Generalized T-Product Tensor BernsteinBounds

作     者：Shih Yu Chang Yimin Wei 

作者机构：Department of Applied Data ScienceSan Jose State UniversitySan JoseCA 95192USA School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied MathematicsFudan UniversityShanghai 200433China 

出 版 物：《Annals of Applied Mathematics》 (应用数学年刊（英文版）)

年 卷 期：2022年第38卷第1期

页      面：25-61页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Innovation Program of Shanghai Municipal Education Commission the National Natural Science Foundation of China under grant No.11771099 

主　　题：T-product tensors T-eigenvalues T-singular values Bernstein bound Courant-Fischer theorem for T.product tensors. 

摘      要：Since Kilmer et *** 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,***,there are very few works dedicated to exploring the behavior of random T-product *** work considers the problem about the tail behavior of the unitarily invariant norm for the summation of random symmetric T-product *** and antisymmetric Kronecker product tools are main techniques utilized to establish inequalities for unitarily norms of multivariate T-product *** 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 ***,we also apply T-product Bernstein inequality to bound Ky Fan norm of covariance T-product tensor induced by hypergraph signal processing.