Webs}, + author = {Chabert-Liddell, Saint-Clair and Barbillon, Pierre and Donnet, Sophie}, + date = {2023-03-27}, + eprint = {2206.00560}, + eprinttype = {arxiv}, + eprintclass = {stat}, + doi = {10.48550/arXiv.2206.00560}, + url = {http://arxiv.org/abs/2206.00560}, + urldate = {2023-05-22}, + abstract = {Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.}, + pubstate = {preprint}, + keywords = {Statistics - Applications,Statistics - Methodology}, + file = {/home/polarolouis/Zotero/storage/M74TXGCF/Chabert-Liddell et al. - 2023 - Learning common structures in a collection of netw.pdf;/home/polarolouis/Zotero/storage/A35M8KNP/2206.html} +} + +@article{daudinMixtureModelRandom2008, + title = {A Mixture Model for Random Graphs}, + author = {Daudin, J.-J. and Picard, F. and Robin, S.}, + date = {2008-06-01}, + journaltitle = {Statistics and Computing}, + shortjournal = {Stat Comput}, + volume = {18}, + number = {2}, + pages = {173--183}, + issn = {1573-1375}, + doi = {10.1007/s11222-007-9046-7}, + url = {https://doi.org/10.1007/s11222-007-9046-7}, + urldate = {2023-06-16}, + abstract = {The Erdös–Rényi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it does not fit well to real-world networks. The vertices of those networks are often structured in unknown classes (functionally related proteins or social communities) with different connectivity properties. The stochastic block structures model was proposed for this purpose in the context of social sciences, using a Bayesian approach. We consider the same model in a frequentest statistical framework. We give the degree distribution and the clustering coefficient associated with this model, a variational method to estimate its parameters and a model selection criterion to select the number of classes. This estimation procedure allows us to deal with large networks containing thousands of vertices. The method is used to uncover the modular structure of a network of enzymatic reactions.}, + langid = {english}, + keywords = {Mixture models,Random graphs,Variational~method}, + file = {/home/polarolouis/Zotero/storage/439HK27B/Daudin et al. - 2008 - A mixture model for random graphs.pdf;/home/polarolouis/Zotero/storage/HVVF5MNY/daudin2007.pdf.pdf} +} + +@article{desjardins-proulxEcologicalInteractionsNetflix2017, + title = {Ecological Interactions and the {{Netflix}} Problem}, + author = {Desjardins-Proulx, Philippe and Laigle, Idaline and Poisot, Timothée and Gravel, Dominique}, + date = {2017-08-10}, + journaltitle = {PeerJ}, + shortjournal = {PeerJ}, + volume = {5}, + pages = {e3644}, + publisher = {{PeerJ Inc.}}, + issn = {2167-8359}, + doi = {10.7717/peerj.3644}, + url = {https://peerj.com/articles/3644}, + urldate = {2023-06-15}, + abstract = {Species interactions are a key component of ecosystems but we generally have an incomplete picture of who-eats-who in a given community. Different techniques have been devised to predict species interactions using theoretical models or abundances. Here, we explore the K nearest neighbour approach, with a special emphasis on recommendation, along with a supervised machine learning technique. Recommenders are algorithms developed for companies like Netflix to predict whether a customer will like a product given the preferences of similar customers. These machine learning techniques are well-suited to study binary ecological interactions since they focus on positive-only data. By removing a prey from a predator, we find that recommenders can guess the missing prey around 50\% of the times on the first try, with up to 881 possibilities. Traits do not improve significantly the results for the K nearest neighbour, although a simple test with a supervised learning approach (random forests) show we can predict interactions with high accuracy using only three traits per species. This result shows that binary interactions can be predicted without regard to the ecological community given only three variables: body mass and two variables for the species’ phylogeny. These techniques are complementary, as recommenders can predict interactions in the absence of traits, using only information about other species’ interactions, while supervised learning algorithms such as random forests base their predictions on traits only but do not exploit other species’ interactions. Further work should focus on developing custom similarity measures specialized for ecology to improve the KNN algorithms and using richer data to capture indirect relationships between species.