Tensor and Coupled Decompositions in Block Terms: Uniqueness and Irreducibility
Résumé
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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Lahat_Jutten_SPARS2019_poster.pdf (260.8 Ko)
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