Eigenvalues and principal component loadings of heavily overlapped vibrational spectra.

In order to illustrate the possibilities of principal component analysis in determining the number of components in a system of heavily overlapped spectra, several numerical spectral models were formed of bands with very close parameters. The models consisted of three bands, whose peak positions were locally shifted and noise added. For all the cases the relations between eigenvalues and principal component loadings were considered. It was shown that for those complex spectra for which peak positions and band halfwidths can be determined with high accuracy, eigenvalues criteria could easily indicate the number of components. For all analyzed models, the consideration of the shape of loadings was proven to have a high importance. In limited number of cases the shape of a loading can make the results of eigenvalue analysis more understandable. It has been shown that the noise can be treated as a main limitation in the application of the method to this type of the spectra.