Canonical decomposition of semi-symmetric semi-nonnegative three-way arrays . - Archive ouverte HAL Access content directly
Conference Papers Year : 2011

Canonical decomposition of semi-symmetric semi-nonnegative three-way arrays .

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.
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hal-00908655 , version 1 (25-11-2013)

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Julie Coloigner, Laurent Albera, Amar Kachenoura, Lotfi Senhadji. Canonical decomposition of semi-symmetric semi-nonnegative three-way arrays .. Signals, Systems and Computers (ASILOMAR), Nov 2011, Pacific Grove, CA, United States. pp.444 - 448, ⟨10.1109/ACSSC.2011.6190038⟩. ⟨hal-00908655⟩
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