Extraction of pure species spectra from mixture spectra is important in characterizing unknown mixtures as well as in the monitoring of chemical reactions. In many designed experimental studies, the mixture concentrations are completely known and partial knowledge of the spectra of some of species in a mixture may also be available. In this study, we extend the methods of ordinary least squares (OLS), principal component regression (PCR), and non-negative matrix factorization (NMF) to incorporate such additional information. The performances of the three proposed methods are evaluated using simulated and experimental data. Among these, the proposed constrained NMF (cNMF) method is shown to be best-suited for obtaining feasible and accurate estimates of pure species spectra from mixture spectra.