Pseudo alternating least squares algorithm for trilinear decomposition



In chemistry, PARAFAC is one of the most widely used algorithms for trilinear decomposition. However, the problem of PARAFAC requiring an accurate estimation of the number of factors in the system under study limits its applications to some extent. This troublesome problem has been tackled by the pseudo alternating least squares (PALS) algorithm designed in this paper. PALS is a unique algorithm which tries to alternately optimize three different objective functions to obtain the solutions for the trilinear decomposition model. It has the outstanding feature of being resistant to the influence of N (the number of factors chosen in calculation), which has been proved mathematically under some mild conditions. Although the optimization procedure of PALS is different from that of PARAFAC, an alternating least squares scheme, and hinders a straightforward analysis of its convergence properties, studies on simulated as well as real data arrays reveal that PALS can often converge to satisfactory results within a reasonable computation time, even if excess factors are used in calculation. Copyright © 2001 John Wiley & Sons, Ltd.