2021/09/22 by Shih Yu Chang, Yimin Wei, Chang, Shih Yu +1 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2109.10880
openalex publication_date 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Bounds estimation of Ky Fan k-norm for functions of the symmetric random T-product tensors summation.