@Article{AAM-38-25,
author = {Chang , Shih Yu and Wei , Yimin},
title = {Generalized T-Product Tensor Bernstein Bounds},
journal = {Annals of Applied Mathematics},
year = {2022},
volume = {38},
number = {1},
pages = {25--61},
abstract = {<p style="text-align: justify;">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&nbsp; apply T-product Bernstein inequality to bound Ky Fan norm of covariance T-product tensor induced by hypergraph signal processing.</p>},
issn = {},
doi = {https://doi.org/10.4208/aam.OA-2021-0012},
url = {http://global-sci.org/intro/article_detail/aam/20172.html}
}