Robust discriminant feature selection via joint L2,1-norm distance minimization and maximization

Discriminative Feature Selection (DFS) is an algorithm, proposed recently for effective feature selection by considering both joint linear discriminant analysis and row sparsity regularization. However, this method is not robust enough to protect the data from outliers, because it utilizes the squared L2-norm distance metric. To overcome this problem, we present in this paper, a novel discriminative feature selection algorithm, which uses the robust L2,1-norm for measuring the distances in DFS. Although the algorithm is apparently simple, it should not be considered trivial because of its non-convexity. Also, we present an analysis of the convergence, both theoretical and empirical. More importantly, we proposed an iterative algorithm to achieve optimal results. Experimental results, using various data sets, demonstrate the effectiveness of the proposed method.