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• W2991057509 abstract "The epsilon alternating least squares ($epsilon$-ALS) is developed and analyzed for canonical polyadic decomposition (approximation) of a higher-order tensor where one or more of the factor matrices are assumed to be columnwisely orthonormal. It is shown that the algorithm globally converges to a KKT point for all tensors without any assumption. For the original ALS, by further studying the properties of the polar decomposition, we also establish its global convergence under a reality assumption not stronger than those in the literature. These results completely address a question concerning the global convergence raised in [L. Wang, M. T. Chu and B. Yu, emph{SIAM J. Matrix Anal. Appl.}, 36 (2015), pp. 1--19]. In addition, an initialization procedure is proposed, which possesses a provable lower bound when the number of columnwisely orthonormal factors is one. Armed with this initialization procedure, numerical experiments show that the $epsilon$-ALS exhibits a promising performance in terms of efficiency and effectiveness." @default.
• W2991057509 created "2019-12-05" @default.
• W2991057509 creator A5068922983 @default.
• W2991057509 date "2019-11-25" @default.
• W2991057509 modified "2023-10-16" @default.
• W2991057509 title "The Epsilon-Alternating Least Squares for Orthogonal Low-Rank Tensor Approximation and Its Global Convergence" @default.
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• W2991057509 doi "https://doi.org/10.48550/arxiv.1911.10921" @default.
• W2991057509 hasPublicationYear "2019" @default.
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