From da06fd43850656847f4eb54e71f40e0680e33824 Mon Sep 17 00:00:00 2001
From: Louis Lacoste <louis.lacoste@hotmail.fr>
Date: Sun, 18 Aug 2024 20:11:21 +0200
Subject: [PATCH] contexte : relu

---
 rapport/chapter2-context.tex | 22 ++++++++++++----------
 1 file changed, 12 insertions(+), 10 deletions(-)

diff --git a/rapport/chapter2-context.tex b/rapport/chapter2-context.tex
index 23aaf88..61ec4d4 100644
--- a/rapport/chapter2-context.tex
+++ b/rapport/chapter2-context.tex
@@ -102,8 +102,8 @@ adapts the Stochastic Block Model (SBM)
 to bipartite graphs.
 
 \textit{Note :}\begin{small}
-    Please note that we prefer the term ``BiSBM`` and will use both LBM and BiSBM to
-    designate the Stochastic Block Model applied on bipartite networks.
+    Please note that we prefer the term \enquote{BiSBM} and will use both LBM and BiSBM to
+    designate the Stochastic Block Model adapted to bipartite networks.
 \end{small}
 
 This model supposes that:
@@ -130,10 +130,11 @@ This model supposes that:
 Parameters
 \begin{itemize}
     \item $\pi_{\bullet} = \mathbb{P}(Z_i = \bullet)$ for rows and $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ for columns
-    \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$, probability of connectivity knowing node membership blocks.
+    \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$, parameter influencing the probability and value of a link knowing node
+          membership blocks.
 \end{itemize}
 
-On \ref{fig:LBMvisu}, $\bm{\pi}$ are the probabilities for a row node to belong
+On figure~\ref{fig:LBMvisu}, $\bm{\pi}$ are the probabilities for a row node to belong
 to the row block of corresponding color, $\bm{\rho}$ are the probabilities for
 a column node to belong to the column block of corresponding color and
 $\bm{\alpha}$ is a matrix $Q_1 \times Q_2$ of the connectivity parameters
@@ -143,20 +144,19 @@ of the network we are referring to this connectivity matrix.
 This model can be used to easily generate bipartite graphs with complex and
 very varied structures. But when trying to determine the structure of a given
 network we need to find those parameters and as the row and column block
-memberships are \emph{latent} i.e.,\ they are not known and must be inferred.
+memberships are \emph{latent} i.e.,\ they are not known, they must be inferred.
 
-For this a common approach is to use a \emph{variational} EM algorithm (proposed
+For this a common approach is to use a \emph{variational} EM algorithm, proposed
 for SBM in~\cite{daudinMixtureModelRandom2008} and for LBM in
-~\cite{govaertEMAlgorithmBlock2005}) those groups and the required parameters
+~\cite{govaertEMAlgorithmBlock2005}. The groups and required parameters
 can be inferred by maximizing a lower bound of the likelihood.
 
 \section{colSBM model, a joint model for a collection of networks}
 \label{sec:colsbm-model-a-joint-model-for-a-collection-of-networks}
 The \emph{colSBM} model introduced by ~\cite{chabert-liddellLearningCommonStructures2024a}
 propose an extension of the SBM model to collections of simple (or unipartite)
-networks. A collection is a set of networks which nodes are not common or linked
-between different networks, the interactions have the same valuations and
-are of the same type.
+networks. A collection is a set of networks which nodes are not in common nor
+linked between different networks and the interactions have the same valuations.
 
 The model can retrieve the shared structure in a collection, indicate if
 networks should be grouped in a collection and in a large pool of networks,
@@ -164,3 +164,5 @@ collections with common structures.
 
 The next step after designing this collection model for unipartite networks was
 to extend it to the bipartite case.
+
+% DONE Relu
\ No newline at end of file