基于CCH的SVM几何算法及其应用  

CCH-Based Geometric Algorithms for SVM and the Applications

作　　者：彭新俊[1,2] 王翼飞[3] 

机构地区：[1]上海师范大学计算数学系,上海200234 [2]科学计算上海高校重点实验室,上海200234 [3]上海大学数学系,上海200444

出　　处：《应用数学和力学》2009年第1期90-100,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(30571059);国家高科技研究发展计划(863)专项资助项目(2006AA02Z190);上海市重点学科资助项目(S30405)

摘　　要：支持向量机(support vector machine(SVM))是一种数据挖掘中新型机器学习方法.提出了基于压缩凸包(compressed convex hull(CCH))的SVM分类问题的几何算法.对比简约凸包(reduced convex hull(RCH)),CCH保持了数据的几何体形状,并且易于得到确定其极点的充要条件.作为CCH的实际应用,讨论了该几何算法的稀疏化方法及概率加速算法.数值试验结果表明所讨论的算法可降低核计算并取得较好的性能.The support vector machine （SVM） is a novel machine learning tool in data mining. The geometric approach based on the compressed convex hull （CCH） with a mathematical framework is introduced to solve SVM classification problems. Compared with the reduced convex hull （RCH）, CCH preserves the shape of geometric solid for the data set; meanwhile,it is easy to give the necessary and sufficient condition of determining its extreme points. As the practical applications of CCH, spare and probabilistic speed-up geometric algorithms were developed. Results of some numerical experiments show that the proposed algorithms can reduce the kernel evaluation and display nice performances.

关 键 词：支持向量机 压缩凸包 核参数 几何方法 概率加速 

分 类 号：O235[理学—运筹学与控制论] TP18[理学—数学]