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.
