A Novel Non-Iterative Algorithm for Low-Multilinear-Rank Tensor Approximation

José Henrique de Morais Goulart 1 Pierre Comon 1
1 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
Abstract : Low-rank tensor approximation algorithms are building blocks in tensor methods for signal processing. In particular, approximations of low multilinear rank (mrank) are of central importance in tensor subspace analysis. This paper proposes a novel non-iterative algorithm for computing a low-mrank approximation, termed sequential low-rank approximation and projection (SeLRAP). Our algorithm generalizes sequential rank-one approximation and projection (SeROAP), which aims at the rank-one case. For third-order mrank-(1,R,R) approximations, SeLRAP's outputs are always at least as accurate as those of previously proposed methods. Our simulation results suggest that this is actually the case for the overwhelmingly majority of random third- and fourth-order tensors and several different mranks. Though the accuracy improvement is often small, we show it can make a large difference when repeatedly computing approximations, as happens, e.g., in an iterative hard thresholding algorithm for tensor completion.
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Communication dans un congrès
25th European Signal Conference (EUSIPCO), Aug 2017, Kos, Greece. Proceedings of the 25th European Signal Conference (EUSIPCO)
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https://hal.archives-ouvertes.fr/hal-01531231
Contributeur : José Henrique De Morais Goulart <>
Soumis le : jeudi 1 juin 2017 - 13:39:54
Dernière modification le : jeudi 22 juin 2017 - 14:34:35

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José Henrique de Morais Goulart, Pierre Comon. A Novel Non-Iterative Algorithm for Low-Multilinear-Rank Tensor Approximation. 25th European Signal Conference (EUSIPCO), Aug 2017, Kos, Greece. Proceedings of the 25th European Signal Conference (EUSIPCO). <hal-01531231>

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