Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition

Na Li; Stefan Kindermann; Carmeliza Navasca

doi:10.1016/j.laa.2011.12.002

Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition

Na Li
, Stefan Kindermann
, Carmeliza Navasca

Industrial Mathematics Institute

Research output: Contribution to journal › Article › peer-review

Abstract

We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.

Original language	English
Pages (from-to)	796-812
Number of pages	17
Journal	Linear Algebra and its Applications
Volume	438
Issue number	2
DOIs	https://doi.org/10.1016/j.laa.2011.12.002
Publication status	Published - 15 Jan 2013

Fields of science

101 Mathematics
102 Computer Sciences
101014 Numerical mathematics
101020 Technical mathematics
102005 Computer aided design (CAD)

JKU Focus areas

Engineering and Natural Sciences (in general)

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10.1016/j.laa.2011.12.002

Cite this

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title = "Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition",

abstract = "We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.",

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AU - Navasca, Carmeliza

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N2 - We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.

AB - We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.

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DO - 10.1016/j.laa.2011.12.002

M3 - Article

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VL - 438

SP - 796

EP - 812

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - 2

ER -

Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition

Abstract

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