Racines en haut et feuilles en bas : les arbres en mathstuxette
1. The document discusses methods for clustering and differential analysis of Hi-C matrices, which represent the 3D organization of DNA.
2. It proposes extending Ward's hierarchical clustering to directly use Hi-C similarity matrices while enforcing adjacency constraints. A fast algorithm was also developed.
3. A new method called "treediff" was created to perform differential analysis of Hi-C matrices based on the Wasserstein distance between hierarchical clusterings. Software implementations of these methods were also developed.
Méthodes à noyaux pour l’intégration de données hétérogènestuxette
The document discusses a presentation about multi-omics data integration methods using kernel methods. The presentation introduces kernel methods, how they can be used to integrate heterogeneous omics data, and examples of applications. Specifically, it discusses using kernel methods to perform unsupervised transformation-based integration of multi-omics data. It also presents an application of constrained kernel hierarchical clustering to analyze Hi-C data by directly using Hi-C matrices as kernels.
Racines en haut et feuilles en bas : les arbres en mathstuxette
1. The document discusses methods for clustering and differential analysis of Hi-C matrices, which represent the 3D organization of DNA.
2. It proposes extending Ward's hierarchical clustering to directly use Hi-C similarity matrices while enforcing adjacency constraints. A fast algorithm was also developed.
3. A new method called "treediff" was created to perform differential analysis of Hi-C matrices based on the Wasserstein distance between hierarchical clusterings. Software implementations of these methods were also developed.
Méthodes à noyaux pour l’intégration de données hétérogènestuxette
The document discusses a presentation about multi-omics data integration methods using kernel methods. The presentation introduces kernel methods, how they can be used to integrate heterogeneous omics data, and examples of applications. Specifically, it discusses using kernel methods to perform unsupervised transformation-based integration of multi-omics data. It also presents an application of constrained kernel hierarchical clustering to analyze Hi-C data by directly using Hi-C matrices as kernels.
Méthodologies d'intégration de données omiquestuxette
This document presents a presentation on multi-omics data integration methods given by Nathalie Vialaneix on December 13, 2023. The presentation discusses different types of omics data that can be integrated, both vertically across different levels of omics data on the same samples and horizontally across similar types of omics data on different samples. It also discusses different analysis approaches that can be taken, including supervised and unsupervised methods. The rest of the presentation focuses on unsupervised transformation-based integration methods using kernels.
The document discusses current and future work on analyzing Hi-C data and differential analysis of Hi-C matrices. It describes a clustering method developed to partition chromosomes based on Hi-C matrix similarity. It also introduces a new method called treediff for differential analysis of Hi-C data that calculates the distance between hierarchical clusterings. Current work includes reviewing differential analysis methods, investigating differential subtrees with multiple testing control, and inferring chromatin interaction networks.
Can deep learning learn chromatin structure from sequence?tuxette
This document discusses a deep learning model called ORCA that can predict chromatin structure from DNA sequence. The model uses a neural network with an encoder to extract features from sequence and a decoder to predict Hi-C matrices. It was trained on Hi-C data from multiple cell types and can predict interactions between regions at various resolutions. The model accurately captures features like CTCF-mediated loops and can predict effects of structural variants on chromatin structure. It allows for in silico mutagenesis to study how mutations may alter 3D genome organization.
Multi-omics data integration methods: kernel and other machine learning appro...tuxette
The document discusses multi-omics data integration methods, particularly kernel methods. It describes how kernel methods transform data into similarity matrices between samples rather than relying on variable space. Multiple kernel integration approaches are presented that combine multiple similarity matrices into a consensus kernel in an unsupervised manner, such as through a STATIS-like framework that maximizes the similarity between kernels. Examples of applications to datasets from the TARA Oceans expedition are given.
This document provides an overview of the MetaboWean and Idefics projects. MetaboWean aims to study the co-evolution of gut microbiota and epithelium during suckling-to-weaning transition in rabbits, using metabolomics, metagenomics, and single-cell RNA sequencing data. Idefics integrates multiple omics datasets from human skin samples to understand relationships between microorganisms and molecules and how they are structured in patient groups. The datasets include metagenomics, metabolomics, and proteomics from host and microbiota.
