A sparse robust model for large scale multi-class classification based on K-SVCR

K-Support Vector Classification Regression (K-SVCR) is a multi-classification method based on "1-vs-1-vs-rest" structure, which provides better forecasting results since all the data are given full consideration while the centre of attention is a two-class partition. However, K-SVCR is not only sensitive to outliers but also time consuming. In this paper, we propose a robust least-squares version of K-SVCR (K-RLSSVCR) based on squares epsilon-insensitive ramp loss and truncated least squares loss, which partially depress the impact of outliers on the new model via its nonconvex epsilon-insensitive ramp loss and truncated least squares loss. With Concave-Convex Procedure (CCP), the solution of K-RLSSVCR is reduced to solving only a system of linear equations per iteration. For training large-scale problems, we derive an equivalent K-RLSSVCR model in primal space (Primal K-RLSSVCR) by the representer theorem, which may have a sparse solution if the corresponding kernel matrix has a low rank. We design a sparse K-RLSSVCR (K-SRLSSVCR) algorithm to achieve a sparse solution of the Primal K-RLSSVCR based on approximating the kernel matrix by a low-rank matrix. Experimental results on artificial data set and benchmark data sets show that the proposed method has better or comparable performance in classification to other related algorithms but with remarkably less training time and memory consumption, especially when used to train large-scale problems. (C) 2018 Elsevier B.V. All rights reserved.