  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.
