Changing LPM

annexe.tex

@@ -112,6 +112,17 @@
     \cite{biernackiAssessingMixtureModel2000,daudinMixtureModelRandom2008,chabert-liddellLearningCommonStructures2024}
 \end{frame}
 
+\begin{frame}{Practical problems of choosing $Q_1, Q_2$}
+    \begin{alertblock}{Exploration problems}
+        \begin{itemize}
+            \item Sensitivity to initializations. \uncover<2->{$\rightarrow$ \textbf{Spectral
+                          clustering} and \textbf{split \& merge} approach}
+            \item Exploration of a 2D grid is costly. \uncover<3->{$\rightarrow$ \textbf{Greedy
+                          approach} and \textbf{sliding window}}
+        \end{itemize}
+    \end{alertblock}
+\end{frame}
+
 \begin{frame}
     \frametitle{Choice of $(Q_1,Q_2)$ - Greedy approach}
     \begin{columns}
@@ -173,7 +184,6 @@
 \section{Simulations}
 % Ajouter les graphiques de résultats de simulations
 
-
 \section{Data}
 \begin{frame}
     \addtocounter{figure}{1}

dessin-LPM.tex

@@ -0,0 +1,78 @@
+\documentclass[tikz]{standalone}
+\usepackage{tikz}
+\usepackage{xcolor}
+
+\definecolor{lightorange}{HTML}{E69F00}
+\definecolor{darkorange}{HTML}{D55E00}
+\definecolor{lightblue}{HTML}{56B4E9}
+\definecolor{darkblue}{HTML}{0072B2}
+
+
+\usetikzlibrary{trees, positioning, shapes, calc, fit}
+
+\begin{document}
+
+\begin{tikzpicture}[
+        level distance=1.5cm,
+        level 1/.style={sibling distance=4cm},
+        level 2/.style={sibling distance=1.5cm},
+        every node/.style={circle, draw, minimum size=6mm},
+        edge from parent/.style={draw, -latex}
+    ]
+
+    % ======================
+    % ARBRE PHYLOGENETIQUE
+    % ======================
+
+    \node (root) {$i=0$}
+    child {
+            node[fill=lightorange] {$i=1$}
+            child { node[fill=darkorange] {$i=3$} }
+            child { node[fill=darkorange] {$i=4$} }
+            child { node[fill=darkorange] {$i=5$} }
+        }
+    child {
+            node[fill=lightblue] {$i=2$}
+            child { node[fill=darkblue] {$i=6$} }
+            child { node[fill=darkblue] {$i=7$} }
+        };
+
+    % Labels des niveaux
+
+    \node[left=1cm of root-1-1,draw=none] (l2) {$l=2$};
+    \node[above=0.4cm of l2,draw=none] (l1) {$l=1$};
+    \node[above=0.4cm of l1,draw=none] (l0) {$l=0$};
+
+    % ======================
+    % ESPACE LATENT (droite)
+    % ======================
+
+    \begin{scope}[xshift=6cm, yshift=-3.5cm]
+
+        % Axes
+        \draw[->] (-0.5,0) -- (4,0) node[right,draw=none] {};
+        \draw[->] (0,-0.5) -- (0,4) node[above,draw=none] {};
+
+        % Points correspondant aux noeuds
+        \node[inner sep=1.5pt] (g0) at (2,2) {$\gamma_{0,0}$};
+
+        \node[inner sep=1.5pt, left of = g0, fill = lightorange] (g11) {$\gamma_{1,1}$};
+        \node[inner sep=1.5pt, right of = g0, fill = lightblue] (g12) {$\gamma_{1,2}$};
+
+        \node[inner sep=1.5pt, above  = 0.5cm of g11, fill=darkorange]  (g23) {$\gamma_{2,3}$};
+        \node[inner sep=1.5pt, above right = 0.1cm of g23, fill=darkorange]  (g24) {$\gamma_{2,4}$};
+        \node[inner sep=1.5pt, below = 0.5cm of g11, fill=darkorange]  (g25) {$\gamma_{2,5}$};
+
+        \node[inner sep=1.5pt, right = 0.05 cm of g25, fill=darkblue] (g26) {$\gamma_{2,6}$};
+        \node[inner sep=1.5pt, above of = g12, fill=darkblue] (g27) {$\gamma_{2,7}$};
+
+        \path (g0) edge[densely dotted] (g11) edge[densely dotted] (g12);
+        \path (g11) edge[densely dotted] (g23) edge[densely dotted] (g24) edge[densely dotted] (g25);
+        \path (g12) edge[densely dotted] (g27) edge[densely dotted] (g26);
+
+        \node [inner xsep=6pt, inner ysep=3pt, draw = black, fit={(g25) (g26)}, rectangle] {};
+    \end{scope}
+
+\end{tikzpicture}
+
+\end{document}

