A proximal classifier with consistency

Note that for GEPSVM proposed in [1], the predicted class of a testing point is determined by comparing two distances between the testing point and two hyperplanes, while the optimization problems are based on comparing two distances between a hyperplane and two kinds of the training points. So there exists some inconformity between the decision process and the training process. In this paper, we propose a new proximal classifier, called PCC for short, with consistency, which is always based on comparing two distances between a point (the testing point in the decision process and the training point in the training process) and two hyperplanes. This consistency not only makes our PCC to be more reasonable logically, but also naturally leads to a simpler decision function with less computation cost. Furthermore, in our PCC two general eigenvalue problems in GEPSVM are replaced by two simple eigenvalues problems with a parameter δ. In addition, different regularization terms are introduced in the formulation of our PCC, avoiding the singular problems possibly appeared in GEPSVM. Experimental results on several benchmark data sets show that our PCC is not only faster, but also has better generalization.