Automated procedure to predict the number of components in spectroscopic data

Abstract

We have compared various statistical methods to estimate the number of components that contribute to a set of spectra. The methods are tested both on simulated and on experimental data. No assumptions are made about noise level, since this in most experimental situations is unknown. For tests that formally require such information we have devised novel criteria for their predictions. The criteria have been integrated with the NIPALS algorithm to create a routine that in an automated way predicts the number of components. We find that the methods almost always predict the correct number of components when the quality of data is high. Also for multi-component samples and at high-noise levels most of these methods make satisfactory predictions. Those that gave the overall best results were the factor indicator function (IND) and the imbedded error function (IE). The F-test also worked well, but it has the disadvantage that a significance level must be chosen rather arbitrarily. The residual standard deviation (RSD), the root mean square (RMS), the χ-squared and the residual percentage variance (RPV) tests also gave satisfactory results. Less good were the eigenvalue (EV) and the reduced eigenvalue (REV). The ability of all indicators to predict the number of components was significantly improved when the degree of digitalization of the spectra was increased.