Fast randomized algorithms for computing the generalized tensor SVD based on the tubal product

2023/05/08 by Salman Ahmadi‐Asl, Ahmadi-Asl, Salman, Ugochukwu O. Ugwu +1
Computer Science · Mathematics · #Advanced Neural Network Applications #Computational Physics and Python Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2305.05031

openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the important actions of the underlying data tensors and use them to get small sketches of the original data tensors, which are easier to be handled. Due to the small size of the sketch tensors, deterministic approaches are applied to them to compute their GTSVDs. Then, from the GTSVD of the small sketch tensors, the GTSVD of the original large-scale data tensors is recovered. Some experiments are conducted to show the effectiveness of the proposed approach.

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