摘要
针对正定核函数的支持向量机所导出的凸二次优化问题,提出了一个离散型神经网络模型。利用Karush-Kuhn-Tucker(KKT)条件和投影理论构造投影方程,使得投影方程的解与优化问题的解一一对应;进一步基于投影方程建立离散神经网络;理论结果表明,网络的平衡点与优化问题的最优解相对应,且网络具有全局指数收敛性。相比于连续网络,所提出的网络结构简单,减少了计算的复杂度;所得理论结果保证了网络能够有效求解支持向量机中的优化问题。最后,利用分类问题和标准数据集进行实验,数值结果验证了本文所设计的网络在求解支持向量机优化问题的有效性。
This paper proposes a discrete-time neural network model to solve the convex optimization problem deduced by a positive-kernel-based support vector machine(SVM).First,the projection equations are constructed through the Karush-Kuhn-Tucker(KKT)conditions and projection theory so that there exists a one-to-one correspondence between the solution of projection equations and the optimal solution of optimization problem,and then a discrete-time neural network was constructed by projection equations.Second,the obtained theoretical results indicate that the equilibrium point of the proposed neural network corresponds to the optimal solution of the optimization problem,and the proposed neural network is globally exponentially convergent.Compared with some continuous neural networks,the architecture of proposed neural network is simple,which decreases the computational complexity.Finally,some classification problems and benchmarking data sets are used in the experiment.The numeral results show the efficiency of the proposed neural network for solving the optimization problem in SVM.
作者
刘凤秋
张红旭
LIU Feng-qiu;ZHANG Hong-xu(School of Applied Sciences,Harbin University of Science and Technology,Harbin 150080,China)
出处
《哈尔滨理工大学学报》
CAS
北大核心
2018年第4期133-139,144,共8页
Journal of Harbin University of Science and Technology
基金
国家自然科学基金(11201100)
黑龙江省自然科学基金(A201213)
关键词
离散神经网络
支持向量机
凸优化
全局指数收敛
discrete-time neural network
support vector machine
convex optimization
global exponential convergent
