Ramp loss least squares support vector machine

• A novel support vector machine (RLSSVM) for binary classification.
• RLSSVM has the sparseness which is controlled by the ramp loss.
• The non-convexity of RLSSVM can be efficiently solved by the Concave-Convex Procedure (CCCP).

In this paper, we propose a novel sparse least squares support vector machine, named ramp loss least squares support vector machine (RLSSVM), for binary classification. By introducing a non-convex and non-differentiable loss function based on the ɛ-insensitive loss function, RLSSVM has several improved advantages compared with the plain LSSVM: firstly, it has the sparseness which is controlled by the ramp loss, leading to its better scaling properties; secondly, it can explicitly incorporate noise and outlier suppression in the training process, and thirdly, the non-convexity of RLSSVM can be efficiently solved by the Concave-Convex Procedure (CCCP). Experimental results on several benchmark datasets show the effectiveness of our method.