A low-cost variational-Bayes technique for merging mixtures of probabilistic principal component analyzers

International audienceMixtures of probabilistic principal component analyzers (MPPCA) have shown effective for modeling high-dimensional data sets living on nonlinear manifolds. Briefly stated, they conduct mixture model estimation and dimensionality reduction through a single process. This paper makes two contributions: first, we disclose a Bayesian technique for estimating such mixture models. Then, assuming several MPPCA models are available, we address the problem of aggregating them into a single MPPCA model, which should be as parsimonious as possible. We disclose in detail how this can be achieved in a cost-effective way, without sampling nor access to data, but solely requiring mixture parameters. The proposed approach is based on a novel variational-Bayes scheme operating over model parameters. Numerous experimental results and discussion are provided

Interactive unsupervised classication and visualization for browsing an image collection

International audienceIn this paper, we propose an approach for interactive navigation in an image collection. As structured groups are more appealing to users than flat image collections, we propose an image clustering algorithm that can handle time-varying collections. A 3D graph-based visualization technique reflects the classification state. While this visualization is itself interactive, we show hos user feedback may assist the classification, thus enabling a user to improve it

Aggregation of probabilistic PCA mixtures with a variational-Bayes technique over parameters

International audienceThis paper proposes a solution to the problem of aggre- gating versatile probabilistic models, namely mixtures of probabilistic principal component analyzers. These models are a powerful generative form for capturing high-dimensional, non Gaussian, data. They simulta- neously perform mixture adjustment and dimensional- ity reduction. We demonstrate how such models may be advantageously aggregated by accessing mixture pa- rameters only, rather than original data. Aggregation is carried out through Bayesian estimation with a specific prior and an original variational scheme. Experimental results illustrate the effectiveness of the proposal

Parsimonious reduction of Gaussian mixture models with a variational-Bayes approach

International audienceAggregating statistical representations of classes is an important task for current trends in scaling up learning and recognition, or for addressing them in distributed in- frastructures. In this perspective, we address the problem of merging probabilistic Gaus- sian mixture models in an efficient way, through the search for a suitable combination of components from mixtures to be merged. We propose a new Bayesian modelling of this combination problem, in association to a variational estimation technique, that handles efficiently the model complexity issue. A main feature of the present scheme is that it merely resorts to the parameters of the original mixture, ensuring low computational cost and possibly communication, should we operate on a distributed system. Experimental results are reported on real dat

Component-level aggregation of probabilistic PCA mixtures using variational-Bayes

Technical Report. This report of an extended version of our ICPR'2010 paper.This paper proposes a technique for aggregating mixtures of probabilistic principal component analyzers, which are a powerful probabilistic generative model for coping with a high-dimensional, non linear, data set. Aggregation is carried out through Bayesian estimation with a specific prior and an original variational scheme. We demonstrate how such models may be aggregated by accessing model parameters only, rather than original data, which can be advantageous for learning from distributed data sets. Experimental results illustrate the effectiveness of the proposal

An Overview of Interaction Techniques and 3D Representations for Data Mining

International audienceAn Overview of Interaction Techniques and 3D Representations for Data Minin

Parsimonious variational-Bayes mixture aggregation with a Poisson prior

International audienceThis paper addresses merging of Gaussian mixture models, which answers growing needs in e.g. distributed pattern recognition. We propose a probabilistic model over the parameter set, that extends the weighted bipartite matching problem to our mixture aggregation task. We then derive a variational- Bayes associated estimation algorithm, that ensure low cost and parsimony, as confirmed by experimental results

Geo-temporal structuring of a personal image database with two-level variational-Bayes mixture estimation

International audienceThis paper addresses unsupervised hierarchical classication of personal documents tagged with time and geolocation stamps. The target application is browsing among these documents. A rst partition of the data is built, based on geo-temporal measurement. The events found are then grouped according to geolocation. This is carried out through tting a two-level hierarchy of mixture models to the data. Both mixtures are estimated in a Bayesian setting, with a variational proce- dure: the classical VBEM algorithm is applied for the ner level, while a new variational-Bayes-EM algorithm is introduced to search for suitable groups of mixture components from the ner level. Experimental results are reported on articial and real data

Sur l'analyse de réseaux de sociabilité de la société paysanne médiévale

National audienceL'histoire des sociétés rurales médiévales que nous connaissons a été construite à partir des traces qui nous sont parvenues, très souvent issues de la noblesse ou l'église de cette époque. De ce fait, le monde paysan, qui représente 90% de la population, est assez mal connu. L'étude d'une de ces sociétés, focalisée sur une zone géographique restreinte couverte par une documentation abondante, nous permet de reconstituer des réseaux de sociabilités. Nous analysons ces réseaux à l'aide d'outils de visualisation et nous montrons à la fois les changements structurels liés à des événements tels que les guerres et des analogies entre les graphes associés à ces réseaux et les graphes " petit monde "

Procédé et dispositif d'affichage de scène tridimensionnelle sur une surface d'affichage de forme arbitraire non plane

The invention relates to a method and to a device for displaying a three-dimensional scene on a display surface having an arbitrary non-planar shape, for correct viewing by a user having a given position in a three-dimensional spatial reference system. The method comprises displaying a display image comprising pixels which represent the three-dimensional scene. The invention comprises: a first step (A1) of projecting a three-dimensional model of the display surface onto a projection plane (PL) in perspective, the projection in perspective having a projection centre which is dependent on the position of the user in the spatial reference system, making it possible to obtain a projection image (Iproj) of the display surface from the point of view of the user; and a second step (A2) of calculating a projection of the three-dimensional scene on the display surface using said projection image (Iproj).L’invention concerne un procédé et un dispositif d’affichage de scène tridimensionnelle sur une surface d’affichage de forme arbitraire non plane, pour visualisation correcte par un utilisateur ayant une position donnée dans un référentiel spatial tridimensionnel. Le procédé comporte l’affichage d’une image d’affichage comportant des pixels représentatifs de la scène tridimensionnelle. Il comporte :- une première phase (A1) de projection en perspective d’un modèle tridimensionnel de la surface d’affichage sur un plan de projection (PL), la projection en perspective ayant un centre de projection dépendant de la position de l’utilisateur dans le référentiel spatial, permettant d’obtenir une image de projection (Iproj) de la surface d’affichage du point de vue de l’utilisateur,-une deuxième phase (A2) de calcul d’une projection de la scène tridimensionnelle sur la surface d’affichage utilisant ladite image de projection (Iproj)