Combined feature selection and classification using DCA

In this paper we introduce a new method using the zero-norm l₀ for the combined feature selection-supervised classification problem. Discontinuity at the origin for l₀ makes the solution of the corresponding optimization problem difficult. To overcome this drawback we use a robust DC (difference of convex functions) programming approach which is a general framework for non-convex continuous optimisation. We consider a continuous approximation to l₀ in an appropriate way such that the resulting problem can be formulated in terms of a DC program. Our DCA (DC algorithm) requires the solution of one linear program at each iteration. Preliminary computational experiments on some real-world data sets show that the proposed method is promising for the combined feature selection-classification and more efficient than the standard FSV (feature selection concave) approach.