A fast alternating least squares method for third-order tensors based on a compression procedure

Autor:	Tomonori Murakoshi, Takayasu Matsuo
Rok vydání:	2015
Předmět:	Third order Mathematical optimization Matrix (mathematics) Physics::Instrumentation and Detectors Computation Non-linear least squares Compression (functional analysis) Singular value decomposition Compression procedure Computer Science::Numerical Analysis Algorithm SIMPLE algorithm Mathematics
Zdroj:	JSIAM Letters. 7:5-8
ISSN:	1883-0617 1883-0609
DOI:	10.14495/jsiaml.7.5
Popis:	The alternating least squares (ALS) method is frequently used for the computation of the canonical polyadic decomposition (CPD) of tensors. It generally gives accurate solutions, but demands much time. A strong alternative to this is the alternating slice-wise diagonalization (ASD) method. It limits its targets only to third-order tensors, and in exchange for this restriction, it fully utilizes a compression technique based on matrix singular value decomposition and consequently achieves high efficiency. In this paper, we propose a new simple algorithm, Reduced ALS, which lies somewhere between ALS and ASD; it employs a similar compression procedure to ASD, but applies it more directly to ALS. Numerical experiments show that Reduced ALS runs as fast as ASD, avoiding instability ASD sometimes exhibits.
Databáze:	OpenAIRE
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