# Sur le Web, ces 365 derniers jours

## lundi 11 novembre 2013

• OSCILLATIONS DANS DES ÉQUATIONS DE LIÉNARD ET DES ÉQUATIONS D'ÉVOLUTION SEMI-LINÉAIRES
Dans ce travail, on étudier, au voisinage d'un point d'équilibre, l'existence et l'unicité et la dépendance régulière des solutions presque-périodique (p.p.), présqu'automorphe (p.a.), asymptotiquement p.p., asymptotiquement p.a., pseudo p.p., pseudo p.a., pseudo p.p. avec poids, pseudo p.a. avec poids de la famille d'équations de Liénard forcée suivantes x''(t) + f(x(t), p). x'(t) + g(x(t), p) = ep(t), (1) où le terme ep est de la même nature que la solution, et p est un paramètre dans un espace de Banach. On utilise le théorème des fonctions implicites au voisinage de l'équilibre. On étudier aussi deux cas particuliers de la famille (1) qui sont x''(t) + f1(x(t)). x'(t) + g1(x(t))= e(t), x''(t) + f2(x(t), q). x'(t) + g2(x(t), q) = e(t). On établit aussi un nouveau résultat sur la dépendance différentielle des solutions S-asymptotiquement presque-périodique du problème de Cauchy x'(t)=A(t) x(t)+f(t, x(t),u(t) ) x(0) = ζ , par rapport à la condition initial et le contrôle u. On applique cet résultat sur une équation parabolique avec coefficients périodique par rapport au temps.

## lundi 28 octobre 2013

• Classification non supervisée d'un graphe de co-expression avec des méta-données pour la détection de micro-ARNs
Nous présentons dans cet article une méthode de classification non supervisée de sommets d'un graphe qui est utilisée dans un contexte biologique particulier. La problématique est de détecter de manière non supervisée des micro-ARNs probables. Pour ce faire, nous utilisons une approche multi-noyaux permettant d'intégrer des informations sur le graphe de co-expression et des informations supplémentaires sur les sommets de ce graphe. Cette approche est rendue robuste par une technique de bagging de classifications. Les résultats obtenus donnent des groupes de miRNAs potentiels dont certains permettent de discriminer avec une bonne confiance les vrais miRNAs des faux positifs.

## jeudi 24 octobre 2013

• Bayesian Model Averaging of Stochastic Block Models to Estimate the Graphon Function and Motif Frequencies in a W-graph Model
W-graph refers to a general class of random graph models that can be seen as a random graph limit. It is characterized by both its graphon function and its motif frequencies. The stochastic block model is a special case of W-graph where the graphon function is block-wise constant. In this paper, we propose a variational Bayes approach to estimate the W-graph as an average of stochastic block models with increasing number of blocks. We derive a variational Bayes algorithm and the corresponding variational weights for model averaging. In the same framework, we derive the variational posterior frequency of any motif. A simulation study and an illustration on a social network complete our work.

## vendredi 18 octobre 2013

• Graph-Based Approaches to Clustering Network-Constrained Trajectory Data
Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network and its influence on evaluating the similarity between trajectories. In this paper, we present an approach to clustering such network-constrained trajectory data. More precisely we aim at discovering groups of road segments that are often travelled by the same trajectories. To achieve this end, we model the interactions between segments w.r.t. their similarity as a weighted graph to which we apply a community detection algorithm to discover meaningful clusters. We showcase our proposition through experimental results obtained on synthetic datasets.

• Regularization in Relevance Learning Vector Quantization Using l one Norms
We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those spectral bands which are not necessary for classification. In particular, we consider the sparsity in the relevance profile enforced by LASSO optimization. The latter one is obtained by a gradient learning scheme using a differentiable parametrized approximation of the $l_{1}$-norm, which has an upper error bound. We extend this regularization idea also to the matrix learning variant of LVQ as the natural generalization of relevance learning.

## jeudi 17 octobre 2013

• Playing with Parameters: Cross-parameterization in Graphs
When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard"). A natural subject for investigation is what happens when we parameterize such a problem by the size of an optimal solution of a different problem. We provide a framework for doing such analysis. In particular, we investigate seven natural vertex problems, along with their respective parameters: α (the size of a maximum independent set), τ (the size of a minimum vertex cover), ω (the size of a maximum clique), χ (the chromatic number), γ (the size of a minimum dominating set), i (the size of a minimum independent dominating set) and ν (the size of a minimum feedback vertex set). We study the parameterized complexity of each of these problems with respect to the standard parameter of the others.

