Regularization Path for ν-Support Vector Classification

doi:10.1109/TNNLS.2012.2183644

Regularization Path for ν-Support Vector Classification

2012-05-01

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DOI：10.1109/TNNLS.2012.2183644

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The nu-support vector classification (nu-SVC) proposed by Scholkopf et al. has the advantage of using a regularization parameter. for controlling the number of support vectors and margin errors. However, compared to C-SVC, its formulation is more complicated, and to date there are no effective methods for computing its regularization path. In this paper, we propose a new regularization path algorithm, which is designed on the basis of a modified formulation of nu-SVC and traces the solution path with respect to the parameter.. Through theoretical analysis and confirmatory experiments, we show that our algorithm can avoid the infeasible updating path under several assumptions (i.e., Assumptions 1 and 2), and fit the entire solution path in a finite number of steps. When the regularization path of nu-SVC is available, a novel approach proposed by Yang and Ong can be applied to obtain the global optimal solution of common validation functions for nu-SVC, and the computation for the whole process is minimal. Numerical experiments show that it is more efficient than various kinds of grid search methods for selecting the optimal regularization parameter nu.

Keywords:

Model selection

nu-support vector classification regularization

solution path

Regularization Path for ν-Support Vector Classification

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