Simultanous search for all modes in multilinear models

0341572 - ÚTIA 2011 RIV US eng C - Conference Paper (international conference)
Tichavský, Petr - Koldovský, Zbyněk
Simultanous search for all modes in multilinear models.
Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 2010. Dallas: IEEE, 2010, s. 4114-4117. ISBN 978-1-4244-4296-6.
[2010 IEEE International Conference on Acoustics, Speech, and Signal Processing. Dallas, TX (US), 14.03.2010-19.03.2010]
R&D Projects: GA MŠMT 1M0572; GA ČR GA102/09/1278
Grant - others:GA ČR(CZ) GP102/07/P384
Program: GP
Institutional research plan: CEZ:AV0Z10750506
Keywords : tensor factorization * multilinear models
Subject RIV: BB - Applied Statistics, Operational Research
http://library.utia.cas.cz/separaty/2010/SI/tichavsky-simultanous search for all modes in multilinear models.pdf

Parallel factor (PARAFAC) analysis is an extension of a low rank decomposition to higher way arrays, usually called tensors. Most of existing methods are based on an alternating least square (ALS) algorithm that proceeds iteratively, and minimizes a criterion (that is usually quadratic) of the fit with respect to individual factors one by one. Convergence of this approach is known to be slow, if some of the factor contain nearly co-linear vectors. This problem can be partly alleviated by an enhanced line search (ELS) by Rajih et al. (2008). In this paper we show that the method originally proposed by Paatero (1997), consisting in optimization with respect to all modes simultaneously, can be simplified, and can far outperform the ALS-ELS in ill--conditioned data in all modes.
Permanent Link: http://hdl.handle.net/11104/0184511