| 基于CCH的SVM几何算法及其应用 |
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| 引用本文： | 彭新俊,王翼飞.基于CCH的SVM几何算法及其应用[J].应用数学和力学(英文版),2009,30(1):89-100. |
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| 作者姓名： | 彭新俊 王翼飞 |
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| 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);Yi-fei WANG(Department of Mathematics,Shanghai University,Shanghai,200444,P.R.China)
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| 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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| 摘 要： | 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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| 关 键 词： | 模式识别理论 人工智能 控制论 SVM |
| 收稿时间： | 2008-05-16 |
CCH-based geometric algorithms for SVM and applications |
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| Xin-jun Peng,Yi-fei Wang.CCH-based geometric algorithms for SVM and applications[J].Applied Mathematics and Mechanics(English Edition),2009,30(1):89-100. |
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| Authors: | Xin-jun Peng Yi-fei Wang |
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| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China;
2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University,Shanghai 200234, P. R. China;
3. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | 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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| Keywords: | support vector machine(SVM) compressed convex hull kernel parameter geometric approach probailistic speed-up |
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