In FrenchDecember 18th: Séminaire de statistique et applications, Institut de Mathématiques de Luminy, Marseille, Fouille de données pour des grands graphes.
La recherche de groupes de sommets d'un grand graphe fortement liés et
l'étude des relations existant entre ces groupes est une thématique
d'intérêt dans plusieurs domaines applicatifs : réseaux sociaux, réseaux
biologiques, recherche d'information, etc. Dans cette optique, nous
présenterons des méthodes d'organisation de sommets sur des cartes de
faibles dimensions. Ces méthodes sont soit des adaptations d'algorithmes
de cartes auto-organisatrices à des données non vectorielles par le
biais de noyaux, soit des algorithmes stochastiques ou déterministes de
recuit conduisant à l'optimisation d'un critère de qualité de
l'organisation du graphe. Nous illustrerons notre propos sur des réseaux
sociaux réels.
In FrenchDecember 8th: Journées FREMIT, Toulouse, Fouille de données pour de grands graphes. Recherche de communautés et organisation.
September 15th: CENATAV, Havana, Cuba, Short courses on functional data analysis and statistical learning. Part 1: Introduction to FDA and linear models.
This first presentation first introduces Functional Data Analysis
(FDA) on a practical point of view (which kind of data/problems are
concerned by this field ?) and on a theoretical point of view (how
can we modelize it and what are the issues of this model ?). Then,
we present in details two linear tools that have been adapted to FDA
: the PCA and the linear regression model. Several methodologies
have been proposed and theoretically studied to answer these two
problems in the functional context, including dimension reduction and
smoothing. A review of these methods will be made, giving an overview
of the first common practices in FDA.
September 16th: CENATAV, Havana, Cuba, Short courses on functional data analysis and statistical learning. Part 2: Several nonlinear models and methods for FDA.
This second presentation gives an overview of several nonlinear
methods for FDA. The first one is a nonparametric method, the
nonparametric regression kernel. After introducing its spirit in
the multidimensional context, we show how it has been adapted to
functional data, either in the regression and in the classification
context and we present several results on its performances. Then,
we focus on neural networks (multilayer perceptrons) that have
become a popular tools the past years. Also, we give an overview
of the practical and theoretical aspects of this tool in the
functional context. Finally, we will introduce a semiparametric
model, namely the Functional Inverse Regression. We present several
versions of this model and provide a presentation of its links with
the Factorial Discriminant Analysis. Finally, an application to the
use of neural networks in the functional context is developped.
September 17th: CENATAV, Havana, Cuba, Short courses on functional data analysis and statistical learning. Part 3: FDA and Statistical learning theory.
This third presentation focuses on the main points of statistical
learning theory. After giving a simple presentation of several
aspects of this theory, we introduce SVM tools in the multidimensional
context and develop several results about this model. Then a first
generalization of a consistency result to the functional context is
presented for the k-nearest neighbors method. We then show how this
can be applied also to SVM and, more generally, how SVM can be used to
classify curves by defining relevant kernels.
September 18th: CENATAV, Havana, Cuba, Short courses on functional data analysis and statistical learning. Part 4: Influence of the sampling on Functional Data Analysis.
This last presentation will provide several results about the
problem of a partial information about the curves due to the
fact that, in applications, only a discrete sampling of the
curves is known. First, are presented several methods for
estimating the true observed curves and among others, a focus
on splines approaches and Sobolev spaces is given. Then, a
general method to define consistent classifiers or regression
function is presented, providing the fact that only a discrete
sampling of the data is known. Finally, this method (still
under development) is presented for SVM and several open
questions related to it are also reviewed.
In FrenchMarch 21st: Séminaire de l’unité BIA, INRA, Toulouse, Fouille de données issues d’un grand graphe par carte de Kohonen à noyau.
La recherche de groupes de sommets d'un grand graphe fortement
liés et l'étude des relations existant entre ces groupes est une
thématique d'intérêt dans plusieurs domaines applicatifs : réseaux
sociaux, réseaux biologiques, recherche d'information, etc. Dans
ce but, nous avons proposé une méthode de type "carte de Kohonen"
adapté à des données non vectorielles, de type graphe, par
l'utilisation d'un noyau construit à partir du Laplacien du graphe.
Cette méthode a été utilisée pour l'étude d'un réseau social réel
issu d'archives médiévales.
February, 1st: Rencontres BoSanTouVal, Universidad de Valladolid, Spain, Graph mining with kernel self-organizing map.
Plusieurs modifications de l'algorithme de cartes auto-organisatrices
permettent de s'intéresser à des données non vectorielles. Récemment,
nous avons introduit une version par noyau qui s'adapte à un très
grand nombre de types de données. Nous montrerons comment cette version
est reliée aux précédentes modifications du SOM et nous illustrerons
son utilisation par une application à la classification de sommets de
graphes.
