Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/14045
Title: New ALS methods with extrapolating search directions and optimal step size for complex-valued tensor decompositions
Authors: Chen, Y
Han, D
Qi, L 
Issue Date: 2011
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on signal processing, 2011, v. 59, no. 12, 5985548, p. 5888-5898 How to cite?
Journal: IEEE transactions on signal processing 
Abstract: In signal processing, data analysis and scientific computing, one often encounters the problem of decomposing a tensor into a sum of contributions. To solve such problems, both the search direction and the step size are two crucial elements in numerical algorithms, such as alternating least squares algorithm (ALS). Owing to the nonlinearity of the problem, the often used linear search direction is not always powerful enough. In this paper, we propose two higher-order search directions. The first one, geometric search direction, is constructed via a combination of two successive linear directions. The second one, algebraic search direction, is constructed via a quadratic approximation of three successive iterates. Then, in an enhanced line search along these directions, the optimal complex step size contains two arguments: modulus and phase. A current strategy is ELSCS that finds these two arguments alternately. So it may suffer from a local optimum. We broach a direct method, which determines these two arguments simultaneously, so as to obtain the global optimum. Finally, numerical comparisons on various search direction and step size schemes are reported in the context of blind separation-equalization of convolutive DS-CDMA mixtures. The results show that the new search directions have greatly improve the efficiency of ALS and the new step size strategy is competitive.
URI: http://hdl.handle.net/10397/14045
ISSN: 1053-587X
EISSN: 1941-0476
DOI: 10.1109/TSP.2011.2164911
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