CCH-based geometric algorithms for SVM and applications

作者：Peng Xin jun^*; Wang Yi fei

来源：Applied Mathematics and Mechanics, 2009, 30(1): 89-100.

DOI：10.1007/s10483-009-0110-6

• support vector machine (SVM)
• compressed convex hull
• kernel parameter
• geometric approach
• probabilistic speed-up

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.

• 出版日期2009-1
• 单位上海师范大学; 上海大学