Non-orthogonal tensor diagonalization

Petr Tichavský, Anh Huy Phan, Andrzej Cichocki

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    Abstract

    Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It has a link to an approximate joint diagonalization (AJD) of a set of matrices. In this paper, we derive (1) a new algorithm for a symmetric AJD, which is called two-sided symmetric diagonalization of an order-three tensor, (2) a similar algorithm for a non-symmetric AJD, also called a two-sided diagonalization of an order-three tensor, and (3) an algorithm for three-sided diagonalization of order-three or order-four tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and in certain scenarios they can outperform traditional CP decomposition methods. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to tensor block-term decomposition. The proposed algorithm can either outperform the existing block-term decomposition algorithms, or produce good initial points for their application.

    Original languageEnglish
    Pages (from-to)313-320
    Number of pages8
    JournalSignal Processing
    Volume138
    DOIs
    Publication statusPublished - 1 Sep 2017

    Keywords

    • Block-term decomposition
    • Canonical polyadic decomposition
    • Joint matrix diagonalization
    • Multilinear models
    • Parallel factor analysis

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