Under-Determined tensor diagonalization for decomposition of difficult tensors

Petr Tichavský, Anh Huy Phan, Andrzej Cichocki

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    Analysis of multidimensional arrays, usually called tensors, often becomes difficult in cases when the tensor rank (a minimum number of rank-one components) exceeds all the tensor dimensions. Traditional methods of canonical polyadic decomposition of such tensors, namely the alternating least squares, can be used, but a presence of a large number of false local minima can make the problem hard. Usually, multiple random initializations are advised in such cases, but the question is how many such random initializations are sufficient to get a good chance of finding the right solution. It appears that the number of the initializations can be very large. We propose a novel approach to the problem. The given tensor is augmented by some unknown parameters to the shape that admits ordinary tensor diagonalization, i.e., transforming the augmented tensor into an exact or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices. Three possible constraints are proposed to make the optimization problem well defined. The method can be modified for an under-determined block-term decomposition.

    Original languageEnglish
    Title of host publication2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages1-4
    Number of pages4
    ISBN (Electronic)9781538612514
    DOIs
    Publication statusPublished - 9 Mar 2018
    Event7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017 - Curacao
    Duration: 10 Dec 201713 Dec 2017

    Publication series

    Name2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017
    Volume2017-December

    Conference

    Conference7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017
    CityCuracao
    Period10/12/1713/12/17

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