Discriminative Semi-supervised Feature Selection via Manifold Regularization

by Zenglin Xu, Rong Jin, Michael R. Lyu and Irwin King

This paper talks about feature selection via SVM. The semi-supervised part is enabled by adding a manifold regularizer. The method is to multiply the feature with a diagonal 0-1 matrix (selecting features). With these variables in the optimization as well, we get the optimization for this problem. The key idea to solve this problem is to reformulate it with the dual of SVM but leaving the feature selecting variables alone. Then the optima is the saddle point of the optimization problem. This kind of problem can be found in multiple-kernel learning, which has a standard algorithm (alternating optimization w.r.t. difference variables).

The idea of using SVM for feature selection is not new. The contribution might be the semi-supervised setting. In my own research it seems that we still do not have a clear goal of achieving this with other methods. hmm...