Mathematics > Numerical Analysis
[Submitted on 25 Jul 2022 (v1), last revised 20 Jan 2024 (this version, v11)]
Title:A Randomized Algorithm for Tensor Singular Value Decomposition using an Arbitrary Number of Passes
View PDF HTML (experimental)Abstract:Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms need (2q+2) passes over the data tensor to compute a t-SVD, where q is a non-negative integer number (power iteration parameter). In this paper, we propose an efficient and flexible randomized algorithm that can handle any number of passes q, which not necessary need be even. The flexibility of the proposed algorithm in using fewer passes naturally leads to lower computational and communication costs. This advantage makes it particularly appropriate when our task calls for several tensor decompositions or when the data tensors are huge. The proposed algorithm is a generalization of the methods developed for matrices to tensors. The expected/ average error bound of the proposed algorithm is derived. Extensive numerical experiments on random and real-world data sets are conducted, and the proposed algorithm is compared with some baseline algorithms. The extensive computer simulation experiments demonstrate that the proposed algorithm is practical, efficient, and in general outperforms the state of the arts algorithms. We also demonstrate how to use the proposed method to develop a fast algorithm for the tensor completion problem.
Submission history
From: Salman Ahmadi-Asl [view email][v1] Mon, 25 Jul 2022 21:32:51 UTC (14,008 KB)
[v2] Wed, 27 Jul 2022 08:14:57 UTC (14,008 KB)
[v3] Fri, 29 Jul 2022 13:52:41 UTC (14,008 KB)
[v4] Wed, 3 Aug 2022 15:44:27 UTC (14,008 KB)
[v5] Sat, 3 Dec 2022 19:01:11 UTC (14,008 KB)
[v6] Tue, 20 Dec 2022 14:55:49 UTC (14,008 KB)
[v7] Wed, 11 Jan 2023 14:50:52 UTC (6,908 KB)
[v8] Wed, 22 Feb 2023 22:10:24 UTC (6,841 KB)
[v9] Tue, 28 Feb 2023 13:53:08 UTC (7,049 KB)
[v10] Sun, 26 Nov 2023 17:56:29 UTC (7,976 KB)
[v11] Sat, 20 Jan 2024 14:33:35 UTC (7,872 KB)
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