On the application of principal component analysis and factor analysis in electron spectroscopy: the limit of detectability of factors in a set of noisy spectra

Based on the geometrical look on the mathematical structure of a set of noisy spectra composed of two factors, some general properties of any set of noisy spectra are derived and discussed. It is then pointed out that the ability to detect the presence of lower contributing factor depends on the choice of the criterion applied together with principal component analysis (PCA). The efficiency of two particular criteria were compared by the application to sets of simulated spectra of known composition. The comparison showed that the detection limit can be improved by a factor of 2 or 3 by a proper choice of the criterion. Removing the less informative parts of the spectra results in an additional improvement of the detection limit.