2022/03/05 by Minghui Ding, Ding, Minghui, Wei, Yimin +1
Computer Science · Mathematics · #Advanced Neural Network Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Parallel Computing and Optimization Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2203.02761
openalex publication_date 2022/03/05 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
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 transform matrix being a factor matrix of the higher order singular value decomposition. Continuing along this vein, this paper explores realizing the O-SVD more efficiently by 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.