## mercredi 9 octobre 2013

• Metacognition: towards a new approach to quality of life.
PURPOSE: Recent studies have demonstrated that various diseases states (e.g., schizophrenia, Alzheimer's disease) and events (e.g., a stroke) alter a person's perception of their physical and mental status. Most often this involves alterations in a person's metacognitive capabilities, and this can question the conceptual model of quality of life (QoL) based on a "perspectivist" approach. METHODS: Using the example of schizophrenia, we applied a philosophical model, developed by Griffin, to deal with this potential threat to the validity of QoL assessment. RESULTS: Patients with schizophrenia are at risk for being impaired in their ability to assess their QoL. We hypothesise that metacognition (i.e., the ability to attribute mental states in terms of beliefs and goals to one's self and others) is a formal condition to assess QoL. This particular skill is important because self-reflection is necessary for making a qualitative judgment. A link between this psychological concept and the philosophical concept of reflexivity may be established. We propose a conceptual approach to QoL that takes into account the patient's reflexivity. This approach is derived from Griffin's theory based on the list of "prudential values" and the satisfaction of the informed desires of the individual. CONCLUSION: The ability of patients to evaluate and value their life should be considered to enrich the concept of QoL. The approach derived from Griffin's theory might constitute a new avenue for QoL research.

## vendredi 4 octobre 2013

• Existence and regularity of solution for a Stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion
The Cahn-Hilliard/Allen-Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms in the context of surface processes. For such an equation we consider a multiplicative space-time white noise with diffusion coefficient of sub-linear growth. Using technics from semigroup theory, we prove existence, and path regularity of stochastic solution depending on that of the initial condition. Our results are also valid for the stochastic Cahn-Hilliard equation with unbounded noise diffusion, for which previous results were established only in the framework of a bounded diffusion coefficient. We prove that the path regularity of stochastic solution depends on that of the initial condition, and are identical to those proved for the stochastic Cahn-Hilliard equation and a bounded noise diffusion coefficient. If the initial condition vanishes, they are strictly less than 2-d/2 in space and 1/2-d/8 in time. As expected from the theory of parabolic operators in the sense of Petrovski, the bi-Laplacian operator seems to be dominant in the combined model.

## mercredi 25 septembre 2013

• mu-Limit Sets of Cellular Automata from a Computational Complexity Perspective
This paper is about μ-limit sets of cellular automata, i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution, starting from an initial μ-random confi guration. More precisely, we investigate the computational complexity of these sets and of decision problems concerning them. Our main results are: fi rst, that such a set can have a Σ_3-hard language, second that it can contain only α-complex confi gurations and third that any non-trivial property concerning these sets is at least Π_3-hard. We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study di fferent types of (non-)convergence of the probability of appearance of a word in the evolution.

## dimanche 22 septembre 2013

• Splitting up method for the 2D stochastic Navier-Stokes equations
In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the Lie-Trotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given either with periodic boundary conditions. In particular, we prove that the strong speed of the convergence in probability is almost $1/2$. This is shown by means of an $L^2(\Omega,P)$ convergence localized on a set of arbitrary large probability. The assumptions on the diffusion coefficient depend on the fact that some multiple of the Laplace operator is present or not with the multiplicative stochastic term. Note that if one of the splitting steps only contains the stochastic integral, then the diffusion coefficient may not contain any gradient of the solution.

## lundi 16 septembre 2013

• Asymptotics for regression models under loss of identifiability
This paper discusses the asymptotic behavior of regression models under general conditions. First, we give a general inequality for the difference of the sum of square errors (SSE) of the estimated regression model and the SSE of the theoretical best regression function in our model. A set of generalized derivative functions is a key tool in deriving such inequality. Under suitable Donsker condition for this set, we give the asymptotic distribution for the difference of SSE. We show how to get this Donsker property for parametric models even if the parameters characterizing the best regression function are not unique. This result is applied to neural networks regression models with redundant hidden units when loss of identifiability occurs.

