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Contribution à la décomposition de données multimodales avec des applications en apprentisage de dictionnaires et la décomposition de tenseurs de grande taille.

Abstract : In this work, we are interested in special mathematical tools called tensors, that are multidimensional arrays defined on tensor product of some vector spaces, each of which has its own coordinate system and the number of spaces involved in this product is generally referred to as order. The interest for these tools stem from some empirical works (for a range of applications encompassing both classification and regression) that prove the superiority of tensor processing with respect to matrix decomposition techniques. In this thesis framework, we focused on specific tensor model named Tucker and established new approaches for miscellaneous tasks such as dictionary learning, online dictionary learning, large-scale processing as well as the decomposition of a tensor evolving with respect to each of its modes. New theoretical results are established and the efficiency of the different algorithms, which are based either on alternate minimization or coordinate gradient descent, is proven via real-world problems.
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Abraham Traoré. Contribution à la décomposition de données multimodales avec des applications en apprentisage de dictionnaires et la décomposition de tenseurs de grande taille.. Apprentissage [cs.LG]. Normandie Université, 2019. Français. ⟨NNT : 2019NORMR068⟩. ⟨tel-02415573⟩

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