A Novel Outlook on Feature Selection as a Multi-objective Problem

Feature selection is the process of choosing, or removing, features to obtain the most informative feature subset of minimal size. Such subsets are used to improve performance of machine learning algorithms and enable human understanding of the results. Approaches to feature selection in literature exploit several optimization algorithms. Multi-objective methods also have been proposed, minimizing at the same time the number of features and the error. While most approaches assess error resorting to the average of a stochastic K-fold cross-validation, comparing averages might be misleading. In this paper, we show how feature subsets with different average error might in fact be non-separable when compared using a statistical test. Following this idea, clusters of non-separable optimal feature subsets are identified. The performance in feature selection can thus be evaluated by verifying how many of these optimal feature subsets an algorithm is able to identify. We thus propose a multi-objective optimization approach to feature selection, EvoFS, with the objectives to i. minimize feature subset size, ii. minimize test error on a 10-fold cross-validation using a specific classifier, iii. maximize the analysis of variance value of the lowest-performing feature in the set. Experiments on classification datasets whose feature subsets can be exhaustively evaluated show that our approach is able to always find the best feature subsets. Further experiments on a high-dimensional classification dataset, that cannot be exhaustively analyzed, show that our approach is able to find more optimal feature subsets than state-of-the-art feature selection algorithms.