## lundi 26 août 2013

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

## mercredi 7 août 2013

• sexy-rgtk: a package for programming RGtk2 GUI in a user-friendly manner
There are many di erent ways to program Graphical User Interfaces (GUI) in R. (Lawrence and Verzani, 2012) provides an overview of the available methods, describing ways to program R GUI with RGtk2, qtbase and tcltk. More recently, the package shiny, for building interactive web applications, was also released (the rst version has been published on December, 2012). By automatically indexing all objects and methods available in RGtk2, we developed a method for creating GTK2-based GUI, in a friendlier and more compact manner. Widgets are accessible with simple functions and options, as is more natural for a R language programmer.

• SOMbrero : Cartes auto-organisatrices stochastiques pour l'intégration de données décrites par des tableaux de dissimilarités
Dans de nombreuses situations réelles, les individus sont décrits par des jeux de données multiples qui ne sont pas nécessairement de simples tableaux numériques mais peuvent être des données complexes (graphes, variables qualitatives, texte...). Un cas typique est celui des graphes étiquetés dans lequel les individus (les sommets du graphe) sont décrits à la fois par leurs relations les uns aux autres mais aussi par des attributs de natures diverses. Dans (Villa-Vialaneix et al, 2013 ; Olteanu et al , 2013), nous avons proposé d'utiliser des cartes auto-organisatrices (Kohonen, 2011) pour combiner classification et visualisation en projetant les individus étudiés sur une grille de faible dimension. Notre approche permet de traiter des données non numériques par le biais de noyaux ou de dissimilarités, et est basée sur une version stochastique de l'apprentissage de cartes auto-organisées. Les différentes dissimilarités sont combinées et la combinaison est optimisée au cours de l'apprentissage de la carte.

## mardi 4 juin 2013

• Estimation de la fonction graphon d'un W-graphe. Application au réseau de la blogosphere politique française
Networks have been widely used in many scientific fiels, and in particular in social sciences, in order to represent interactions between objects of interest. Since the earlier work of Moreno in 1934, many random graph models have been proposed to extract knowledge from these structured data sets. For instance, the stochastic block model (SBM) allows the search of groups of vertices sharing homogeneous connection profiles. In this work, we consider the W-graph model which is known to generalize many random graph models but for which very few methods exist to perform inference on real data. First, we recall that the SBM model can be represented as a W-graph with a block-constant graphon function. Using a variational Bayes expectation maximization algorithm, we then approximate the posterior distribution over the model parameters of a SBM model and we show how this variational approximation can be integrated in order to estimate the posterior distribution of W-graph graph function. In this Bayesian framework, we also derive the occurrence probability of a motif. In practice, this allows to test if a motif is over-represented in a given network. All the results presented here are tested on simulated data and the French political blogosphere network.

## dimanche 2 juin 2013

• Problèmes de convergence, optimisation d'algorithmes et analyse stochastique de systèmes de files d'attente avec rappels.
Pour optimiser la gestion des réseaux de télécommunication, nous considérons le système de file d'attente M^X / G / 1 avec rappels et clients impatients. En utilisant la méthode des variables supplémentaires, nous obtenons les fonctions génératrices partielles de l'état stationnaire conjointe de l'état du serveur et du nombre de clients dans le groupe de rappels. Pour compléter l'analyse du modèle considéré, nous calculons la distribution stationnaire de la chaîne de Markov induite, grâce à laquelle nous présentons la propriété de la décomposition stochastique. Cependant, la fonction génératrice de la distribution stationnaire du nombre de clients dans le groupe de rappels, est obtenue sous une forme explicite, très complexe et ne révèle pas la nature de la distribution en question. Alors, nous étudions le comportement asymptotique de la variable aléatoire représentant le nombre de clients en orbite et dans le système pour des valeurs limites des différents paramètres. Nous complétons notre travail par des exemples numériques.

## samedi 25 mai 2013

• Bayesian non parametric inference of discrete valued networks
We present a non parametric bayesian inference strategy to automatically infer the number of classes during the clustering process of a discrete valued random network. Our methodology is related to the Dirichlet process mixture models and inference is performed using a Blocked Gibbs sampling procedure. Using simulated data, we show that our approach improves over competitive variational inference clustering methods.

## vendredi 26 avril 2013

• Asymptotic behavior of compositions of under-relaxed nonexpansive operators
In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.

