基于自适应调节极大熵的孪生支持向量回归机

Twin support vector regression based on adaptive adjustment maximum entropy

孪生支持向量回归机(Twin Support Vector Regression,TSVR)的数学模型是求解一对约束优化问题,如何将约束优化问题转化为无约束优化问题进行求解是一个难题.在TSVR约束优化模型的基础上,依据最优化理论提出TSVR的无约束优化问题.然而,无约束优化问题的目标函数有可能不可微,为解决这个问题,引入极大熵函数,确保优化问题都是可微的.标准的极大熵函数法有可能发生数值溢出,所以对极大熵函数法进行了改进,提出自适应调节极大熵函数法来逼近TSVR的不可微项,并提出基于自适应调节极大熵函数法的TSVR学习算法.实验结果表明,和其他回归方法相比,所提算法不仅能够提高回归精度,而且效率得到了较大的提高.

The mathematical model of twin support vector regression(TSVR)is to solve a pair of constrained optimization problems.How to transform constrained optimization problems into unconstrained optimization problems is a difficult problem.Based on the TSVR constrained optimization model,the unconstrained optimization problem of TSVR is established according to the optimization theory.In order to solve the problem of unconstrained optimization,the maximum entropy function is introduced to transform the original optimization problem into a differentiable unconstrained optimization problem.However,the standard maximum entropy function method may lead to the occurrence of numerical spillovers.In this paper,we improve the maximum entropy function method,propose the adaptive maximum entropy function method,and use it to approximate the non-differentiable term of TSVR.We propose a TSVR model based on the adaptive maximum entropy function method.The experimental results show that compared with other regression methods,the proposed algorithm can not only improve the regression accuracy,but also greatly improve the efficiency.