}, + langid = {english}, + file = {/home/polarolouis/Zotero/storage/3L7JALP4/Desjardins-Proulx et al. - 2017 - Ecological interactions and the Netflix problem.pdf} +} + +@article{doreRelativeEffectsAnthropogenic2021, + title = {Relative Effects of Anthropogenic Pressures, Climate, and Sampling Design on the Structure of Pollination Networks at the Global Scale}, + author = {Doré, Maël and Fontaine, Colin and Thébault, Elisa}, + date = {2021}, + journaltitle = {Global Change Biology}, + volume = {27}, + number = {6}, + pages = {1266--1280}, + issn = {1365-2486}, + doi = {10.1111/gcb.15474}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.15474}, + urldate = {2023-06-21}, + abstract = {Pollinators provide crucial ecosystem services that underpin to wild plant reproduction and yields of insect-pollinated crops. Understanding the relative impacts of anthropogenic pressures and climate on the structure of plant–pollinator interaction networks is vital considering ongoing global change and pollinator decline. Our ability to predict the consequences of global change for pollinator assemblages worldwide requires global syntheses, but these analytical approaches may be hindered by variable methods among studies that either invalidate comparisons or mask biological phenomena. Here we conducted a synthetic analysis that assesses the relative impact of anthropogenic pressures and climatic variability, and accounts for heterogeneity in sampling methodology to reveal network responses at the global scale. We analyzed an extensive dataset, comprising 295 networks over 123 locations all over the world, and reporting over 50,000 interactions between flowering plant species and their insect visitors. Our study revealed that anthropogenic pressures correlate with an increase in generalism in pollination networks while pollinator richness and taxonomic composition are more related to climatic variables with an increase in dipteran pollinator richness associated with cooler temperatures. The contrasting response of species richness and generalism of the plant–pollinator networks stresses the importance of considering interaction network structure alongside diversity in ecological monitoring. In addition, differences in sampling design explained more variation than anthropogenic pressures or climate on both pollination networks richness and generalism, highlighting the crucial need to report and incorporate sampling design in macroecological comparative studies of pollination networks. As a whole, our study reveals a potential human impact on pollination networks at a global scale. However, further research is needed to evaluate potential consequences of loss of specialist species and their unique ecological interactions and evolutionary pathways on the ecosystem pollination function at a global scale.}, + langid = {english}, + keywords = {anthropogenic pressures,climate,connectance,data,generalism,human impacts,plant-pollinator,pollination networks,richness,sampling effects,specialization}, + file = {/home/polarolouis/Zotero/storage/89ZXBJQP/10.1111@gcb.15474.pdf.pdf;/home/polarolouis/Zotero/storage/IVR6RGG7/Doré et al. - 2021 - Relative effects of anthropogenic pressures, clima.pdf;/home/polarolouis/Zotero/storage/WSJ4DV98/gcb.html} +} + +@article{govaertEMAlgorithmBlock2005, + title = {An {{EM}} Algorithm for the Block Mixture Model}, + author = {Govaert, G. and Nadif, M.}, + date = {2005-04}, + journaltitle = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, + volume = {27}, + number = {4}, + pages = {643--647}, + issn = {1939-3539}, + doi = {10.1109/TPAMI.2005.69}, + abstract = {Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.}, + eventtitle = {{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}}, + keywords = {Approximation algorithms,Classification algorithms,Clustering algorithms,Clustering methods,Data mining,EM algorithm,Index Terms- Block mixture model,Maximum likelihood estimation,Parameter estimation,Partitioning algorithms,Self organizing feature maps,Sparse matrices,variational approximation.