An Alternating Simultaneously Minimizing Diagonal Matrix Error and Covariant Matrix Error Trilinear Decomposition Algorithm for Second-Order Calibration

摘要

An alternating trilinear decomposition algorithm based on simultaneously minimizing diagonal matrix error and covariant matrix error (ADCE) is developed for three-way data analysis. By alternatively optimizing three objective functions with intrinsic relationships, ADCE algorithm keeps the 'second-order advantage' of second-order calibration methods and provides a natural way to avoid the two-factor degeneracies, which is intrinsic in the traditional PARAFAC algorithm. The simulated results and real experimental results show ADCE algorithm has the features of fast convergence rate as well as insensitivity to the overestimated factor number, in other words, it not only avoids the dilemma of identifying the actual component number accurately in practical problem but also converges fast, which is rather difficult to handle for the traditional PARAFAC algorithm.