引用本文:刘峤,方佳艳.定点孪生支持向量机[J].控制与决策,2020,35(2):272-284
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定点孪生支持向量机
刘峤,方佳艳
( 电子科技大学信息与软件工程学院,成都611731)
摘要:
孪生支持向量机(TWSVM)以及最近提出的各种变体模型均是在高维空间内独立求解两个带有约束条件的对偶二次规划问题(QPP).然而,由于每个对偶的QPP所需求解的对偶变量的数量由他类样本的数量决定,当需要处理大规模数据集时,这种直接求解标准QPP的方法将会导致非常高的计算复杂度.为此,提出一种改进的孪生支持向量机模型,称为定点孪生支持向量机(FP-TWSVM).所提模型将传统的TWSVM及其变体模型中处在高维空间内的对偶QPP转化成一系列有限个一维空间内的单峰函数优化问题.可以采用高效的线性搜索方法求解这些一维的单峰函数优化问题,例如斐波那契算法、黄金分割法.在标准数据集包括大规模数据集上的数值实验验证了FP-TWSVM算法的有效性.实验结果表明,FP-TWSVM在保持与其他模型相当的分类精度的同时,具有更快的训练速度,消耗更少的内存空间.
关键词:  孪生支持向量机  定点  单峰函数  线性搜索方法  二次规划
DOI:10.13195/j.kzyjc.2018.0531
分类号:TP181
基金项目:国家自然科学基金重点项目(61133016);国家自然科学基金面上项目(61772117);四川省科技厅科技支撑项目(2017GZ0308);十三五装备预研领域基金项目(61403120102).
Fixed-point twin support vector machine
LIU Qiao,FANG Jia-yan
(School of Information and Software Engineering,University of Electronic Science and Technology of China,Chengdu611731,China)
Abstract:
The twin support vector machines(TWSVMs) and the recently proposed variant models are all designed to solve two dual quadratic programming problems(QPPs) with constraint conditions independently in high dimensional space. However, since each dual QPP involves a set of dual variables with its size determined by the number of samples of other classes, when we need to cope with large-scaled datasets, the method of directly solving QPP will lead to very high computational complexity. Therefore, this paper proposes an improved twin support vector machine model, known as a fixed-point TWSVM(FP-TWSVM). This model transforms the traditional TWSVM and its variant models into a series of unimodal function optimization problems in one-dimensional space. Efficient linear search methods are used such as Fibonacci algorithm and golden section method to solve these one-dimensional unimodal function optimization problems. The validity of FP-TWSVM algorithm is verified by numerical experiments on several datasets including large datasets. The experimental results show that the FP-TWSVM has faster training speed and consumes less memory space while maintaining vertically the same classification accuracy as other models.
Key words:  twin support vector machine  fixed-point  unimodal function  line search methods  quadratic programming

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