CCH-based geometric algorithms for SVM and applications

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CCH-based geometric algorithms for SVM and applications

The support vector machine (SVM) is a novel machine learning tool in data mining. In this paper, 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 solids for data sets; meanwhile, it is easy to give the necessary and sufficient condition for determining its extreme points. As practical applications of CCH, spare and probabilistic speed-up geometric algorithms are developed. Results of numerical experiments show that the proposed algorithms can reduce kernel calculations and display nice performances.

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作 者: Xin-jun PENG Yi-fei WANG  
作者单位:Xin-jun PENG(Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;Scientific Computing Key Laboratory of Shanghai Universities,Shanghai Normal University,Shanghai 200234,P.R.China)
5MvJk K2f:t$[TN0Yi-fei WANG(Department of Mathematics,Shanghai University,Shanghai,200444,P.R.China) 
刊 名:应用数学和力学(英文版)  EI SCI
英文刊名:APPLIED MATHEMATICS AND MECHANICS 
年,卷(期):2009 30(1) 
分类号:O3 
关键词:support vector machine(SVM)   compressed convex hull   kernel parameter   geometric approach   probailistic speed-up  
机标关键词:support vector machineconvex hullnumerical experimentssufficient conditionmachine learningextreme pointsdata mining 
基金项目:国家自然科学基金,国家高技术研究发展计划(863计划),国家高技术研究发展计划(863计划),上海市重点学科建设项目 
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