Generalized Fisher Score for Feature Selection

TL;DR

This paper introduces a generalized Fisher score method for feature selection that jointly selects features to improve over traditional independent Fisher score methods, using a novel optimization approach.

Contribution

It proposes a new joint feature selection method based on maximizing a lower bound of Fisher score, formulated as a QCLP and solved with a cutting plane algorithm.

Findings

Outperforms traditional Fisher score in experiments

Achieves better feature subset quality than state-of-the-art methods

Demonstrates effectiveness on benchmark datasets

Abstract

Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims at finding an subset of features, which maximize the lower bound of traditional Fisher score. The resulting feature selection problem is a mixed integer programming, which can be reformulated as a quadratically constrained linear programming (QCLP). It is solved by cutting plane algorithm, in each iteration of which a multiple kernel learning problem is solved alternatively by multivariate ridge regression and projected gradient descent. Experiments on benchmark data sets indicate that the proposed method outperforms Fisher score as well as many other state-of-the-art feature selection methods.