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Tensor and Coupled Decompositions in Block Terms: Uniqueness and Irreducibility

Lahat, Dana and Jutten, Christian Tensor and Coupled Decompositions in Block Terms: Uniqueness and Irreducibility. (2019) In: Workshop on Signal Processing with Adaptative Sparse Structured Representations (SPARS 2019), 1 July 2019 - 4 July 2019 (Toulouse, France).

(Document in English)

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In this work, we present recent results concerning decompositions of tensors and ensembles of matrices in sum of terms that are not necessarily rank-1. We formulate mathematically the concept of irreducibility, which is the enabling factor that allows these low-rank terms to exist as “blocks” without being further factorized into terms of smaller rank. We first demonstrate these results on tensors. Next, we generalize our results to a coupled factorization of several matrices that cannot be written as a single tensor. This coupled factorization is inspired by data fusion, and generalizes independent component analysis in several directions.

Item Type:Conference or Workshop Item (Paper)
HAL Id:hal-02397453
Audience (conference):National conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Institut polytechnique de Grenoble (FRANCE)
Other partners > Université Grenoble Alpes - UGA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
ERC : European Research Council (Europe) - ANR : Agence nationale de la recherche (France)
Deposited On:28 Nov 2019 11:23

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