On simplex-based method for self-modeling curve resolution of two-way data

A method for self-modeling curve resolution (SMCR) of two-way data is proposed. This method comprises a new simplex-based procedure for directly determining the pure variables and an optimization algorithm to improve the resolution iteratively. First, it is demonstrated that with specific normalization, the two-way data points are contained in a simplex with the vertices constituted by the pure variables. This elucidates a precise geometry of an old discovery that two-way data points are bracketed by the pure variables. Second, a property of the simplex is given, which implies that the vertices of a simplex maximize a certain quadratic form over all the elements in the simplex. A procedure for determining pure variables in two-way data is then developed. Finally, an optimization algorithm to refine the resolution is suggested. The geometry of the algorithm is to locate a simplex that embraces the two-way data. With a good starting estimate that is as close as possible to the true pure profiles, the proposed method is expected to give improved resolution compared to traditional resolution techniques. The proposed method is evaluated using two simulated data sets and two data sets from hyphenated chromatography-diode array detection (HPLCDAD) of polyaromatric hydrocarbon in air particle samples. The results reveal that the proposed method gives favorable resolution for the four data sets. (C) 2002 Elsevier Science B.V. All rights reserved.