Randomized Algorithms for Computing the Generalized Tensor SVD Based on the Tensor Product

doi:10.1007/s42967-024-00461-3

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (2): 605-621.doi: 10.1007/s42967-024-00461-3

Randomized Algorithms for Computing the Generalized Tensor SVD Based on the Tensor Product

Salman Ahmadi-Asl^1,2, Naeim Rezaeian², Ugochukwu O. Ugwu³

1. Lab of Machine Learning and Knowledge Representation, Innopolis University, Innopolis, 420500, Russia;
2. Peoples' Friendship University of Russia, Moscow, 125009, Russia;
3. Department of Mathematics, Colorado State University, Fort Collins, USA

收稿日期:2024-02-10 修回日期:2024-07-19 出版日期:2026-04-07 发布日期:2026-04-07
通讯作者: Salman Ahmadi-Asl,E-mail:salman.ahmadiasl@gmail.com E-mail:salman.ahmadiasl@gmail.com

Randomized Algorithms for Computing the Generalized Tensor SVD Based on the Tensor Product

Salman Ahmadi-Asl^1,2, Naeim Rezaeian², Ugochukwu O. Ugwu³

1. Lab of Machine Learning and Knowledge Representation, Innopolis University, Innopolis, 420500, Russia;
2. Peoples' Friendship University of Russia, Moscow, 125009, Russia;
3. Department of Mathematics, Colorado State University, Fort Collins, USA

Received:2024-02-10 Revised:2024-07-19 Online:2026-04-07 Published:2026-04-07
Contact: Salman Ahmadi-Asl,E-mail:salman.ahmadiasl@gmail.com E-mail:salman.ahmadiasl@gmail.com

摘要/Abstract

摘要： This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tensor 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 handle. Due to the small size of the tensor sketches, deterministic approaches are applied to them to compute their GTSVD. Then, from the GTSVD of the small tensor sketches, the GTSVD of the original large-scale data tensors is recovered. Some experiments are conducted to show the effectiveness of the proposed approach.

关键词: Randomized algorithms, Generalized tensor singular value decomposition (GTSVD), Tensor product (T-product)

Abstract: This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tensor 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 handle. Due to the small size of the tensor sketches, deterministic approaches are applied to them to compute their GTSVD. Then, from the GTSVD of the small tensor sketches, the GTSVD of the original large-scale data tensors is recovered. Some experiments are conducted to show the effectiveness of the proposed approach.

Key words: Randomized algorithms, Generalized tensor singular value decomposition (GTSVD), Tensor product (T-product)

中图分类号:

Salman Ahmadi-Asl, Naeim Rezaeian, Ugochukwu O. Ugwu. Randomized Algorithms for Computing the Generalized Tensor SVD Based on the Tensor Product[J]. Communications on Applied Mathematics and Computation, 2026, 8(2): 605-621.

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Randomized Algorithms for Computing the Generalized Tensor SVD Based on the Tensor Product

Randomized Algorithms for Computing the Generalized Tensor SVD Based on the Tensor Product

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