球结构支持向量机的改进算法及仿真研究

Improved Algorithm Based on Sphere Structure SVMs and Simulation

球结构支持向量机算法将多类样本数据的每一类用各自的超球来界定,从而显著地降低了二次规划的复杂程度。在该算法的基础上,提出了子超球支持向量机多分类算法。新算法改进了超球重叠区域的训练和决策方法,提高了多分类问题的分类精度。定义了重叠频数、重叠总频数和重叠率等概念,并在此基础上分析了径向基核函数的参数σ对超球相互位置的影响。对两组实际数据仿真实验验证了该算法的有效性和对σ分析的正确性,同时表明正确选择σ可得到较高的分类精度。

Sphere structure SVMs classify multi-class data by their own hyperspheres,so the computational complexity of a quadratic programming problem is reduced obviously.Based on sphere structure SVMs,a new algorithm called sub-hypersphere SVMs was proposed to solve multi-class classification problems.It improved the method of training and judging in the overlap of the hyperspheres to improve classification precision.The definitions,overlap numbers and total overlap numbers and overlap ratio,were given which were relative to the overlap of the hyperspheres.According to the definitions above,the effect of the kernel parameterσ（radial basis function）was analyzed on the position of hyperspheres. Simulations were performed on two groups of real data.The results show that the new algorithm is effective and the analysis ofσis correct.