Margin based feature selection - Theory and algorithms

Feature selection is the task of choosing a small set out of a given set of features that capture the relevant properties of the data. In the context of supervised classification problems the relevance is determined by the given labels on the training data. A good choice of features is a key for building compact and accurate classifiers. In this paper we introduce a margin based feature selection criterion and apply it to measure the quality of sets of features. Using margins we devise novel selection algorithms for multi-class classification problems and provide theoretical generalization bound. We also study the well known Relief algorithm and show that it resembles a gradient ascent over our margin criterion. We apply our new algorithm to various datasets and show that our new Simba algorithm, which directly optimizes the margin, outperforms Relief.