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 (ν) 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.

在本文中，提出了一种新颖的二进制分类器，称为GPTSVM（通过几何解释的投影双支持向量机）。秉承原始PTSVM的精神，GPTSVM尝试寻找两个投影轴，每个类别一个，这样一类的投影样本就沿着其自身的投影轴与另一类别的投影样本很好地分离了。在GPTSVM中引入了一对参数（ν），以控制支持向量的分数和误差范围的界限。此外，GPTSVM可以解释为两个简化凸包（RCH）上的一对最小Mahalanobis范式问题。然后，基于著名的吉尔伯特算法提出了一种有效的GPTSVM几何算法。这样，无需使用任何专门的优化工具箱即可非常快速地解决GPTSVM的双重问题。