Three-way data resolution by alternating slice-wise diagonalization (ASD) method

A new approach, the alternating slice-wise diagonalization (ASD) method, is developed for three-way data resolution. First, based on the least squares principle and the constraints inherent in the resolution of the trilinear model, a criterion, the slice-wise diagonalization (SD) loss, is proposed for trilinear analysis of three-way data. This criterion provides a natural way to avoid the two-factor degeneracy, which is difficult to handle for the PARAFAC algorithm. Second, by alternatingly minimizing the SD loss, a procedure is developed for identifying the parameters of the trilinear model. Experimental results show that the resolved profiles of chemical meaning are very stable with respect to the component number provided that the number is chosen to be equal to or greater than the actual one. This enables the ASD method to achieve resolution without concern about the actual component number. This approach is different from the traditional ones, since the determination of the actual component number is a critical step for conventional chemometric resolution techniques. Moreover, the convergence rate of the algorithm for the ASD method is much higher than that of the PARAFAC algorithm. Copyright (C) 2000 John Wiley & Sons, Ltd.