Generalized elastic net optimal scoring problem for feature selection

Abstract

Linear discriminant analysis (LDA) is a well-known tool for classification and dimensionality reduction. As an equivalent form of LDA, optimal scoring is presented to solve the classification problem by regression. In this paper, we propose a generalized elastic net optimal scoring problem (GenOS) to find sparse discriminant vectors, where the generalized elastic et is the combination of the ℓ2-norm and ℓq-norm (0<q⩽1). In GenOS, ℓq-norm is imposed to confer sparsity to discriminant vectors and ℓ2-norm is added to enhance the performance of the classifier. Then, a new efficient algorithm based on block coordinate descent (BCD) method is developed to solve GenOS approximately and the convergence is also established. Simulated data and real-world data are used to empirically illustrate the effectiveness of the proposed model.