Some surprising properties of multivariate curve resolution-alternating least squares (MCR-ALS) algorithms

In this paper, some surprising properties are discussed related to multivariate curve resolution-alternating least squares (MCR-ALS) algorithms. The analytical solution of the feasible regions opens the door to follow the convergence tracks of MCR algorithms on Borgen plot at least in case of three-component systems. Using Borgen plot, a hitherto unknown discrepancy of MCR-ALS algorithms has been revealed, i.e. the sub- and even the final solutions can be outside of the range of the data matrix R. Anew constraint, i.e. 'zero orthogonal part for the estimated profiles' for MCR-ALS algorithms is suggested to speed up the convergence. If the minimal constraint, i.e. non-negativity, can be only used, then the band solution should be preferred. This recommendation is strengthened by simulated investigations. However if the practical problem is simple enough, i.e. the concentration profiles are well-separated, and/or there are no minor components, and/or the spectra are different enough, and/or there is zero range in either for concentration or spectral profiles, and/or all necessary further constraints are known and applied etc., then MCR-ALS algorithms can work properly. Copyright (C) 2009 John Wiley & Sons, Ltd.