Information extraction from a complex multicomponent system by target factor analysis

A theoretical investigation into the mechanism of information extraction by target factor analysis (TFA) is presented from experimental data in the form of a matrix, and the results were validated using composite spectra obtained by open-path Fourier transform-infrared (FT-IR) spectrometry. The composite spectra were generated by adding the spectral information of a target molecule with known path-integrated concentrations to the raw open-path FT-IR spectra obtained in a pristine atmosphere. Target molecules are deemed to be detected when the weighted correlation coefficient between the calculated spectrum of the analyte and its reference spectrum exceeds 0.90. The effective detection by TFA is shown to depend on the variation of their concentrations over the period of the measurement and not necessarily on the magnitude of concentration. When TFA fails to detect an analyte at high, but relatively constant, concentration that varies so little as to have low variance, blank spectra, i.e., spectra in which the analyte is known to be absent, are included in the data matrix. This procedure effectively increases the variance of the concentrations in the whole data set, and TFA detects the analyte.