Year: 2022
Author: Shih Yu Chang, Yimin Wei
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 1 : pp. 25–61
Abstract
Since Kilmer et al. introduced the new multiplication method between two third-order tensors around 2008 and third-order tensors with such multiplication structure are also called as T-product tensors, T-product tensors have been applied to many fields in science and engineering, such as low-rank tensor approximation, signal processing, image feature extraction, machine learning, computer vision, and the multi-view clustering problem, etc. However, there are very few works dedicated to exploring the behavior of random T-product tensors. This work considers the problem about the tail behavior of the unitarily invariant norm for the summation of random symmetric T-product tensors. Majorization and antisymmetric Kronecker product tools are main techniques utilized to establish inequalities for unitarily norms of multivariate T-product tensors. The Laplace transform method is integrated with these inequalities for unitarily norms of multivariate T-product tensors to provide us with Bernstein bound estimation of Ky Fan $k$-norm for functions of the symmetric random T-product tensors summation. Finally, we also apply T-product Bernstein inequality to bound Ky Fan norm of covariance T-product tensor induced by hypergraph signal processing.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2021-0012
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 1 : pp. 25–61
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: T-product tensors T-eigenvalues T-singular values Bernstein bound Courant-Fischer theorem for T-product tensors.
Author Details
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