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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (4): 455-461    DOI:
    
The study on the optimize algorithm of support vector machine based on variational inequalities
YUAN Yu-ping1, AN Zeng-long2, SHA Qi1
1. Information and Computation Sci., Heilongjiang Bayi Agricultural Univ., Daqing 163319, China;
2. Economics and Management Sci., Heilongjiang Bayi Agricultural Univ., Daqing 163319, China
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Abstract  Since the standard support vector machine model is a quadratic programming, the algorithm process will be more and more complicated with the increasing size of the data. In this article, a new model of a strictly convex quadratic programming is constructed which is based on the K-SVCR algorithm. The main feature of the present model is that it can transform the first-order optimality conditions into the variational inequality problems, and turn complementary problems into smooth equations by the use of the Fischer-Burmeister (FB) function. A more smooth and faster Newton algorithm is established. And this article expounds that the generated sequence by the algorithm is global convergent. After testing a standard data set, the efficiency of the algorithm was proposed. The algorithm has better performance on the training accuracy and run-time compared with the K-SVCR algorithm. The results of this experiment indicate that this algorithm was feasible and efficient.

Key words： variational inequality      support vector machine(SVM)      Newton algorithm      linear complementarity     
Received: 04 August 2015      Published: 01 December 2018
CLC:  TP181  
  TP391  
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YUAN Yu-ping
AN Zeng-long
SHA Qi
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YUAN Yu-ping, AN Zeng-long, SHA Qi. The study on the optimize algorithm of support vector machine based on variational inequalities. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 455-461.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I4/455


基于变分不等式的支持向量机优化算法研究

由于标准支持向量机模型是一个二次规划问题, 随着数据规模的增大, 求解 算法过程会越来越复杂. 在K-SVCR算法结构的基础上, 构造了严格凸的二次规划 新模型, 该模型的主要特点是可以将其一阶最优化条件转化为变分不等式问题, 利 用Fischer-Burmeister (FB)函数将互补问题转化为光滑方程组; 建立光滑快速牛顿算 法求解, 并证明了该算法所产生的序列是全局收敛; 利用标准数据集测试提出算法的 有效性, 在训练正确率和运行时间上与K-SVCR算法相比都有较好的表现, 实验结果 表明该算法可行且有效.

关键词： 变分不等式,  支持向量机,  牛顿算法,  线性互补 
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