最值间距支持向量机

计算机科学 ›› 2012, Vol. 39 ›› Issue (4): 205-209.

最值间距支持向量机

王至超,张化祥

(山东师范大学信息科学与工程学院济南250014);(山东省分布式计算机软件新技术重点实验室济南250014)

出版日期:2018-11-16 发布日期:2018-11-16

Twin Distance of Minimum and Maximum Support Vector Machine

Online:2018-11-16 Published:2018-11-16

摘要/Abstract

摘要： GEPSVM(Proximal Support Vcctor Machine Classification via Gcncralizcd Eigcnvalucs)是近年提出来的一种新的二分类SVM，其核心思想是通过求解广义特征方程得到两个最优超平面，然后通过计算样本到超平面的距离来决定样本所属类别。与传统SVM相比，GEPSVM降低了时间复杂度，但仍存在奇异性等问题。提出了一种新的算法 TDMSVM(Twin Distance of Minimum and Maximum Support Vector Machine)，其通过求解标准特征方程得到两个最优超平面，使超平面满足到本类样例的平均距离最小化，同时到另一类样例的平均距离最大化。通过理论分析和实验证明，与C}EPSVM相比，`I'DMSVM有以下优势:进一步降低了时间复杂度;不需引入正则项，从而提高了泛化性能; 克服了奇异性。

关键词: 模式识别，特征向量，支持向量机，拉格朗日乘子法

Abstract: GEPSVM is a newly proposed binary SVM in recent years. It learns two optimal hyperplanes by solving the generalized eigenequation and determines the categories of patterns based on the distances between test sample and the two hyperplanes. Compared with traditional SVM, GEPSVM can reduce the time complexity, but it still leaves singulari- ty issues unsolved. This paper introduced a new algorithm丁DMSVM(Twin Distance of Minimum and Maximum Sup- port Vector Machinc)which seeks two optimal hyperplanes through solving the standard eigenequation and requires the minimal average distance between the same class of samples and hyperplanes. Compared with GEPSVM, I}DMSVM has the following advantages:it further reduces the time complexity and does not rectuire the introduction of regular items which improves the generalization performance and avoids singularity.

Key words: Pattern recognition,Eigenvector,Support vector machine,I_agrange multiplier method

王至超,张化祥. 最值间距支持向量机[J]. 计算机科学, 2012, 39(4): 205-209. https://doi.org/

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