Quantifying the Relative Importance of Variables and Groups of Variables in Remote Sensing Classifiers Using Shapley Values and Game Theory

Sacha D. Nandlall, Koreen Millard

Abstract: Remote sensing image classification applications often involve determining which variables are the most important to obtain the best accuracy. Common metrics for assessing variable importance such as a mean decrease in accuracy (MDA) typically provide values in scaled units that are difficult to interpret, and do not easily accommodate user-defined groups of variables. In this letter, an improved method of quantifying the importance of classifier variables is developed and demonstrated in the context of land-cover classification using the random forest algorithm. The proposed method employs concepts from game theory and relies on a metric known as the Shapley value, which allows the importance of variables to be easily interpreted by providing a quantitative assessment of each variable's contribution to classifier accuracy. Moreover, unlike MDA, the method also applies to arbitrary, user-defined groups of variables. The approach described herein thus provides a robust alternative to single-variable selection using MDA and can be used with any type of classifier.