马氏度量下局部化广义特征值最接近支持向量机

Localized GEPSVM Based on Mahalanobis Metric

局部化广义特征值最接近支持向量机(Localized GEPSVM,LGEPSVM)是从广义特征值最接近支持向量机(GEPSVM:Proximal Support Vector Machine via Generalized Eigenvalues)衍生而来,其原理是在GEPSVM通过求解广义特征值获得两个彼此不平行的超平面的基础上,分别求解两个超平面的凸壳,修改GEPSVM的分类判据为将测试样本归为距其最近凸壳所属的那一类.分析和实验表明,LGEPSVM较之GEPSVM具有更高的分类精度.然而,由于LGEPSVM在训练和分类过程中都涉及凸壳计算问题,因而费时较多.为了缓解这一问题,本文提出的基于马氏度量的最小椭圆凸壳算法MLGEPSVM(LGEPSVM based on Mahalanobis Metric),即分类时只需要判断样本与对应椭圆凸壳的距离.较之LGEPSVM和GEPSVM,MLGEPSVM具有如下几个特点:(1)给出了马氏度量下的椭圆凸壳计算方法,(2)分类速度更快,(3)更低的存储空间,每类样本仅需存储椭圆凸壳(可通过中心和协方差表示),而不是所有的凸壳顶点.在人工和标准数据集上的实验,验证了MLGEPSVM的上述性能.

GEPSVM(Proximal Support Vector Machine via Generalized Eigenvalues)have been played more attention in machine learning and pattern recognition.It adopts data fitting to construct classifier,and further leading to two Generalized Eigenvalue problems.One of its variants is Localized GEPSVM,shortly LGEPSVM.Instead of the closest nonparallel planes of GEPSVM,LGEPSVM classifies an unknown sample to the closest convex hulls on the projection plane.Experimental results show that LGEPSVM able to achieve comparable or even better test correctness than GEPSVM.However,due to training convex hull,LGEPSVM would cost much time in training stage.To speed training LGEPSVM,in this paper,we propose a new version LGEPSVM,termed as MLGEPSVM,based on Mahalanobis metric.Concretely,MLGEPSVM aims to find two ellipsoidal convex hulls,and then classify the samples to the class corresponding to its closest ellipsoid.Compared to LGEPSVM and GEPSVM,advantages of MLGEPSVM lie in three aspects:(1)calculation method of ellipsoid convex hull,(2)faster classification speed,and(3)less storage requirement,only ellipsoid convex hull of each class will be stored(the sample center and covariance matrix).Finally,analysis and experiments on artificial and UCI benchmark datasets will validate our foresaid superiorities.