Title :
Canonical decomposition of semi-symmetric semi-nonnegative three-way arrays
Author :
Coloigner, Julie ; Albera, Laurent ; Kachenoura, Amar ; Senhadji, Lotfi
Author_Institution :
Inserm, Rennes, France
Abstract :
In this paper, we focus on a special case of canonical decomposition, say the canonical decomposition of three-way arrays, which have two equal and nonnegative loading matrices. This problem has a great interest in blind source separation, particularly in magnetic resonance spectroscopy, where each observation spectrum is a nonnegative linear combination of different constituent spectra. In order to achieve the semi-symmetric semi-nonnegative canonical decomposition of a given three-way array, we propose a novel technique named ELS-ALSsym+, which optimizes an unconstrained problem obtained by means of a square change of variable. The method is compared with a Levenberg-Marquardt-like approach recently submitted for publication in Linear Algebra and its applications and classical methods, which uses no a priori about the considered array, such as the ELS-ALS technique. Such a comparison is made in terms of performance and numerical complexity on random synthetic arrays.
Keywords :
arrays; computational complexity; least squares approximations; matrix decomposition; optimisation; ELS-ALSsym+ technique; Levenberg-Marquardt-like approach; alternating least squares; blind source separation; constituent spectra; enhanced line search; linear algebra; magnetic resonance spectroscopy; nonnegative linear combination; nonnegative loading matrices; numerical complexity; observation spectrum; random synthetic arrays; semisymmetric seminonnegative canonical decomposition; semisymmetric seminonnegative three-way arrays; unconstrained problem optimization; Analytical models; Brain modeling; Tensile stress;
Conference_Titel :
Signals, Systems and Computers (ASILOMAR), 2011 Conference Record of the Forty Fifth Asilomar Conference on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
978-1-4673-0321-7
DOI :
10.1109/ACSSC.2011.6190038