IMPROVED PRINCIPAL COMPONENT ANALYSIS OF NOISY DATA

Several tests exist for determining the number of principal factors, n, when applying principal component analysis (PCA) to a series of spectra. However, as the signal/noise (S/N) ratio of the data begins to decrease, the discriminating power of these tests to accurately determine n also decreases. If the correlation function response values, r(o), normally used in PCA to form the correlation/covarlance matrix are replaced by their autoconvolution values, r(sym), the discriminating power of PCA can be markedly improved for noisy data. r(sym) is a measure of the symmetry of the correlation function and gains its power in PCA from the fact that the symmetry of the correlation function suffers much less degradation in the presence of noise than does the correlation response, r(o). A comparison is made between the use of r(o) and r(sym) values with computer-generated synthetic spectra and with real ESCA spectra derived from known physical mixtures of cobalt aluminate and cobalt oxide.