Nonlinear Relevance Estimation of Multicollinear Features for Reducing the Input Dimensionality of Optical Spectroscopy Inverse Problem

Abstract

In this study we considered an inverse problem of optical spectroscopy. It consists in determining concentrations of the ingredient ions of multicomponent water solutions by their spectra. The problem of describing the spectra of multicomponent solutions is nonlinear and has no adequate mathematical model. Because of this, machine learning methods using experimental data were chosen to solve this problem. At the same time, inverse problems of spectroscopy are characterized by high input dimensionality with a large number of features, more or less relevant. In their turn, some of the relevant features are redundant due to their multicollinearity. This is caused by the fact that the characteristic lines have a width of several spectrum channels. Presence of redundant features leads to a deterioration in the quality of machine learning solution of the problem. Thus, there is a need for a feature selection procedure that takes into account both their relevance and redundancy, as well as their nonlinear relationship with the determined parameters. In this study, we considered a feature selection procedure based on the iterative selection of features with the highest relevance to the target variable and on the elimination of features with a high relationship with each other. In this selection process, we used a trained neural network to analyze weights and determine feature importance in a nonlinear way. We also used the Pearson correlation coefficient to measure how features are related to one another. Finally, we compared the quality of a neural network solution using spectroscopic data of the full set of input features and of its subsets. These subsets were compiled using the selection procedure under consideration. We also used traditional methods for selecting significant input features as baseline methods.