Rserve, renv, flask, Vue.js dans un docker pour intégrer des données omiques ...tuxette
ASTERICS is an interactive and integrative data analysis tool for omics data. It uses Rserve and PyRserve with Flask and Vue.js in a Docker container to integrate omics data. The backend uses Rserve and PyRserve with Flask on the server side, while the frontend uses Vue.js. This architecture was chosen for its open source and light design. Data communication between Rserve and PyRserve is limited, requiring an object database. ASTERICS is deployed using three Docker containers for R, Python, and
Apprentissage pour la biologie moléculaire et l’analyse de données omiquestuxette
This document summarizes a scientific presentation about molecular biology and omics data analysis. The presentation covers topics related to analyzing large omics datasets using methods like kernel methods, graphical models, and neural networks to learn gene regulation networks and predict phenotypes. Key challenges addressed are handling big data, missing values, non-Gaussian data types like counts and compositional data. The goal is to better understand complex biological systems from multi-omics data.
Quelques résultats préliminaires de l'évaluation de méthodes d'inférence de r...tuxette
The document summarizes preliminary results from evaluating methods for inferring gene regulatory networks from expression data in Bacillus subtilis. It finds that recall of the known network is generally poor (<20% for random forest), but inferred clusters still retain biological information about common regulators. It plans to confirm results, test restricting edges to sigma factors, and explore other inference methods like Bayesian networks and ARACNE.
Intégration de données omiques multi-échelles : méthodes à noyau et autres ap...tuxette
The document discusses methods for integrating multi-scale omics data using kernel and machine learning approaches. It describes how omics data is large, heterogeneous, and multi-scaled, creating bottlenecks for analysis. Methods discussed for data integration include multiple kernel learning to combine different relational datasets in an unsupervised way. The methods are applied to integrate different datasets from the TARA Oceans expedition to identify patterns in ocean microbial communities. Improving interpretability of the methods and making them more accessible to biological users is discussed.
Journal club: Validation of cluster analysis results on validation datatuxette
This document presents a framework for validating cluster analysis results on validation data. It describes situations where clustering is inferential versus descriptive and recommends using validation data separate from the data used for clustering. A typology of validation methods is provided, including validation based on the clustering method or results, and evaluation using internal validation, external validation, visual properties, or stability measures.
The document discusses the differences between overfitting and overparametrization in machine learning models. It explores how random forests may exhibit a phenomenon known as "double descent" where test error initially decreases then increases with more parameters before decreasing again. While double descent has been observed in other models, the document questions whether it is directly due to model complexity in random forests since very large trees may be unable to fully interpolate extremely large datasets.
Selective inference and single-cell differential analysistuxette
This document discusses selective inference and single-cell differential analysis. It introduces the problem of "double dipping" in the standard single-cell analysis pipeline where the same dataset is used for clustering and differential analysis. Two approaches for addressing this are presented: 1) A method that perturbs clusters before testing for differences, and 2) A test based on a truncated distribution that assumes clusters and genes are given separately. Experiments applying these methods to real single-cell datasets are described. The document outlines challenges in extending these approaches to more complex analyses.
SOMbrero : un package R pour les cartes auto-organisatricestuxette
SOMbrero is an R package that implements self-organizing map (SOM) algorithms. It can handle numeric, non-numeric, and relational data. The package contains functions for training SOMs, diagnosing results, and plotting maps. It also includes tools like a shiny app and vignettes to aid users without programming experience. SOMbrero supports missing data imputation and extends SOM to relational datasets through non-Euclidean distance measures.
Graph Neural Network for Phenotype Predictiontuxette
This document describes a study on using graph neural networks (GNNs) for phenotype prediction from gene expression data. The objectives are to determine if including network information can improve predictions, which network types work best, and if GNNs can learn network inferences. It provides background on GNNs and how they generalize convolutional layers to graph data. The authors implemented a GNN model from previous work as a starting point and tested it on different network types to see which network information is most useful for predictions. Their methodology involves comparing GNN performance to other methods like random forests using 10-fold cross validation.
