Spectra data collected from a mixture defines an n-dimensional data space (n is the number of data points), and application of PCA techniques yields a subset of m-eigenvectors that effectively describe all variance in that data space. Bach member of a library of known components is examined based by representing each library spectrum as a vector in the m-dimensional space. Target factor testing techniques yield an angle between this vector and the data space. Those library members that have the smallest angles are considered to be potential mixture members and are ranked accordingly. Every combination of the top y library members is considered as a potential solution and a multivariate least-squares solution is calculated using the mixture spectra for each of the potential solutions. A ranking algorithm is then applied and used to select the combination that is most likely the set of pure components in the mixture.