## jeudi 25 avril 2013

• Weak error in negative Sobolev spaces for the stochastic heat equation
In this paper, we make another step in the study of weak error of the stochastic heat equation by considering norms as functional.

• Weak error expansion of the implicit Euler scheme
In this paper, we extend the Talay Tubaro theorem to the implicit Euler scheme.

• Multiple kernel self-organizing maps
In 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.

## mercredi 13 mars 2013

• Model selection and clustering in stochastic block models with the exact integrated complete data likelihood
The stochastic block model (SBM) is a mixture model used for the clustering of nodes in networks. It has now been employed for more than a decade to analyze very different types of networks in many scientific fields such as Biology and social sciences. Because of conditional dependency, there is no analytical expression for the posterior distribution over the latent variables, given the data and model parameters. Therefore, approximation strategies, based on variational techniques or sampling, have been proposed for clustering. Moreover, two SBM model selection criteria exist for the estimation of the number K of clusters in networks but, again, both of them rely on some approximations. In this paper, we show how an analytical expression can be derived for the integrated complete data log likelihood. We then propose an inference algorithm to maximize this exact quantity. This strategy enables the clustering of nodes as well as the estimation of the number clusters to be performed at the same time and no model selection criterion has to be computed for various values of K. The algorithm we propose has a better computational cost than existing inference techniques for SBM and can be employed to analyze large networks with ten thousand nodes. Using toy and true data sets, we compare our work with other approaches.

## samedi 2 mars 2013

• Cartographie de la Chronique d'Henri de Livonie
The Livonian Chronicle of Henry is the oldest written document about the History of the eastern baltic shores. We try to apply statistical and algorithmical methods on toponimic and chronological data from this chronicle, in order to build static and dynamic maps. With this study we hope to gain some historical insight into both the redaction of the chronicle itself and the events it describes.

## mardi 26 février 2013

• Semi-periodic solutions of difference and differential equations
The spaces of semi-periodic sequences and functions are examined in the relationship to the closely related notions of almost-periodicity, quasi-periodicity and periodicity. Besides the main theorems, several illustrative examples of this type are supplied. As an application, the existence and uniqueness results are formulated for semi-periodic solutions of quasi-linear difference and differential equations.

• S-asymptotically ω-periodic functions and applications to evolution equations.
• Problèmes économétriques d'analyse des séries temporelles à mémoire longue
Les modalités d'investigation de notre thèse sont menées, sous trois angles : épistémologique, statistique et économique. En première partie de la thèse, dans une approche épistémologique, nous spécifions en quoi le concept de mémoire longue peut apparaître, comme un nouveau paradigme kühnien pour la macroéconomie et la finance. En deuxième partie de la thèse, dans une approche statistique, semi-paramétrique, nous proposons trois extensions de la statistique IR (Increment Ratio) de Surgailis et al, (2008). Premièrement, un théorème central limite multidimensionnelle est établi pour un vecteur composé de plusieurs statistiques IR. Deuxièmement, un test d'adéquation de qualité d'ajustement de type chi2 est déduit de ce théorème. Troisièmement, ce théorème nous a permis de construire des versions adaptatives de l'estimateur et du test d'adéquation étudiés dans un cadre semi-paramétrique général. Nous prouvons que l'estimateur adaptatif du paramètre de la mémoire longue suit une propriété d'Oracle. Les simulations que nous avons menées attestent de la précision et de la robustesse de l'estimateur et du test d'adéquation, même dans le cas non gaussien. En troisième partie de la thèse, nous en déduisons deux tests respectivement de stationnarité et de non stationnarité pour les processus I(d) stationnaires et non stationnaires, pour tout réel d tel que (-0.5< d<1.25). Dans une approche économique, au sein de cette troisième partie de la thèse, nous mettons en oeuvre les résultats théoriques précédents comparés à ceux issus d'autres méthodes statistiques: paramétriques, semi-paramétriques ou non paramétriques (ou heuristiques) appliquées à des séries économiques et financières.

## samedi 23 février 2013

• Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process
The purpose of this paper is to estimate the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.