A short and naive introduction to using network in prediction modelstuxette
The document provides an introduction to using network information in prediction models. It discusses representing a network as a graph with a Laplacian matrix. The Laplacian captures properties like random walks on the graph and heat diffusion. Eigenvectors of the Laplacian related to small eigenvalues are strongly tied to graph structure. The document discusses using the Laplacian in prediction models by working in the feature space defined by the Laplacian eigenvectors or directly regularizing a linear model with the Laplacian. This introduces network information and encourages similar contributions from connected nodes. The approaches are applied to problems like predicting phenotypes from gene expression using a known gene network.
Kernel methods and variable selection for exploratory analysis and multi-omic...tuxette
Nathalie Vialaneix
4th course on Computational Systems Biology of Cancer: Multi-omics and Machine Learning Approaches
International course, Curie training
https://training.institut-curie.org/courses/sysbiocancer2021
(remote)
September 29th, 2021
Méthodologies d'intégration de données omiquestuxette
This document presents a presentation on multi-omics data integration methods given by Nathalie Vialaneix on December 13, 2023. The presentation discusses different types of omics data that can be integrated, both vertically across different levels of omics data on the same samples and horizontally across similar types of omics data on different samples. It also discusses different analysis approaches that can be taken, including supervised and unsupervised methods. The rest of the presentation focuses on unsupervised transformation-based integration methods using kernels.
The document discusses current and future work on analyzing Hi-C data and differential analysis of Hi-C matrices. It describes a clustering method developed to partition chromosomes based on Hi-C matrix similarity. It also introduces a new method called treediff for differential analysis of Hi-C data that calculates the distance between hierarchical clusterings. Current work includes reviewing differential analysis methods, investigating differential subtrees with multiple testing control, and inferring chromatin interaction networks.
Can deep learning learn chromatin structure from sequence?tuxette
This document discusses a deep learning model called ORCA that can predict chromatin structure from DNA sequence. The model uses a neural network with an encoder to extract features from sequence and a decoder to predict Hi-C matrices. It was trained on Hi-C data from multiple cell types and can predict interactions between regions at various resolutions. The model accurately captures features like CTCF-mediated loops and can predict effects of structural variants on chromatin structure. It allows for in silico mutagenesis to study how mutations may alter 3D genome organization.
Multi-omics data integration methods: kernel and other machine learning appro...tuxette
The document discusses multi-omics data integration methods, particularly kernel methods. It describes how kernel methods transform data into similarity matrices between samples rather than relying on variable space. Multiple kernel integration approaches are presented that combine multiple similarity matrices into a consensus kernel in an unsupervised manner, such as through a STATIS-like framework that maximizes the similarity between kernels. Examples of applications to datasets from the TARA Oceans expedition are given.
This document provides an overview of the MetaboWean and Idefics projects. MetaboWean aims to study the co-evolution of gut microbiota and epithelium during suckling-to-weaning transition in rabbits, using metabolomics, metagenomics, and single-cell RNA sequencing data. Idefics integrates multiple omics datasets from human skin samples to understand relationships between microorganisms and molecules and how they are structured in patient groups. The datasets include metagenomics, metabolomics, and proteomics from host and microbiota.
Rserve, renv, flask, Vue.js dans un docker pour intégrer des données omiques ...tuxette
ASTERICS is an interactive and integrative data analysis tool for omics data. It uses Rserve and PyRserve with Flask and Vue.js in a Docker container to integrate omics data. The backend uses Rserve and PyRserve with Flask on the server side, while the frontend uses Vue.js. This architecture was chosen for its open source and light design. Data communication between Rserve and PyRserve is limited, requiring an object database. ASTERICS is deployed using three Docker containers for R, Python, and
Apprentissage pour la biologie moléculaire et l’analyse de données omiquestuxette
This document summarizes a scientific presentation about molecular biology and omics data analysis. The presentation covers topics related to analyzing large omics datasets using methods like kernel methods, graphical models, and neural networks to learn gene regulation networks and predict phenotypes. Key challenges addressed are handling big data, missing values, non-Gaussian data types like counts and compositional data. The goal is to better understand complex biological systems from multi-omics data.
