This study proposes two effective algorithms for the qualitative and quantitative analysis of components in a mixture. For cases wherein the spectrum of each component in the mixture can be obtained in advance, we develop a simple process, namely “known component analysis (KCA),” which requires a small number of samples. In contrast, for cases wherein a mixture contains many components or the spectra of some components cannot be obtained, we develop “unknown components analysis (UCA),” whose calculation time is considerably less than those of the traditional algorithms. Compared to KCA, UCA requires more samples to be analyzed to ensure the high accuracy rate. These proposed algorithms provide new ways to detect and measure key biomedical substances.