中文摘要：

投影孪生支持向量机（PTSVM）是最近提出的一种具有较好泛化性能的分类模型,但由于采用内点算法求解二次规划问题,PTSVM的训练速度较慢。针对该缺陷,提出一种快速的、基于几何算法的PTSVM（GPTSVM）。遵循PTSVM的几何思想,提出一种新的二次规划模型,为每类数据产生一个投影方向;然后基于优化理论推导该模型的对偶问题并给予明确的几何解释,并利用计算几何算法求解。实验表明,提出的方法具有更快的训练速度和更好的泛化性能。

英文摘要：

Projection twin support vector machine（ PTSVM） is a recently developed pattern classification algorithm with good generalization performance. However,the training speed of PTSVM is slow because it has to solve quadratic programming（ QP） problem using interior point algorithm. To overcome this drawback,this paper proposed a novel model based on computational geometry with fast training speed. First,in the spirit of PTSVM,this paper presented a novel QP model in order to generate a projection axis for a class. The corresponding dual problem is derived on the basis of optimization theory. It owned an explicit geometric interpretation and could be solved by using computational geometry algorithm. The experimental results show that the proposed method owns faster training speed and achieves better generalization performance in comparison with PTSVM.