Quelques résultats préliminaires de l'évaluation de méthodes d'inférence de r...tuxette
The document summarizes preliminary results from evaluating methods for inferring gene regulatory networks from expression data in Bacillus subtilis. It finds that recall of the known network is generally poor (<20% for random forest), but inferred clusters still retain biological information about common regulators. It plans to confirm results, test restricting edges to sigma factors, and explore other inference methods like Bayesian networks and ARACNE.
Intégration de données omiques multi-échelles : méthodes à noyau et autres ap...tuxette
The document discusses methods for integrating multi-scale omics data using kernel and machine learning approaches. It describes how omics data is large, heterogeneous, and multi-scaled, creating bottlenecks for analysis. Methods discussed for data integration include multiple kernel learning to combine different relational datasets in an unsupervised way. The methods are applied to integrate different datasets from the TARA Oceans expedition to identify patterns in ocean microbial communities. Improving interpretability of the methods and making them more accessible to biological users is discussed.
Journal club: Validation of cluster analysis results on validation datatuxette
This document presents a framework for validating cluster analysis results on validation data. It describes situations where clustering is inferential versus descriptive and recommends using validation data separate from the data used for clustering. A typology of validation methods is provided, including validation based on the clustering method or results, and evaluation using internal validation, external validation, visual properties, or stability measures.
The document discusses the differences between overfitting and overparametrization in machine learning models. It explores how random forests may exhibit a phenomenon known as "double descent" where test error initially decreases then increases with more parameters before decreasing again. While double descent has been observed in other models, the document questions whether it is directly due to model complexity in random forests since very large trees may be unable to fully interpolate extremely large datasets.
Selective inference and single-cell differential analysistuxette
This document discusses selective inference and single-cell differential analysis. It introduces the problem of "double dipping" in the standard single-cell analysis pipeline where the same dataset is used for clustering and differential analysis. Two approaches for addressing this are presented: 1) A method that perturbs clusters before testing for differences, and 2) A test based on a truncated distribution that assumes clusters and genes are given separately. Experiments applying these methods to real single-cell datasets are described. The document outlines challenges in extending these approaches to more complex analyses.
SOMbrero : un package R pour les cartes auto-organisatricestuxette
SOMbrero is an R package that implements self-organizing map (SOM) algorithms. It can handle numeric, non-numeric, and relational data. The package contains functions for training SOMs, diagnosing results, and plotting maps. It also includes tools like a shiny app and vignettes to aid users without programming experience. SOMbrero supports missing data imputation and extends SOM to relational datasets through non-Euclidean distance measures.
Graph Neural Network for Phenotype Predictiontuxette
This document describes a study on using graph neural networks (GNNs) for phenotype prediction from gene expression data. The objectives are to determine if including network information can improve predictions, which network types work best, and if GNNs can learn network inferences. It provides background on GNNs and how they generalize convolutional layers to graph data. The authors implemented a GNN model from previous work as a starting point and tested it on different network types to see which network information is most useful for predictions. Their methodology involves comparing GNN performance to other methods like random forests using 10-fold cross validation.
A short and naive introduction to using network in prediction modelstuxette
The document provides an introduction to using network information in prediction models. It discusses representing a network as a graph with a Laplacian matrix. The Laplacian captures properties like random walks on the graph and heat diffusion. Eigenvectors of the Laplacian related to small eigenvalues are strongly tied to graph structure. The document discusses using the Laplacian in prediction models by working in the feature space defined by the Laplacian eigenvectors or directly regularizing a linear model with the Laplacian. This introduces network information and encourages similar contributions from connected nodes. The approaches are applied to problems like predicting phenotypes from gene expression using a known gene network.
Kernel methods and variable selection for exploratory analysis and multi-omic...tuxette
Nathalie Vialaneix
4th course on Computational Systems Biology of Cancer: Multi-omics and Machine Learning Approaches
International course, Curie training
https://training.institut-curie.org/courses/sysbiocancer2021
(remote)
September 29th, 2021
Kernel methods and variable selection for exploratory analysis and multi-omic...
