Estimating the chemical rank of three-way fluorescence data by vector subspace projection with Monte Carlo simulation

Determining the chemical rank of multiway data is a key step in many chemometric studies. In this study, a novel method, vector subspace projection with Monte Carlo simulation (VSPMCS), is proposed for three-way fluorescence data to achieve this goal. This new method estimates an appropriate chemical rank by comparing the projection residuals which are obtained from vector subspace projection analysis of two similar pseudo matrices constructed by the technology of Monte Carlo simulation. The influences of noise, collinearity, non-trilinear background, analysis speed and solution on this new method are discussed. Moreover, the new method is compared with other five factor-determining methods, i.e., IND, ADD-ONE-UP, CORCONDIA, LTMC and SPPH, which is presented by analyzing two simulation data sets as well as four experimental data sets. The results show a good agreement between simulations and experimentations, suggesting that the new method can accurately and quickly estimate the number of significant components in complicated situations and its precision can be comparable to the other five factor-determining methods. In addition, this new methodology can be extended to determine the chemical rank of higher-order data.