Exact Top-k Feature Selection via l2, 0-Norm Constraint

Abstract

In this paper, we propose a novel robust and pragmatic feature selection approach. Unlike those sparse learning based feature selection methods which tackle the approximate problem by imposing sparsity regularization in the objective function, the proposed method only has one l2,1-norm loss term with an explicit l2,0-Norm equality constraint. An efficient algorithm based on augmented Lagrangian method will be derived to solve the above constrained optimization problem to find out the stable local solution. Extensive experiments on four biological datasets show that although our proposed model is not a convex problem, it outperforms the approximate convex counterparts and state of the art feature selection methods evaluated in terms of classification accuracy by two popular classifiers. What is more, since the regularization parameter of our method has the explicit meaning, i.e. the number of feature selected, it avoids the burden of tuning the parameter, making it a pragmatic feature selection method.