Mutual information for the selection of relevant variables in spectrometric nonlinear modelling

Abstract

Data from spectrophotometers form vectors of a large number of exploitable variables. Building quantitative models using these variables most often requires using a smaller set of variables than the initial one. Indeed, a too large number of input variables to a model results in a too large number of parameters, leading to overfitting and poor generalization abilities. In this paper, we suggest the use of the mutual information measure to select variables from the initial set. The mutual information measures the information content in input variables with respect to the model output, without making any assumption on the model that will be used; it is thus suitable for nonlinear modelling. In addition, it leads to the selection of variables among the initial set, and not to linear or nonlinear combinations of them. Without decreasing the model performances compared to other variable projection methods, it allows therefore a greater interpretability of the results.