principal.tex

@@ -293,16 +293,6 @@
         \end{align*}
     }
 \end{frame}
-\begin{frame}{Practical problems of choosing $Q_1, Q_2$}
-    \begin{alertblock}{Exploration problems}
-        \begin{itemize}
-            \item Sensitivity to initializations. \uncover<2->{$\rightarrow$ \textbf{Spectral
-                          clustering} and \textbf{split \& merge} approach}
-            \item Exploration of a 2D grid is costly. \uncover<3->{$\rightarrow$ \textbf{Greedy
-                          approach} and \textbf{sliding window}}
-        \end{itemize}
-    \end{alertblock}
-\end{frame}
 
 \section{Application}
 \label{sec:application}
@@ -455,19 +445,16 @@
     \frametitle{Conclusion and perspectives}
     \begin{block}{Summary}
         \begin{itemize}
-            \item 4 models including 3 flexible on at least one dimension (adaptability to data).
-            \item Jointly detect classic and less classic structures agnostically.
-            \item Partition a collection in sub-collections with homogeneous structures.
-            \item \texttt{R} package \texttt{colSBM} at \url{https://github.com/GrossSBM/colSBM}
+            \item Joint and agnostic structure detection.
+            \item Partitioning algorithm for collections.
+            \item \texttt{R} package \texttt{colSBM} \faGithub~GrossSBM/colSBM.
+            \item An article under review.
         \end{itemize}
     \end{block}
-    \begin{block}{Future work}
-        \begin{itemize}
-            \item Preprint in redaction
-            \item Implement accounting for density ($\delta$-colBiSBM).
-            \item Apply clustering to data from
-                  \cite{pichonTellingMutualisticAntagonistic2024,doreRelativeEffectsAnthropogenic2021}.
-                  Do interaction type drives the structure of the network?
-        \end{itemize}
+    \begin{block}{Future work: phylogenetic tree and Latent Position Model}
+        \begin{center}
+            \includegraphics[width=0.8\textwidth]{dessin-LPM.pdf}
+        \end{center}
+        \cite{puTreeEnhancedLatentSpace2025,wilmsTreebasedNodeAggregation2022}
     \end{block}
 \end{frame}