}, + file = {/home/polarolouis/Zotero/storage/6IG45HH2/govaert2005.pdf.pdf;/home/polarolouis/Zotero/storage/TL8M3XRF/Govaert et Nadif - 2005 - An EM algorithm for the block mixture model.pdf;/home/polarolouis/Zotero/storage/2Y48IB26/1401917.html} +} + +@article{govaertLatentBlockModel2010, + title = {Latent {{Block Model}} for {{Contingency Table}}}, + author = {Govaert, Gérard and Nadif, Mohamed}, + date = {2010-01-13}, + journaltitle = {Communications in Statistics - Theory and Methods}, + volume = {39}, + number = {3}, + pages = {416--425}, + publisher = {{Taylor \& Francis}}, + issn = {0361-0926}, + doi = {10.1080/03610920903140197}, + url = {https://doi.org/10.1080/03610920903140197}, + urldate = {2023-06-15}, + abstract = {Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, variables, there are other methods, called block clustering methods, which simultaneously consider the two sets and organize the data into homogeneous blocks. This kind of method has practical importance in a wide variety of applications such as text and market basket data analysis. Typically, the data that arise in these applications are arranged as a two-way contingency table. Using Poisson distributions, a latent block model for these data is proposed and, setting it under the maximum likelihood approach and the classification maximum likelihood approach, various algorithms are provided. Their performances are evaluated and compared to a simple use of EM or CEM applied separately on the rows and columns of the contingency table.}, + keywords = {62H17,62H30,Block clustering,Block Poisson mixture model,CEM algorithm,Contingency table,EM algorithm}, + file = {/home/polarolouis/Zotero/storage/PPHP33Z9/Govaert et Nadif - 2010 - Latent Block Model for Contingency Table.pdf;/home/polarolouis/Zotero/storage/UT8TARCX/govaert2010.pdf.pdf} +} + +@article{hollandStochasticBlockmodelsFirst1983, + title = {Stochastic Blockmodels: {{First}} Steps}, + shorttitle = {Stochastic Blockmodels}, + author = {Holland, Paul W. and Laskey, Kathryn Blackmond and Leinhardt, Samuel}, + date = {1983-06-01}, + journaltitle = {Social Networks}, + shortjournal = {Social Networks}, + volume = {5}, + number = {2}, + pages = {109--137}, + issn = {0378-8733}, + doi = {10.1016/0378-8733(83)90021-7}, + url = {https://www.sciencedirect.com/science/article/pii/0378873383900217}, + urldate = {2023-06-15}, + abstract = {A stochastic model is proposed for social networks in which the actors in a network are partitioned into subgroups called blocks. The model provides a stochastic generalization of the blockmodel. Estimation techniques are developed for the special case of a single relation social network, with blocks specified a priori. An extension of the model allows for tendencies toward reciprocation of ties beyond those explained by the partition. The extended model provides a one degree-of-freedom test of the model. A numerical example from the social network literature is used to illustrate the methods.}, + langid = {english}, + file = {/home/polarolouis/Zotero/storage/6F8YT8AD/holland1983.pdf.pdf;/home/polarolouis/Zotero/storage/7DSZ3KD9/Holland et al. - 1983 - Stochastic blockmodels First steps.pdf;/home/polarolouis/Zotero/storage/DUL2RV8Q/holland1983.pdf.pdf;/home/polarolouis/Zotero/storage/G9KZBG9W/0378873383900217.html} +} + +@article{hubertComparingPartitions1985, + title = {Comparing Partitions}, + author = {Hubert, Lawrence and Arabie, Phipps}, + date = {1985-12-01}, + journaltitle = {Journal of Classification}, + shortjournal = {Journal of Classification}, + volume = {2}, + number = {1}, + pages = {193--218}, + issn = {1432-1343}, + doi = {10.1007/BF01908075}, + url = {https://doi.org/10.1007/BF01908075}, + urldate = {2023-07-04}, + abstract = {The problem of comparing two different partitions of a finite set of objects reappears continually in the clustering literature. We begin by reviewing a well-known measure of partition correspondence often attributed to Rand (1971), discuss the issue of correcting this index for chance, and note that a recent normalization strategy developed by Morey and Agresti (1984) and adopted by others (e.g., Miligan and Cooper 1985) is based on an incorrect assumption. Then, the general problem of comparing partitions is approached indirectly by assessing the congruence of two proximity matrices using a simple cross-product measure. They are generated from corresponding partitions using various scoring rules. Special cases derivable include traditionally familiar statistics and/or ones tailored to weight certain object pairs differentially. Finally, we propose a measure based on the comparison of object triples having the advantage of a probabilistic interpretation in addition to being corrected for chance (i.e., assuming a constant value under a reasonable null hypothesis) and bounded between ±1.