• Étude des corrélations spatio-temporelles des appels mobiles en France
Nous proposons dans cet article de présenter une application d'analyse d'une base de données de grande taille issue du secteur des télécommunications. Le problème consiste à segmenter un territoire et caractériser les zones ainsi définies grâce au comportement des habitants en terme de téléphonie mobile. Nous disposons pour cela d'un réseau d'appels inter-antennes construit pendant une période de cinq mois sur l'ensemble de la France. Nous proposons une analyse en deux phases. La première couple les antennes émettrices dont les appels sont similairement distribués sur les antennes réceptrices et vice versa. Une projection de ces groupes d'antennes sur une carte de France permet une visualisation des corrélations entre la géographie du territoire et le comportement de ses habitants en terme de téléphonie. La seconde phase découpe l'année en périodes entre lesquelles on observe un changement de distributions d'appels sortant des groupes d'antennes. On peut ainsi caractériser l'évolution temporelle du comportement des usagers de mobiles dans chacune des zones du pays.

• Classifications croisées de données de trajectoires contraintes
Le clustering (ou classification non supervisée) de trajectoires a fait l'objet d'un nombre considérable de travaux de recherche. La majorité de ces travaux s'est intéressée au cas où les objets mobiles engendrant ces trajectoires se déplacent librement dans un espace euclidien et ne prennent pas en compte les contraintes liées à la structure sous-jacente du réseau qu'ils parcourent (ex. réseau routier). Dans le présent article, nous proposons au contraire la prise en compte explicite de ces contraintes. Nous représenterons les relations entre trajectoires et segments routiers par un graphe biparti et nous étudierons la classification de ses sommets. Nous illustrerons, sur un jeu de données synthétiques, l'utilité d'une telle étude pour comprendre la dynamique du mouvement dans le réseau routier et analyser le comportement des véhicules qui l'empruntent.

## jeudi 21 février 2013

• A test for parameter change in general causal time series using quasi-likelihood estimator
In this paper, we propose a new procedure to test a change in the parameter of a process $X= (X_t)_{t\in \Z}$ belonging to a class of causal models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models. Two statistics $\widehat{Q}^{(1)}_n$ and $\widehat{Q}^{(2)}_n$ are constructed using the quasi-likelihood estimator (QMLE) of the parameter. Under the null hypothesis that there is no change, each of these statistics converges weakly to a well-known distribution and the maximum diverges to infinity under the alternative of one change. Some simulation results are reported.

## vendredi 15 février 2013

• Illustration par quelques exemples des lois strictement stables dans un cône convexe
The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach spaces. Some examples of strictly stable distributions and max-stable distributions are presented in this paper in order to exhibit the relationship between the Poisson process and the stable distributions on convex cones.

## vendredi 1er février 2013

• Carte auto-organisatrice pour graphes étiquetés.
Dans 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.

## vendredi 11 janvier 2013

• A Triclustering Approach for Time Evolving Graphs
This paper introduces a novel technique to track structures in time evolving graphs. The method is based on a parameter free approach for three-dimensional co-clustering of the source vertices, the target vertices and the time. All these features are simultaneously segmented in order to build time segments and clusters of vertices whose edge distributions are similar and evolve in the same way over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make an a priori discretization. Experiments conducted on a synthetic dataset illustrate the good behaviour of the technique, and a study of a real-life dataset shows the potential of the proposed approach for exploratory data analysis.

## jeudi 3 janvier 2013

• A Schelling model with switching agents: decreasing segregation via random allocation and social mobility
We study the behaviour of a Schelling-class system in which a fraction~$f$ of spatially-fixed switching agents is introduced. This new model allows for multiple interpretations, including: (i) random, non-preferential allocation (\textit{e.g.} by housing associations) of given, fixed sites in an open residential system, and (ii) superimposition of social and spatial mobility in a closed residential system. We find that the presence of switching agents in a segregative Schelling-type dynamics can lead to the emergence of intermediate patterns (\textit{e.g.} mixture of patches, fuzzy interfaces) as the ones described in~\cite{HaBe}. We also investigate different transitions between segregated and mixed phases both at $f=0$ and along lines of increasing $f$, where the nature of the transition changes.

## mercredi 26 décembre 2012

• On-line relational SOM for dissimilarity data
In 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.

## vendredi 7 décembre 2012

• Spatial Statistics and Modeling
Les modèles et les méthodes statistiques pour les principaux modèles spatiaux, second ordre, géostatistiques, champs markoviens et processus spatiaux. En s'appuyant sur R, de nombreux exemples illustrent ces méthodes.

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