Accurate on-line ν-support vector learning

The nu-Support Vector Machine (nu-SVM) for classification proposed by Scholkopf et al. has the advantage of using a parameter v on controlling the number of support vectors and margin errors. However, comparing to standard C-Support Vector Machine (C-SVM), its formulation is more complicated, up until now there are no effective methods on solving accurate on-line learning for it. In this paper, we propose a new effective accurate on-line algorithm which is designed based on a modified formulation of the original nu-SVM. The accurate on-line algorithm includes two special steps: the first one is relaxed adiabatic incremental adjustments; the second one is strict restoration adjustments. The experiments on several benchmark datasets demonstrate that using these two steps the accurate on-line algorithm can avoid the infeasible updating path as far as possible, and successfully converge to the optimal solution. It achieves the fast convergence especially on the Gaussian kernel and is faster than the batch algorithm. (C) 2011 Elsevier Ltd. All rights reserved.