}, + langid = {english}, + keywords = {Consensus indices,Measures of agreement,Measures of association}, + file = {/home/polarolouis/Zotero/storage/7TKW7HEM/Hubert et Arabie - 1985 - Comparing partitions.pdf} +} + +@article{kaszewska-gilasGlobalStudiesHostParasite2021, + title = {Global {{Studies}} of the {{Host-Parasite Relationships}} between {{Ectoparasitic Mites}} of the {{Family Syringophilidae}} and {{Birds}} of the {{Order Columbiformes}}}, + author = {Kaszewska-Gilas, Katarzyna and Kosicki, Jakub Ziemowit and Hromada, Martin and Skoracki, Maciej}, + date = {2021-12}, + journaltitle = {Animals}, + volume = {11}, + number = {12}, + pages = {3392}, + publisher = {{Multidisciplinary Digital Publishing Institute}}, + issn = {2076-2615}, + doi = {10.3390/ani11123392}, + url = {https://www.mdpi.com/2076-2615/11/12/3392}, + urldate = {2023-06-15}, + abstract = {The quill mites belonging to the family Syringophilidae (Acari: Prostigmata: Cheyletoidea) are obligate ectoparasites of birds. They inhabit different types of the quills, where they spend their whole life cycle. In this paper, we conducted a global study of syringophilid mites associated with columbiform birds. We examined 772 pigeon and dove individuals belonging to 112 species (35\% world fauna) from all zoogeographical regions (except Madagascan) where Columbiformes occur. We measured the prevalence (IP) and the confidence interval (CI) for all infested host species. IP ranges between 4.2 and 66.7 (CI 0.2–100). We applied a bipartite analysis to determine host–parasite interaction, network indices, and host specificity on species and whole network levels. The Syringophilidae–Columbiformes network was composed of 25 mite species and 65 host species. The bipartite network was characterized by a high network level specialization H2′ = 0.93, high nestedness N = 0.908, connectance C = 0.90, and high modularity Q = 0.83, with 20 modules. Moreover, we reconstructed the phylogeny of the quill mites associated with columbiform birds on the generic level. Analysis shows two distinct clades: Meitingsunes + Psittaciphilus, and Peristerophila + Terratosyringophilus.}, + issue = {12}, + langid = {english}, + keywords = {Acari,biodiversity,bipartite-example,network,pigeons and doves,quill mites}, + file = {/home/polarolouis/Zotero/storage/VXVQ5CPH/Kaszewska-Gilas et al. - 2021 - Global Studies of the Host-Parasite Relationships .pdf} +} + +@online{larousseDefinitionsBipartiBipartite, + title = {Définitions : biparti, bipartite - Dictionnaire de français Larousse}, + shorttitle = {Définitions}, + author = {Larousse, Éditions}, + url = {https://www.larousse.fr/dictionnaires/francais/biparti/9503}, + urldate = {2023-06-17}, + abstract = {biparti, bipartite - Définitions Français : Retrouvez la définition de biparti, bipartite, ainsi que les difficultés... - synonymes, homonymes, difficultés, citations.}, + langid = {french}, + file = {/home/polarolouis/Zotero/storage/MA2VH6NX/9503.html} +} + +@article{maeldoreMaelDorePollinationNetworks2020, + title = {{{MaelDore}}/{{Pollination}}\_networks: {{R}} Scripts for {{Doré}} et al., 2020 - {{Relative}} Effects of Anthropogenic Pressures, Climate, and Sampling Design on the Structure of Pollination Networks at the Global Scale}, + shorttitle = {{{MaelDore}}/{{Pollination}}\_networks}, + author = {MaelDore}, + date = {2020-11-25}, + publisher = {{Zenodo}}, + doi = {10.5281/ZENODO.4290503}, + url = {https://zenodo.org/record/4290503}, + urldate = {2023-06-21}, + abstract = {R scripts for Doré et al., 2020 - Relative effects of anthropogenic pressures, climate, and sampling design on the structure of pollination networks at the global scale}, + keywords = {data,plant-pollinator} +} + +@book{ottawafield-naturalistsclubCanadianFieldnaturalist1976, + title = {The {{Canadian}} Field-Naturalist}, + author = {Ottawa Field-Naturalists' Club and Club, Ottawa Field-Naturalists'}, + date = {1976}, + volume = {90}, + pages = {1--568}, + publisher = {{Ottawa Field-Naturalists' Club}}, + location = {{Ottawa}}, + issn = {0008-3550}, + url = {https://www.biodiversitylibrary.org/item/89149}, + pagetotal = {568}, + file = {/home/polarolouis/Zotero/storage/DFN9BYBR/28045499.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}, + author = {Pavlopoulos, Georgios A and Kontou, Panagiota I and Pavlopoulou, Athanasia and Bouyioukos, Costas and Markou, Evripides and Bagos, Pantelis G}, + date = {2018-04-01}, + journaltitle = {GigaScience}, + shortjournal = {GigaScience}, + volume = {7}, + number = {4}, + pages = {giy014}, + issn = {2047-217X}, + doi = {10.1093/gigascience/giy014}, + url = {https://doi.org/10.1093/gigascience/giy014}, + urldate = {2023-06-15}, + abstract = {The latest advances in high-throughput techniques during the past decade allowed the systems biology field to expand significantly. Today, the focus of biologists has shifted from the study of individual