Estimation of component spectra by the principal components method

The principal components method enables component spectra from pigment mixtures to be estimated by evaluating the eigenvectors of the second moment matrix. The components are linear combinations of these eivenvectors, but cannot be identified unambiguously. With the conditions of non-negativity of spectral values and of concentrations, this ambiguity can be limited; components spectra for 2 and 3 components were calculated earlier. In the present work, maximal dissimilarity of component spectra is assumed as a further condition. An algorithm based on linear programming is described; it enables any number of components to be estimated from eigenvectors of the second moment matrix with better reliability than previously.