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

In trilinear decomposition, one first tries to estimate the number of underlying factors in the system studied, and then employs trilinear decomposition 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 factors, either overestimation or underestimation of the underlying factors will lead the results of PARAFAC to be erroneous. Most of the existing factor-determining methods are established on the basis of factor analysis. These procedures are originally designed for two-way data sets. Only after the three-way data array was unfolded into two-way data set, could then these factor-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 collinearity and varying backgrounds, the present authors advocated incorporating the advantages of trilinear data array into the factor-determining procedure. Hence, a novel factor-determining method has been proposed specifically for trilinear decomposition. Experiments have demonstrated that the proposed method has the features of easy implementation and excellent performance even when heavy collinearity and varying backgrounds are present.