biological components to the study of complex biological systems and their dynamics at a larger scale. Through the discovery of novel bioentity relationships, researchers reveal new information about biological functions and processes. Graphs are widely used to represent bioentities such as proteins, genes, small molecules, ligands, and others such as nodes and their connections as edges within a network. In this review, special focus is given to the usability of bipartite graphs and their impact on the field of network biology and medicine. Furthermore, their topological properties and how these can be applied to certain biological case studies are discussed. Finally, available methodologies and software are presented, and useful insights on how bipartite graphs can shape the path toward the solution of challenging biological problems are provided.}, + file = {/home/polarolouis/Zotero/storage/2KJFL3SB/Pavlopoulos et al. - 2018 - Bipartite graphs in systems biology and medicine .pdf;/home/polarolouis/Zotero/storage/A2Y2EGPA/pavlopoulos2018.pdf.pdf;/home/polarolouis/Zotero/storage/UK2MK5FW/pavlopoulos2018.pdf.pdf;/home/polarolouis/Zotero/storage/XP7G4PZF/4875933.html} +} + +@article{ramos-jilibertoTopologicalChangeAndean2010, + title = {Topological Change of {{Andean}} Plant–Pollinator Networks along an Altitudinal Gradient}, + author = {Ramos-Jiliberto, Rodrigo and Domínguez, Daniela and Espinoza, Claudia and López, Gioconda and Valdovinos, Fernanda S. and Bustamante, Ramiro O. and Medel, Rodrigo}, + date = {2010-03-01}, + journaltitle = {Ecological Complexity}, + shortjournal = {Ecological Complexity}, + volume = {7}, + number = {1}, + pages = {86--90}, + issn = {1476-945X}, + doi = {10.1016/j.ecocom.2009.06.001}, + url = {https://www.sciencedirect.com/science/article/pii/S1476945X09000622}, + urldate = {2023-06-15}, + abstract = {Pollination interaction networks exhibit structural regularities across a wide range of natural environments. Long-tailed degree distribution, nestedness, and modularity are the most prevalent topological patterns found in most bipartite networks analyzed up to day. In this work we evaluate the variation of these topological properties along an altitudinal gradient. To this end, we examined four plant–pollinator networks from the Chilean Andes at 33°S, in range from 1800 to 3600m elevation. Our results indicate that network topology is strongly and systematically affected by elevation. At increasing altitude, the number of potential visitors per plant decreased, and species’ degree distributions are closer to random expectations. On the other hand, the nested structure of mutualistic interactions systematically decreased with elevation, and network modularity was significantly higher than random expectations over the entire altitudinal range. In addition, at increasing elevations the pollination networks were organized in fewer and more strongly connected modules. Our results suggest that the severe abiotic conditions found at increased elevations translate into less organized pollination networks.}, + langid = {english}, + keywords = {bipartite-example,Chile,Complexity,Degree distribution,Modularity,Mutualistic networks,Nestedness,Power law}, + file = {/home/polarolouis/Zotero/storage/ATY3ZP2X/Ramos-Jiliberto et al. - 2010 - Topological change of Andean plant–pollinator netw.pdf;/home/polarolouis/Zotero/storage/HPBGUP65/ramos-jiliberto2010.pdf.pdf;/home/polarolouis/Zotero/storage/I33MZQQ7/ramos-jiliberto2010.pdf.pdf;/home/polarolouis/Zotero/storage/YJX8XBNW/S1476945X09000622.html} +} + +@article{snijdersEstimationPredictionStochastic1997, + title = {Estimation and {{Prediction}} for {{Stochastic Blockmodels}} for {{Graphs}} with {{Latent Block Structure}}}, + author = {Snijders, Tom A.B. and Nowicki, Krzysztof}, + date = {1997-01-01}, + journaltitle = {Journal of Classification}, + shortjournal = {J. of Classification}, + volume = {14}, + number = {1}, + pages = {75--100}, + issn = {1432-1343}, + doi = {10.1007/s003579900004}, + url = {https://doi.org/10.1007/s003579900004}, + urldate = {2023-06-15}, + abstract = {blockmodeling for graphs is proposed. The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong. Statistical procedures are derived for estimating the probabilities of edges and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this strategy is practical only for small graphs. A Bayesian estimator, based on the Gibbs sampling, is proposed. This estimator is practical also for large graphs. When ML estimators are used, the block structure can be predicted based on predictive likelihood. When Gibbs sampling is used, the block structure can be predicted from posterior predictive probabilities. A side result is that when the number of vertices tends to infinity while the probabilities remain constant, the block structure can be recovered correctly with probability tending to 1.