Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.Comment: 17 pages, 7 figures, submitted to IEEE Transactions on Signal Processin

Compressive Classification

This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain in multi-antenna communications. The diversity, which is shown to determine the rate at which the probability of misclassification decays in the low noise regime, is shown to depend on the geometry of the source, the geometry of the measurement system and their interplay. The measurement gain, which represents the counterpart of the coding gain, is also shown to depend on geometrical quantities. It is argued that the diversity order and the measurement gain also offer an optimization criterion to perform dictionary learning for compressive classification applications.Comment: 5 pages, 3 figures, submitted to the 2013 IEEE International Symposium on Information Theory (ISIT 2013

Détection et Reconnaissance des Gestes Emblématiques

Session "Atelier IHMA"National audienceDans cette contribution, nous présentons un système de reconnaissance en ligne de gestes emblématiques et son utilisation pour le contrôle d'un robot mobile. Ce système comporte quatre sous-systèmes : un premier qui permet de détecter la personne et d'extraire les mouvements de la partie supérieure de cette personne. Un second, permet d'isoler les mouvements, une troisième permet de reconnaître un des mouvements appris a priori. Enfin le dernier module, traduit les mouvements reconnus en termes de contrôle d'un robot mobile à roues. Dans notre approche, nous avons surtout traité du problème de la généralisation : faire l'apprentissage sur une base réduite de personnes et utiliser cette connaissance pour reconnaître n'importe quelle personne, indépendamment de sa morphologie, de son âge, de son sexe et de son positionnement par rapport au capteur. Nous détaillons les résultats obtenus pour la reconnaissance ainsi que l'utilisation du système dans des scenarios de contrôle d'un robot