Error preserving correction: A method for CP decomposition at a target error bound

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    9 Citations (Scopus)

    Abstract

    In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, especially, when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does not have an optimal solution. In such cases, norms of some rank-1 tensors become significantly large and cancel each other. This makes algorithms getting stuck in local minima while running a huge number of iterations does not improve the decomposition. In this paper, we propose an error preservation correction method to deal with such problem. Our aim is to seek an alternative tensor, which preserves the approximation error, but norms of rank-1 tensor components of the new tensor are minimized. Alternating and all-at-once correction algorithms have been developed for the problem. In addition, we propose a novel CPD with a bound constraint on the norm of the rank-one tensors. The method can be useful for decomposing tensors that cannot be performed by traditional algorithms. Finally, we demonstrate an application of the proposed method in image denoising and decomposition of the weight tensors in convolutional neural networks.

    Original languageEnglish
    Article number8579207
    Pages (from-to)1175-1190
    Number of pages16
    JournalIEEE Transactions on Signal Processing
    Volume67
    Issue number5
    DOIs
    Publication statusPublished - 1 Mar 2019

    Keywords

    • bounded CPD
    • Canonical polyadic decomposition (CPD)
    • degeneracy
    • PARAFAC
    • tensor decomposition for ill conditioned problems

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