Geometric projection twin support vector machine for pattern classification

In this paper, a novel binary classifier termed as GPTSVM (projection twin support vector machine via Geometric Interpretation) is presented. In the spirit of original PTSVM, GPTSVM tries to seek two projection axes, one for each class, such that the projected samples of one class are well separated from that of the other class along its own projection axis. A pair of parameters (nu) are introduced in GPTSVM to control the bounds of the fractions of the support vectors and the error margins. Moreover, GPTSVM can be interpreted as a pair of minimum Mahalanobis norm problems on two reduced convex hulls (RCHs). Then, an efficient geometric algorithm for GPTSVM is presented based on the well-known Gilbert's algorithm. By doing so, the dual problem of GPTSVM can be solved very fast without resorting to any specialized optimization toolbox. The experimental results on several UCI benchmark data sets, traffic accident prediction data, and large scale NDCC database show the feasibility and effectiveness of the proposed algorithm.