Multiple sub-hyper-spheres support vector machine for multi-class classification

Support vector machine (SVM) is originally proposed to solve binary classification problem. Multi-class classification is solved by combining multiple binary classifiers, which leads to high computation cost by introducing many quadratic programming (QP) problems. To decrease computation cost, hyper-sphere SVM is put forward to compute class-specific hyper-sphere for each class. If all resulting hyper-spheres are independent, all training and test samples can be correctly classified. When some of hyper-spheres intersect, new decision rules should be adopted. To solve this problem, a multiple sub-hyper-sphere SVM is put forward in this paper. New algorithm computed hyper-spheres by SMO algorithm for all classes first, and then obtained position relationships between hyper-spheres. If hyper-spheres belong to the intersection set, overlap coefficient is computed based on map of key value index and mother hyper-spheres are partitioned into a series of sub-hyper-spheres. For the new intersecting hyper-spheres, one similarity function or same error sub-hyper-sphere or different error sub-hyper-sphere are used as decision rule. If hyper-spheres belong to the inclusion set, the hyper-sphere with larger radius is partitioned into sub-hyper-spheres. If hyper-spheres belong to the independence set, a decision function is defined for classification. With experimental results compared to other hyper-sphere SVMs, our new proposed algorithm improves the performance of the resulting classifier and decreases computation complexity for decision on both artificial and benchmark data set.