Graphes, noyaux et cartes de Kohonen
1. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Journée FREMIT
Nathalie Villa-Vialaneix
Projet I(M+RI)T en collaboration avec T. Dkaki, J.M. Inglebert &
S. Gadat
Institut de Mathématiques de Toulouse, France -
nathalie.villa@math.univ-toulouse.fr
16 octobre 2007
Nathalie Villa FREMIT - 16 oct 07
2. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Sommaire
1 Les graphes
2 Classification de sommets, noyau et cartes de Kohonen
Laplacien
Noyau de la chaleur
Kernel SOM
3 Perspectives
Nathalie Villa FREMIT - 16 oct 07
3. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Sommaire
1 Les graphes
2 Classification de sommets, noyau et cartes de Kohonen
Laplacien
Noyau de la chaleur
Kernel SOM
3 Perspectives
Nathalie Villa FREMIT - 16 oct 07
4. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Graphes et réseaux sociaux (ANRT Graphes-Comp)
Graphe construit à partir d’un corpus d’archives médiévales
À partir de 1000 contrats agraires
(1250-1350), on construit un graphe pondéré :
sommets : les paysans trouvés dans les contrats ;
poids : nombre de contrats où deux paysans sont cités
simultanément.
Nathalie Villa FREMIT - 16 oct 07
5. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Graphes et réseaux sociaux (ANRT Graphes-Comp)
Graphe construit à partir d’un corpus d’archives médiévales
À partir de 1000 contrats agraires
(1250-1350), on construit un graphe pondéré :
sommets : les paysans trouvés dans les contrats ;
poids : nombre de contrats où deux paysans sont cités
simultanément.
Grand graphe :
Nombre de sommets : 615
Nombre d’arêtes : 4193
Somme des poids : 40 329
Diamètre : 10
Densité : 2,2%
Nathalie Villa FREMIT - 16 oct 07
6. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Autres domaines d’application
Web :
Nathalie Villa FREMIT - 16 oct 07
7. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Autres domaines d’application
Graphes de protéines :
Nathalie Villa FREMIT - 16 oct 07
8. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Problématique
Deux objectifs :
1 Trouver des sous-groupes homogènes (classification) ;
2 Représenter le graphe dans sa globalité, de manière lisible
(visualisation).
Nathalie Villa FREMIT - 16 oct 07
9. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Sommaire
1 Les graphes
2 Classification de sommets, noyau et cartes de Kohonen
Laplacien
Noyau de la chaleur
Kernel SOM
3 Perspectives
Nathalie Villa FREMIT - 16 oct 07
10. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Laplacien d’un graphe
Pour un graphe
de sommets V = {x1, . . . , xn}
pondérés par (wi,j)i,j=1,...,n (positifs) tels que, pour tout
i, j = 1, . . . , n, wi,j = wj,i et di = n
j=1 wi,j
on résume le graphe par son Laplacian, L = (Li,j)i,j=1,...,n :
Li,j =
−wi,j if i j
di if i = j
;
Nathalie Villa FREMIT - 16 oct 07
11. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Propriétés du Laplacien I [von Luxburg, 2007]
Composantes connexes
Le noyau de la matrice L est engendré par les indicatrices
IA1
, . . . , IAk
des sommets des k composantes connexes du graphe.
Nathalie Villa FREMIT - 16 oct 07
12. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Propriétés du Laplacien II [Villa et al., 2007]
Communauté parfaite : Sous-graphe complet (clique) dont tous
les sommets ont les mêmes voisins à l’extérieur de la clique.
Détermination de communautés parfaites
Les communautés parfaites d’un graphe non pondéré
correspondent à des groupes de m sommets pour lesquels il
existe m vecteurs propres ayant les mêmes coordonnées
nulles.
Nathalie Villa FREMIT - 16 oct 07
13. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Propriétés du Laplacien III [von Luxburg, 2007]
Problème de la coupe optimale
Supposons maintenant que notre graphe soit connexe.
Le problème (optimisation discrète) de trouver une partition du
graphe en k groupes de sommets, A1, . . . , Ak qui minimise
1
2
k
i=1 j∈Ai,j Ai
wj,j
est approché par le problème d’optimisation continue suivant
min
H∈Rn×k
Tr HT
LH subject to HT
H = I
Nathalie Villa FREMIT - 16 oct 07
14. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Spectral clustering
Méthode
1 Déterminer les k derniers vecteurs propres,
u1, . . . , uk de L et poser U = [u1, . . . , uk ] ;
2 Utiliser un algorithme de classification
(typiquement k-means) pour classer les lignes
de U en k groupes.
