A generalized S–K algorithm for learning <f>ν</f>-SVM classifiers

The S–K algorithm (Schlesinger–Kozinec algorithm) and the modified kernel technique due to Friess et al. have been recently combined to solve SVM with <f>L2</f> cost function. In this paper, we generalize S–K algorithm to be applied for soft convex hulls. As a result, our algorithm can solve <f>ν</f>-SVM based on <f>L1</f> cost function. Simple in nature, our soft algorithm is essentially a algorithm for finding the <f>ε</f>-optimal nearest points between two soft convex hulls. As only the vertexes of the hard convex hulls are used, the obvious superiority of our algorithm is that it has almost the same computational cost as that of the hard S–K algorithm. The theoretical analysis and some experiments demonstrate the performance of our algorithm. [Copyright &y& Elsevier]