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Conference Papers Year : 2019

Tensor and Coupled Decompositions in Block Terms: Uniqueness and Irreducibility

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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Dates and versions

hal-02397453 , version 1 (06-12-2019)

Identifiers

  • HAL Id : hal-02397453 , version 1
  • OATAO : 25048

Cite

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. ⟨hal-02397453⟩
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