A Randomized Singular Value Decomposition for Third-Order Oriented Tensors

Minghui Ding (), Yimin Wei () and Pengpeng Xie ()
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Minghui Ding: Ocean University of China
Yimin Wei: Fudan University
Pengpeng Xie: Ocean University of China

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 1, No 14, 358-382

Abstract: Abstract The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product-based third-order tensor singular value decomposition with the transformation matrix being a factor matrix of the higher-order singular value decomposition. Continuing along this vein, this paper explores realizing the O-SVD efficiently by drawing a connection to the tensor-train rank-1 decomposition and gives a truncated O-SVD. Motivated by the success of probabilistic algorithms, we develop a randomized version of the O-SVD and present its detailed error analysis. The new algorithm has advantages in efficiency while keeping good accuracy compared with the current tensor decompositions. Our claims are supported by numerical experiments on several oriented tensors from real applications.

Keywords: Oriented tensor; Singular value decomposition; Truncation; Randomized algorithm; 65F30; 65F99; 15A69 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02177-5

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