Efficient way to estimate the optimum number of factors for trilinear decomposition

In trilinear decomposition, one first tries to estimate the number of under lying factors in the system studied, and then employs trilinear decompositi on methods such as PARAFAC to obtain the desired characteristic profiles of the underlying factors and their relative contributions. Since the results of PARAFAC are heavily dependent on the estimation of the underlying facto rs, either overestimation or underestimation of the underlying factors will lead the results of PARAFAC to be erroneous. Most of the existing factor-d etermining methods are established on the basis of factor analysis. These p rocedures are originally designed for two-way data sets. Only after the thr ee-way data array was unfolded into two-way data set, could then these fact or-determining methods be used. It is obvious that the trilinear character of the data array is not utilized in the factor-determining procedure. With a view to cope with non-ideal experimental conditions, such as heavy colli nearity and varying backgrounds, the present authors advocated incorporatin g the advantages of trilinear data array into the factor-determining proced ure. Hence, a novel factor-determining method has been proposed specificall y for trilinear decomposition. Experiments have demonstrated that the propo sed method has the features of easy implementation and excellent performanc e even when heavy collinearity and varying backgrounds are present. (C) 200 1 Elsevier Science BN. All rights reserved.