Neural Networks for Complex Data

Artificial neural networks are simple and efficient machine learning tools. Defined originally in the traditional setting of simple vector data, neural network models have evolved to address more and more difficulties of complex real world problems, ranging from time evolving data to sophisticated data structures such as graphs and functions. This paper summarizes advances on those themes from the last decade, with a focus on results obtained by members of the SAMM team of Universit\'e Paris

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are. This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discusses the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications

Multiple kernel self-organizing maps

International audienceIn a number of real-life applications, the user is interested in analyzing several sources of information together: a graph combined with the additional information known on its nodes, numerical variables measured on individuals and factors describing these individuals... The combination of all sources of information can help him to understand the dataset in its whole better. The present article focuses on such an issue, by using self-organizing maps. The use a kernel version of the algorithm allows us to combine various types of information and automatically tune the data combination. This approach is illustrated on a simulated example

On-line relational SOM for dissimilarity data

International audienceIn some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this framework. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual combination of all elements in the data set. However, this latter approach suffers from two main drawbacks. First, its complexity can be large. Second, only a batch version of this algorithm has been studied so far and it often provides results having a bad topographic organization. In this article, an on-line version of relational SOM is described and justified. The algorithm is tested on several datasets, including categorical data and graphs, and compared with the batch version and with other SOM algorithms for non vector data

Batch kernel SOM and related Laplacian methods for social network analysis

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts

Carte auto-organisatrice pour graphes étiquetés.

National audienceDans de nombreux cas d'études concrets, l'analyse de données sur les graphes n'est pas limitée à la seule connaissance du graphe. Il est courant que des informations supplémentaires soient disponibles sur les sommets et que l'utilisateur souhaite combiner ces informations à la structure du graphe lui-même pour comprendre l'intégralité des données en sa possession. C'est ce problème que nous souhaitons aborder dans cet article, en nous focalisant sur une méthode de fouille de données qui combine classification (non supervisée) et visualisation : les cartes auto-organisatrices. Nous expliquons comment l'utilisation de méthodes à noyaux permet de combiner de manière efficace des informations de natures diverses (graphe, variables numériques, facteurs, variables textuelles...) pour décortiquer la structure des données et en offrir une représentation simplifiée. Notre approche est illustrée sur divers exemples : un premier exemple, sur des données simulées, permet de comprendre comment se comporte l'algorithme. Un second exemple illustre la méthode sur un graphe réel de plusieurs centaines de sommets, qui modélise un corpus de documents médiévaux

A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved

Which dissimilarity is to be used when extracting typologies in sequence analysis? A comparative study

International audienceOriginally developed in bioinformatics, sequence analysis is being increasingly used in social sciences for the study of life-course processes. The methodology generally employed consists in computing dissimilarities between the trajectories and, if typologies are sought, in clustering the trajectories according to their similarities or dissemblances. The choice of an appropriate dissimilarity measure is a major issue when dealing with sequence analysis for life sequences. Several dissimilarities are available in the literature, but neither of them succeeds to become indisputable. In this paper, instead of deciding upon one dissimilarity measure, we propose to use an optimal convex combination of different dissimilarities. The optimality is automatically determined by the clustering procedure and is defined with respect to the within-class variance