T-Singular Values and T-Sketching for Third Order Tensors

2021/03/01 by Liqun Qi, Gaohang Yu, Qi, Liqun +1 · 2 citations
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2103.00976

openalex publication_date 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based upon the T-SVD (tensor SVD) of third order tensors, introduced by Kilmer and her collaborators, we define T-singular values of third order tensors. T-singular values of third order tensors are nonnegative scalars. The number of nonzero T-singular values is the tensor tubal rank of the tensor. We then use T-singular values to define the tail energy of a third order tensor, and apply it to the error estimation of a tensor sketching algorithm for low rank tensor approximation. Numerical experiments on real world data show that our algorithm is efficient.

Citations

• Fast and Guaranteed Tensor Decomposition via Sketching
• Factorization strategies for third-order tensors

Cited by

• T-product Tensor Expander Chernoff Bound
• T product Tensors Part I: Inequalities

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