Sparse and robust SVM classifier for large scale classification

Support vector machine (SVM) has drawn wide attention in various fields, such as image classification, pattern recognition and disease diagnosis and so on. Nevertheless, it requires much memory and runs very slow in large-scale datasets setting. To reduce computational cost and the required storage, we first design a new sparse and robust SVM model according to our construct truncated smoothly clipped absolute deviation (SCAD) loss and then establish its first-order necessary and sufficient optimality conditions though newly defined proximal stationary point. Following the idea of the proximal stationary point, we define the L-ts support vectors of L-ts-SVM and then show that the L-ts support vectors are a small portion of the whole training set, which is convenient for us to introduce a novel working set in each step. We next present a new alternating direction method of multipliers with working set (L-ts-ADMM) to deal with L-ts-SVM, which proves that the proposed algorithm not only converges to a local minimizer of L-ts-SVM but also possesses a relatively low computational complexity. Finally, the extensive numerical experiments demonstrate that the proposed algorithm enjoys better performance than nine leading state-of-the-art methods with regard to best classification accuracy, smallest number of support vectors and super fast computational speed in large-scale datasets setting.