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Tensor and Coupled Decompositions in Block Terms: Uniqueness and Irreducibility

Dana Lahat 1 Christian Jutten 2
1 IRIT-SC - Signal et Communications
IRIT - Institut de recherche en informatique de Toulouse
2 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
GIPSA-DIS - Département Images et Signal
Abstract : 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.
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Submitted on : Friday, December 6, 2019 - 3:18:57 PM
Last modification on : Wednesday, October 27, 2021 - 10:48:25 AM
Long-term archiving on: : Saturday, March 7, 2020 - 5:19:47 PM

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  • HAL Id : hal-02397453, version 1
  • OATAO : 25048
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Dana Lahat, Christian Jutten. Tensor and Coupled Decompositions in Block Terms: Uniqueness and Irreducibility. SPARS 2019 - Workshop on Signal Processing with Adaptive Sparse Structured Representations, Jul 2019, Toulouse, France. pp.0. ⟨hal-02397453⟩

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