Rank Estimation of Excitation-Emission Matrices Using Frequency Analysis of Eigenvectors

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The number of components in mixtures of fluorophores Is determined by using a new method for matrix rank estimation of excitation-emission matrix (EEM) formated data. Mixture EEMs are decomposed into a set of basis vectors (eigenvectors) using eigenvector analysis. These vectors are then Fourier transformed and their frequency distributions are used as a means of differentiating between primary (spectral) eigenvectors and secondary (noise) eigenvectors. Primary eigenvectors are found to have Fourier spectra weighted toward the lower frequency coefficients, whereas Fourier spectra of secondary eigenvectors are found to be weighted toward the high frequency coefficients. An empirical algorithm for rank estimation based on the frequency distributions of eigenvectors is compared to traditional rank estimation methods. Finally, the method developed in this study is applied to 12 blind coded EEMs of mixtures of polynuclear aromatic hydrocarbons of known composition. © 1986, American Chemical Society. All rights reserved.

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Analytical Chemistry

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