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Séminaire MIDI : Yassine Zniyed

Titre du séminaire et orateur

Joint dimensionality reduction and factor retrieval.

Yassine Zniyed, Postdoctorant CRAN, Université de Lorraine

Date et lieu

Vendredi 15 mai 2020, 9h.

Par visioconférence

Résumé

In the context of the big data problem, the growing number, denoted here by D, of the available sensing technologies produces a large amount of heterogeneous measurements. Analyzing independently each collected data set is clearly a suboptimal strategy because potential hidden "data correlations" are simply ignored. The challenge here is to consider a sufficiently rich and flexible representation adapted to accurately modelize the problem of interest. The multilinear algebra of tensors is a powerful mathematical framework able to reach this goal. In many practical contexts, D is large. High-order tensor decompositions have to face a new challenge in terms of storage cost and algorithmic stability. In this talk, some new equivalence results between the usual tensor model, namely CPD/PARAFAC, and the Tensor Train decomposition are presented. These results will allow to break the "curse of dimensionality" by reformulating a high-order tensor as a set of low-order tensors, called cores or nodes into the graph-based formalism.

Splitting the initial multidimensional optimization problem into a sum of low dimensionality optimization problems for each node of the graph has at least two advantages. Firstly, ill-converging problems for high dimensional optimization are considerably mitigated. Secondly, thanks to the graph-based formalism, some lattent coupling properties between the nodes of the graph can be revealed. As a consequence, new optimization strategies taking the coupling relations into account can be designed allowing to propose the new estimation scheme called JIRAFE for Joint dImensionality Reduction And Factor rEtrieval. Some realistic applications of this methodological work, such as the multidimensional spectral analysis, are also presented.

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