Regularization of Parallel Factor Analysis (PARAFAC): A New Approach to Determining Groups of Fluorophores in Fluorescence Spectra of Natural Waters

Abstract

Parallel factor analysis (PARAFAC) is widely used in relation to fluorescence excitation/emission spectra to track the movement of water masses and to study seasonal changes in the composition and content of dissolved organic matter. The stage of selecting the number of components is one of the most difficult when using factor analysis. The widely used method of analyzing loads when splitting the original set into halves in many cases does not allow a determination of the best model because of the closeness of their statistical estimates. Because the use of regularization with a penalty for the sum of parameter modules tends to lead to sparse solutions in which some of the coefficients are equal to zero, the use of this approach allows one to select those variables that carry useful information. A procedure is proposed for selecting the number of components when performing parallel factor analysis of fluorescence spectra using a penalty for the 1- and 2-norms of the solution.