Le développement de méthodes de décomposition de tableaux multi-dimensionnels suscite toujours autant d'attention, notamment d'un point de vue applicatif. La plupart des algorithmes, de décompositions tensorielles, existants requièrent une estimation du rang du tenseur et sont sensibles à une surestimation de ce dernier. Toutefois, une telle estimation peut être difficile par exemple pour des rapports signal à bruit faibles. D'un autre côté, estimer simultanément le rang et les matrices de facteurs du tenseur ou du tenseur cœur n'est pas tâche facile tant les problèmes de minimisation de rang sont généralement NP-difficiles. Plusieurs travaux existants proposent d'utiliser la norme nucléaire afin de servir d'enveloppe convexe de la fonction de rang. Cependant, la minimisation de la norme nucléaire engendre généralement un coût de calcul prohibitif pour l'analyse de données de grande taille. Dans cette thèse, nous nous sommes donc intéressés à l'approximation d'un tenseur bruité par un tenseur de rang faible. Plus précisément, nous avons étudié trois modèles de décomposition tensorielle, le modèle CPD (Canonical Polyadic Decomposition), le modèle BTD (Block Term Decomposition) et le modèle MTD (Multilinear Tensor Decomposition). Pour chacun de ces modèles, nous avons proposé une nouvelle méthode d'estimation de rang utilisant une métrique moins coûteuse exploitant la parcimonie de groupe. Ces méthodes de décomposition comportent toutes deux étapes : une étape d'estimation de rang, et une étape d'estimation des matrices de facteurs exploitant le rang estimé. Des simulations sur données simulées et sur données réelles montrent que nos méthodes présentent toutes une plus grande robustesse à la présence de bruit que les approches classiques. / Last decades, tensor decompositions have gained in popularity in several application domains. Most of the existing tensor decomposition methods require an estimating of the tensor rank in a preprocessing step to guarantee an outstanding decomposition results. Unfortunately, learning the exact rank of the tensor can be difficult in some particular cases, such as for low signal to noise ratio values. The objective of this thesis is to compute the best low-rank tensor approximation by a joint estimation of the rank and the loading matrices from the noisy tensor. Based on the low-rank property and an over estimation of the loading matrices or the core tensor, this joint estimation problem is solved by promoting group sparsity of over-estimated loading matrices and/or the core tensor. More particularly, three new methods are proposed to achieve efficient low rank estimation for three different tensors decomposition models, namely Canonical Polyadic Decomposition (CPD), Block Term Decomposition (BTD) and Multilinear Tensor Decomposition (MTD). All the proposed methods consist of two steps: the first step is designed to estimate the rank, and the second step uses the estimated rank to compute accurately the loading matrices. Numerical simulations with noisy tensor and results on real data the show effectiveness of the proposed methods compared to the state-of-the-art methods.

Group sparsity reveals underlying sparsity patterns and contains rich structural information in data. Hence, exploiting group sparsity will facilitate more efficient techniques for recovering large and complicated data in applications such as compressive sensing, statistics, signal and image processing, machine learning and computer vision. This thesis develops efficient algorithms for solving a class of optimization problems with group sparse solutions, where arbitrary group configurations are allowed and the mixed L21-regularization is used to promote group sparsity. Such optimization problems can be quite challenging to solve due to the mixed-norm structure and possible grouping irregularities. We derive algorithms based on a variable splitting strategy and the alternating direction methodology. Extensive numerical results are presented to demonstrate the efficiency, stability and robustness of these algorithms, in comparison with the previously known state-of-the-art algorithms. We also extend the existing global convergence theory to allow more generality.

No description available.

Recent years have witnessed an explosion of multimedia contents available. In 2010 the video sharing website YouTube announced that 35 hours of videos were uploaded on its site every minute, whereas in 2008 users were "only" uploading 12 hours of video per minute. Due to the growth of data volumes, human analysis of each video is no longer a solution; there is a need to develop automated video analysis systems. This thesis proposes a solution to automatically annotate video content with a textual description. The thesis core novelty is the consideration of multiple contextual information to perform the annotation. With the constant expansion of visual online collections, automatic video annotation has become a major problem in computer vision. It consists in detecting various objects (human, car. . . ), dynamic actions (running, driving. . . ) and scenes characteristics (indoor, outdoor. . . ) in unconstrained videos. Progress in this domain would impact a wild range of applications including video search, video intelligent surveillance or human-computer interaction.Although some improvements have been shown in concept annotation, it still remains an unsolved problem, notably because of the semantic gap. The semantic gap is defined as the lack of correspondences between video features and high-level human understanding. This gap is principally due to the concepts intra-variability caused by photometry change, objects deformation, objects motion, camera motion or viewpoint change... To tackle the semantic gap, we enrich the description of a video with multiple contextual information. Context is defined as "the set of circumstances in which an event occurs". Video appearance, motion or space-time distribution can be considered as contextual clues associated to a concept. We state that one context is not informative enough to discriminate a concept in a video. However, by considering several contexts at the same time, we can address the semantic gap. / Recent years have witnessed an explosion of multimedia contents available. In 2010the video sharing website YouTube announced that 35 hours of videos were uploadedon its site every minute, whereas in 2008 users were "only" uploading 12 hours ofvideo per minute. Due to the growth of data volumes, human analysis of each videois no longer a solution; there is a need to develop automated video analysis systems.This thesis proposes a solution to automatically annotate video content with atextual description. The thesis core novelty is the consideration of multiple contex-tual information to perform the annotation.With the constant expansion of visual online collections, automatic video annota-tion has become a major problem in computer vision. It consists in detecting variousobjects (human, car. . . ), dynamic actions (running, driving. . . ) and scenes charac-teristics (indoor, outdoor. . . ) in unconstrained videos. Progress in this domain wouldimpact a wild range of applications including video search, video intelligent surveil-lance or human-computer interaction.Although some improvements have been shown in concept annotation, it still re-mains an unsolved problem, notably because of the semantic gap. The semantic gapis defined as the lack of correspondences between video features and high-level humanunderstanding. This gap is principally due to the concepts intra-variability causedby photometry change, objects deformation, objects motion, camera motion or view-point change. . .To tackle the semantic gap, we enrich the description of a video with multiplecontextual information. Context is defined as "the set of circumstances in which anevent occurs". Video appearance, motion or space-time distribution can be consid-ered as contextual clues associated to a concept. We state that one context is notinformative enough to discriminate a concept in a video. However, by consideringseveral contexts at the same time, we can address the semantic gap.

No description available.

No description available.