基于最佳一致光滑逼近的孪生支持向量机研究

RESEARCH ON TWIN SUPPORT VECTOR MACHINES BASED ON BEST UNIFORM SMOOTHING APPROXIMATION

孪生支持向量机本质为两个二次规划问题,对于其目标函数中约束变量取正号不可微特性,提出一种基于最佳一致逼近的多项式光滑函数构建方法。分别以Bernstain多项式和Chebyshev多项式进行正号函数最佳一致有效光滑逼近。重点突出Chebyshev多项式的最佳一致逼近过程,使用Remez算法构造最佳一致Chebyshev多项式,讨论各阶Chebyshev多项式逼近状况。最后综合最佳一致逼近多项式和样本适应度构建目标优化函数,采用快速Newton-Armijo算法求解目标优化函数,基于UCI数据验证了方法的优越性。

The essence of twin support vector machines（TWSVM） is to optimise two quadratic programming problems. As the positive constrained variable of objective function was not differentiable, this paper presented a constructing method of polynomial smoothing function based on best uniform approximation. Bernstein and Chebyshev polynomial were established to effectively achieve the best uniform smoothing approximation of the positive function. The best uniform approximation of Chebyshev polynomial is emphasized. The best uniform Chebyshev polynomial was established by applying the Remez algorithm, and each order of the Chebyshev polynomial approximation was discussed. Finally, the objective optimal function based on best uniform approximation polynomial and the degree of sample adaption could be got, and the fast Newton-Armijo algorithm was used for solving the objective optimal function. On the basis of UCI data, we validated the advantages of the method.