中文摘要：

基于广义特征值的最接近支持向量机（Proximal Support VectorMachinevia Generalized Eigenvalues，GEPSVM）是一种新的具有与SVM性能相当的两分类方法，通过求解广义特征值来获得两个彼此不平行的拟合两类样本的超平面．其决策是将测试样本归为距其最近的超平面所在的类．然而，该规则在某些情形会导致较差的分类结果．对此，在GEPSVM基础上，通过在类拟合超平面上寻找一个包含了所有训练样本投影的局部凸区域，来决定样本的类别．该局部方法不仅具有较GEPSVM更优的分类性能，同时还衍生出了求解超平面上凸壳的简单且易于核化的新算法．最后在人工和UCI数据集上获得了验证．

英文摘要：

A binary classifier termed as proximal support vector machine via generalized eigenvalues （GEPSVM）, is proposed recently. It aims to obtain two nonparallel planes generated from their corresponding generalized eigenvalue problem and has equivalent test correctness to SVM. In nature, GEPSVM attempts fitting two-class points with two planes. For an unseen sample, according to decision rule of GEPSVM, it will be assigned to the closest planes. In fact, this rule, in most cases, may result in poor test correctness. In this paper, based on GEPSVM, a new classifier named Localized GEPSVM is presented. Instead of two fitting planes, an unknown sample will be classified to the closest localized planes, i. e. , convex hull, which are generated from the projections of two-class training points, respectively. Compared to GEPSVM, LGEPS- VM outperforms GEPSVM in test correctness. Derivatively, LGEPSVM also develops an algo- rithm for solving convex hull on the projective hyperplane. Besides simple geometrical interpretation, this algorithm eases up to kernel version. Finally, Test accuracy of LGEPSVM algorithms will be validated on some artificial and real UCI datasets.