求解互补支持向量机的非单调信赖域算法

求解支持向量机的核心问题是对一个大规模凸二次规划问题进行求解。基于支持向量机的修正模型,得到一个与之等价的互补问题,利用Fischer-Burmeister互补函数,从一个新的角度提出了求解互补支持向量机的非单调信赖域算法。新算法避免了求解Hesse矩阵或矩阵求逆运算,减少了工作量,提高了运算效率。在不需要任何假设的情况下,证明算法具有全局收敛性。数值实验结果表明,对于大规模非线性分类问题,该算法的运行速度比LSVM算法和下降法快,为求解SVM优化问题提供了一种新的可行方法。

A non-monotonic trust region algorithm for solving complementary support vector machine

Solving a large-scale convex quadratic programming problem is the core of the support vector machine. An equivalence complementarity problem can be obtained based on an amended model of the surpport vector machine(SVM), therefore we propose a non-monotonic trust region algorithm for solving the complementarity problem based on the Fischer-Burmeister complementarity function. The new algorithm need not compute any Hesse or the inverse matrix, thus reducing the amount of computational work. Global convergence of the algorithm is proved without any assumptions. Numerical experiments show that the running speed of the algorithm is faster than that of the LSVM algorithm and the descent algorithm when solving large scale nonlinear classification problems and thus it provides a feasible method for solving SVM.