references.bib

@@ -4,7 +4,42 @@
   urldate = {2023-07-03},
   file = {/home/louis/snap/zotero-snap/common/Zotero/storage/I7FWTZC3/mia-ps.inrae.fr.html}
 }
+@article{puTreeEnhancedLatentSpace2025,
+  title        = {Tree-{{Enhanced Latent Space Models}} for {{Two-Mode Networks}}},
+  author       = {Pu, Dan and Fan, Xinyan and Fang, Kuangnan},
+  date         = {2025-06-21},
+  journaltitle = {Journal of Computational and Graphical Statistics},
+  volume       = {0},
+  number       = {0},
+  pages        = {1--9},
+  publisher    = {ASA Website},
+  issn         = {1061-8600},
+  doi          = {10.1080/10618600.2025.2527295},
+  url          = {https://doi.org/10.1080/10618600.2025.2527295},
+  urldate      = {2025-09-23},
+  abstract     = {Latent space models have garnered significant attention in the analysis of two-mode networks. In numerous applications, auxiliary information in the form of a hierarchical tree structure, which elucidates the interrelationships between nodes and provides extensive insights into connectivity patterns, can be easily obtained. To harness the potential of such tree-structured information, we introduce an innovative tree-enhanced latent space model (TLSM) for two-mode networks. In this framework, each node is characterized by a latent embedding vector, reparameterized as the aggregate of intermediate vectors corresponding to nodes within the tree structure. By optimizing the log-likelihood function augmented with a tree-based regularization term, the proposed model facilitates the simultaneous estimation of embedding vectors and the derivation of interpretable community structures. We have developed an efficient Alternating Direction Method of Multipliers (ADMM) algorithm to solve the resulting optimization problem. Theoretical analysis establishes the consistency of the proposed estimator under some mild conditions. Furthermore, comprehensive simulation studies and empirical applications on the Amazon review dataset substantiate the efficacy and practical relevance of the proposed model. Supplementary materials for this article are available online.},
+  keywords     = {Latent space model,Tree-structured information,Two-mode network},
+  annotation   = {Read\_Status: Read\\
+                  Read\_Status\_Date: 2025-09-24T13:31:51.261Z},
+  file         = {/home/louis/snap/zotero-snap/common/Zotero/storage/9DVZDMA7/Appendix.pdf;/home/louis/snap/zotero-snap/common/Zotero/storage/NK5GZXTL/Pu et al. - Tree-Enhanced Latent Space Models for Two-Mode Networks.pdf}
+}
 
+@article{wilmsTreebasedNodeAggregation2022,
+  title        = {Tree-Based {{Node Aggregation}} in {{Sparse Graphical Models}}},
+  author       = {Wilms, Ines and Bien, Jacob},
+  date         = {2022},
+  journaltitle = {Journal of Machine Learning Research},
+  volume       = {23},
+  number       = {243},
+  pages        = {1--36},
+  issn         = {1533-7928},
+  url          = {http://jmlr.org/papers/v23/21-0105.html},
+  urldate      = {2025-10-14},
+  abstract     = {High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical model. We develop a new convex regularized method, called the tree-aggregated graphical lasso or tag-lasso, that estimates graphical models that are both edge-sparse and node-aggregated. The aggregation is performed in a data-driven fashion by leveraging side information in the form of a tree that encodes node similarity and facilitates the interpretation of the resulting aggregated nodes. We provide an efficient implementation of the tag-lasso by using the locally adaptive alternating direction method of multipliers and illustrate our proposal's practical advantages in simulation and in applications in finance and biology.},
+  annotation   = {Read\_Status: New\\
+                  Read\_Status\_Date: 2025-10-14T12:07:34.769Z},
+  file         = {/home/louis/snap/zotero-snap/common/Zotero/storage/V5KN62CY/Wilms et Bien - 2022 - Tree-based Node Aggregation in Sparse Graphical Models.pdf;/home/louis/snap/zotero-snap/common/Zotero/storage/4A8U5CT3/21-0105.html}
+}
 @incollection{AgglomerativeNestingProgram1990,
   title = {Agglomerative {{Nesting}} ({{Program AGNES}})},
   booktitle = {Finding {{Groups}} in {{Data}}},
@@ -375,7 +410,7 @@ Read\_Status\_Date: 2025-09-19T12:33:29.962Z},
   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},
+  keywords = {Mixture models,Random graphs,Variational method},
   file = {/home/louis/snap/zotero-snap/common/Zotero/storage/439HK27B/Daudin et al. - 2008 - A mixture model for random graphs.pdf;/home/louis/snap/zotero-snap/common/Zotero/storage/HVVF5MNY/daudin2007.pdf.pdf}
 }