Nathalie Villa FREMIT - 16 oct 07
15. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Spectral clustering
Méthode
1 Déterminer les k derniers vecteurs propres,
u1, . . . , uk de L et poser U = [u1, . . . , uk ] ;
2 Utiliser un algorithme de classification
(typiquement k-means) pour classer les lignes
de U en k groupes.
Limites du spectral clustering
N’utilise pas la totalité du spectre de L
Ne tient pas compte du poids des vecteurs propres.
Nathalie Villa FREMIT - 16 oct 07
16. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Une version régularisée de L
Régularisation : la matrice de diffusion : pour β > 0,
Kβ = e−βL
= +∞
k=1
(−βL)k
k! .
⇒
kβ
: V × V → R
(xi, xj) → K
β
i,j
noyau de diffusion (ou noyau de la chaleur).
Nathalie Villa FREMIT - 16 oct 07
17. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Interprétation intuitive
kβ(i, j) peut être interprétée comme l’énergie accumulée en i
lorsque l’énergie a été injectée en j au temps 0 et que l’énergie
circule de manière continue dans les arêtes du graphe selon une
fraction qui dépend de β.
Nathalie Villa FREMIT - 16 oct 07
18. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Noyau de la chaleur et RKHS
Principe
Graphe → Espace de Hilbert de grande dimension
(H, ., . )
Dans (H, ., . ), pratiquer un algorithme de classification ou carte
de Kohonen (SOM).
Nathalie Villa FREMIT - 16 oct 07
19. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Resultats pour une grille 7 × 7
Nathalie Villa FREMIT - 16 oct 07
20. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Resultats pour une grille 7 × 7
Nathalie Villa FREMIT - 16 oct 07
21. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Laplacien
Noyau de la chaleur
Kernel SOM
Comparaison avec le « Spectral Clustering »
Nathalie Villa FREMIT - 16 oct 07
22. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Sommaire
1 Les graphes
2 Classification de sommets, noyau et cartes de Kohonen
Laplacien
Noyau de la chaleur
Kernel SOM
3 Perspectives
Nathalie Villa FREMIT - 16 oct 07
23. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Quelques pistes
1 Visualisation globale du graphe sur la carte
Nathalie Villa FREMIT - 16 oct 07
24. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Quelques pistes
1 Visualisation globale du graphe sur la carte
Nathalie Villa FREMIT - 16 oct 07
25. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Quelques pistes
1 Visualisation globale du graphe sur la carte
2 Généralisation de la méthode pour les graphes orientés, la
comparaison de graphes.
Nathalie Villa FREMIT - 16 oct 07
26. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Quelques pistes
1 Visualisation globale du graphe sur la carte
2 Généralisation de la méthode pour les graphes orientés, la
comparaison de graphes.
3 Travail sur les très grands graphes.
Nathalie Villa FREMIT - 16 oct 07
27. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
Quelques pistes
1 Visualisation globale du graphe sur la carte
2 Généralisation de la méthode pour les graphes orientés, la
comparaison de graphes.
3 Travail sur les très grands graphes.
4 Application en recherche d’informations, en confrontation
de connaissances.
Nathalie Villa FREMIT - 16 oct 07
28. Les graphes
Classification de sommets, noyau et cartes de Kohonen
Perspectives
References
References
Villa, N., Boulet, R., Rossi, F. & Jouve, B. (2007).
Batch kernel SOM and related Laplacian methods for graph
mining. Application to a medieval social network.
Neurocomputing.
To appear.
von Luxburg, U. (2007).
A tutorial on spectral clustering.
Technical Report TR-149, Max Planck Institut für biologische
Kybernetik.
Avaliable at http://www.kyb.mpg.de/publications/
attachments/luxburg06_TR_v2_4139%5B1%5D.pdf.
Nathalie Villa FREMIT - 16 oct 07