一种基于Newton-Armijo优化的多项式光滑孪生支持向量机

A polynomial smooth twin support vector machines based on Newton-Armijo optimization

针对光滑孪生支持向量机(smooth twin support vector machines,STWSVM)采用的Sigmoid光滑函数逼近精度低的问题,提出一种基于Newton-Armijo优化的多项式光滑孪生支持向量机(polynomial smooth twin support vector machines based on Newton-Armijo optimization,PSTWSVM-NA)。在PSTWSVM-NA中,引入正号函数,将孪生支持向量机的两个二次规划问题转化为两个不可微的无约束优化问题。随后,引入一族多项式光滑函数对不可微的无约束优化问题进行光滑逼近,并用收敛速度快的Newton-Armijo方法求解新模型。从理论上证明了PSTWSVM-NA模型具有任意阶光滑性,在人工数据和UCI数据集上的实验结果表明该算法具有较高的分类精度和较快的训练效率。

In order to solve the problem of low approximation accuracy of sigmoid smooth function adopted by smooth twin support vector machines(STWSVM),a polynomial smooth twin support vector machines based on Newton-Armijo optimization(PSTWSVM-NA)is proposed.In PSTWSVM-NA,the positive sign function is introduced to transform two quadratic programming problems of TWSVM into two non-differentiable unconstrained optimization problems.Then,a family of polynomial smooth functions are introduced to smooth the non-differentiable unconstrained optimization problem,and Newton Armijo method with fast convergence speed is used to solve the new model.It is proved theoretically that the PSTWSVM-NA model has any order smoothness.Experimental results on artificial data and UCI data sets show that the algorithm has higher classification accuracy and faster training efficiency.