Abstract
The Support vector machines can be posed as quadratic program problems in a variety of ways.This paper investigates a formulation using the two-norm for the misclassification error and appending a bias norm to objective function that leads to a positive definite quadratic program only with the nonnegative constraint under a duality construction. An unconstrained convex program problem, which minimizes a differentiable convex piecewise quadratic function, is proposed as the Lagrangian dual of the quadratic program. Then an exact semismooth Newton support vector machine (ESNSVM) is obtained to solve the program speedily. Some numerical experiments demonstrate that our algorithm is very efficient comparing with the similar algorithms such as LSVM.
This work was supported in part by the National Natural Science Foundation of China under Grant No.60572150 and the Scientific Research Foundation of Weinan Normal Institute under Grant No.06YKS021.
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Shui-Sheng, Z., Hong-Wei, L., Jiang-Tao, C., Li-Hua, Z. (2006). Exact Semismooth Newton SVM. In: Jiao, L., Wang, L., Gao, Xb., Liu, J., Wu, F. (eds) Advances in Natural Computation. ICNC 2006. Lecture Notes in Computer Science, vol 4221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881070_23
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DOI: https://doi.org/10.1007/11881070_23
Publisher Name: Springer, Berlin, Heidelberg
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