Robust low rank canonical polyadic tensor decomposition

Xu Han

doi:10.1117/12.2671880

21 March 2023 Robust low rank canonical polyadic tensor decomposition

Xu Han

Proceedings Volume 12609, International Conference on Computer Application and Information Security (ICCAIS 2022); 126091H (2023) https://doi.org/10.1117/12.2671880
Event: International Conference on Computer Application and Information Security (ICCAIS 2022), 2022, ONLINE, ONLINE

Abstract

With the rapid development of information technique and equipment, the multi-dimensional data has been widely discussed and used in many domains. The Canonical Polyadic tensor Decomposition (CPD) is frequently employed for multi-dimensional data analysis, which has been extensively utilized in signal processing, image processing, computer vision, to name but a few. The satisfied accuracy and essential uniqueness of result computed by CPD can be guaranteed by using of exact rank value. However, the rank of the multi-dimensional data is usually unknown or is hard to obtain because of the noise disturbance in practice, thus the effectiveness of CPD is particularly weak with an inexact rank. To overcome this problem, this paper proposes a Robust CPD (R-CPD) method, which consists of two steps. The R-CPD firstly exploits the group sparsity of the over-estimated loading matrices to sense the real low rank and the group sparsity of the over-estimated loading matrices is pursued by adopting the mixed-norms, then the estimated rank can be used to compute CPD and thus obtain accurate results. Besides this paper provides the mathematical relationship on the mixednorms, nuclear norm (convex envelop of rank) and rank, and the corresponding mathematical proof to ensure the rationality of the proposed method. A series of experiments is implemented to assess the performance of the efficient RCPD method.

Citation Download Citation

Xu Han "Robust low rank canonical polyadic tensor decomposition", Proc. SPIE 12609, International Conference on Computer Application and Information Security (ICCAIS 2022), 126091H (21 March 2023); https://doi.org/10.1117/12.2671880

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KEYWORDS

Matrices

Signal to noise ratio

Autoregressive models

Data analysis

Error analysis

Monte Carlo methods

Image processing

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