A Fast Algorithm of SVM Based on Geometry
基于几何思想的快速支持向量机算法

In the paper, based on geometry theory, a new fast iterative algorithm for support vector machine(SVM) classifier design is presented. It is known that the optimal hyper-plane of SVM is completely constructed using its support vectors. Once all support vectors of two classes are identified, the optimal hyper-plane can be determined. Based on geometric distribution of the trained sample points, the new algorithm establishes an initial candidate support vectors set by locating the two closest points of the two opposite class. The new algorithm starts from two closest points of the opposite classes to seek the support vectors accumulatively. The new algorithm continually seeks the points which are the violators of KKT condition as support vectors. At last, the new algorithm acquires all support vectors and establishes an optimal hyper-plane. To validate the new algorithm, some experiments which compare the new algorithm with the SMO algorithm and DIRECTSVM algorithm are performed. The experimental results have shown the generalization ability of the new algorithm is the same as that of SMO algorithm and DIRECTSVM algorithm. The speed of the new algorithm is superior to the other two algorithms.