Sparse discriminative feature selection

• The proposed method selects features that can preserve the sparse reconstructive relationship of the data.
• A greedy algorithm and a joint selection algorithm are devised to efficiently solve the proposed formulation.
• We incorporate discriminative analysis and l2;1_norm minimization into a joint feature selection.

As sparse representation-based classifier (SRC) is developed, it has drawn more and more attentions in dimension reduction. In this paper, we introduce SRC based measurement criterion into feature selection, and then propose a novel method called sparse discriminative feature selection. Our objective function aims to find a subset of features, which minimize the within-class reconstruction residual and simultaneously maximize the between-class reconstruction residual in the subspace of selected features. A greedy algorithm and a joint selection algorithm are devised to efficiently solve the proposed combinatorial optimization formulation. In particular, our joint selection algorithm adds l2,1-norml2,1-norm minimization into the objective function, which reduces the redundant and learns features weights simultaneously. A new iterative algorithm is also developed to optimize the proposed objective function. Experiments on benchmark data sets demonstrate the performance of our feature selection method.