}, + langid = {english}, + 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} +} + +@dataset{thebaultDatabasePlantpollinatorNetworks2020, + title = {A Database of Plant-Pollinator Networks}, + author = {Thébault, Elisa and Fontaine, Colin}, + date = {2020-12-01}, + publisher = {{Zenodo}}, + doi = {10.5281/zenodo.4300427}, + url = {https://zenodo.org/record/4300427}, + urldate = {2023-06-21}, + abstract = {This database assembles different published datasets of observed interaction networks between plants and pollinators, which were extracted from articles, theses and existing online databases. Each row in the data table corresponds to an interaction between a plant and a pollinator species reported at a given site by a given publication.}, + version = {1}, + keywords = {diversity,flower visitors,mutualistic network,plant-pollinator interaction} +} + +@dataset{thebaultelisaDatabasePlantpollinatorNetworks2020, + title = {A Database of Plant-Pollinator Networks}, + author = {Thébault, Elisa and Fontaine, Colin}, + date = {2020-12-01}, + publisher = {{Zenodo}}, + doi = {10.5281/ZENODO.4300427}, + url = {https://zenodo.org/record/4300427}, + urldate = {2023-06-21}, + abstract = {This database assembles different published datasets of observed interaction networks between plants and pollinators, which were extracted from articles, theses and existing online databases. Each row in the data table corresponds to an interaction between a plant and a pollinator species reported at a given site by a given publication.}, + version = {1}, + keywords = {data,diversity,flower visitors,mutualistic network,plant-pollinator,plant-pollinator interaction} +} + +@dataset{thebaultelisaDatabasePlantpollinatorNetworks2022, + title = {A Database of Plant-Pollinator Networks}, + author = {Thébault, Elisa and Fontaine, Colin}, + editora = {Doré, Maël and Parra, Santiago}, + editoratype = {collaborator}, + date = {2022-06-10}, + publisher = {{Zenodo}}, + doi = {10.5281/ZENODO.6630184}, + url = {https://zenodo.org/record/6630184}, + urldate = {2023-06-21}, + abstract = {This database assembles different published datasets of observed interaction networks between plants and pollinators, which were extracted from articles, theses and existing online databases. Each row in the data table corresponds to an interaction between a plant and a pollinator species reported at a given site by a given publication.}, + version = {2}, + keywords = {data,diversity,flower visitors,mutualistic network,plant-pollinator,plant-pollinator interaction} +} + +@dataset{thebaultelisaDatabasePlantpollinatorNetworks2022a, + title = {A Database of Plant-Pollinator Networks}, + author = {Thébault, Elisa and Fontaine, Colin}, + editora = {Doré, Maël and Parra, Santiago}, + editoratype = {collaborator}, + date = {2022-06-10}, + publisher = {{Zenodo}}, + doi = {10.5281/ZENODO.4300426}, + url = {https://zenodo.org/record/4300426}, + urldate = {2023-06-21}, + abstract = {This database assembles different published datasets of observed interaction networks between plants and pollinators, which were extracted from articles, theses and existing online databases. Each row in the data table corresponds to an interaction between a plant and a pollinator species reported at a given site by a given publication.}, + version = {2}, + keywords = {data,diversity,flower visitors,mutualistic network,plant-pollinator,plant-pollinator interaction} +} + +@online{WebLifeEcological, + title = {Web of {{Life}}: Ecological Networks Database}, + url = {https://www.web-of-life.es/map.php}, + urldate = {2023-06-17}, + keywords = {networks,site}, + file = {/home/polarolouis/Zotero/storage/9WZE8QLQ/map.html} +} + +@online{yumpu.comInsectPollinatorsMer, + title = {Insect Pollinators of the {{Mer Bleue}} Peat Bog of {{Ottawa}} - {{Biodiversity}} ...}, + author = {Yumpu.com}, + url = {https://www.yumpu.com/en/document/view/11762821/insect-pollinators-of-the-mer-bleue-peat-bog-of-ottawa-biodiversity-}, + urldate = {2023-08-06}, + abstract = {Insect pollinators of the Mer Bleue peat bog of Ottawa - Biodiversity ...}, + langid = {english}, + organization = {{yumpu.com}}, + file = {/home/polarolouis/Zotero/storage/DIXT2PYL/insect-pollinators-of-the-mer-bleue-peat-bog-of-ottawa-biodiversity-.html} +}