Laplace核函数的衰减系数研究

Study on Parametric Problem of Laplace Kernel

核函数的衰减系数是影响核函数方法分类性能的重要因素。分析了信号分析理论中关于采样信号的不失真重建问题与Parzen窗函数方法的关系,讨论了核函数残留边带信息量与指定采样频率条件下特征变量的自信息量之间的关系。推导了Laplace核函数在均匀采样条件下的衰减系数的计算公式,分析并给出了非均匀采样情况下衰减系数计算和处理方法。实验结果表明,与传统的基于Gauss核函数的Parzen窗函数法、经典的KNN方法、BP神经网络以及SVM方法相比,提出的Laplace核函数参数设置方法具有较高的总体分类性能。

Parameters of kernel functions are important factors which affect the classification performance heavily. By analyzing the relation between the distortionless rebuilding issue in the field of signal analysis and the Parzen window method, as well as the relation based on information content between the self-entropy of variables and information included in rudimental band, an approximate equation for calculating the parameter of Laplacian kernel was discussed both in ideal condition and in practical applications. Experimental results show that the proposed method coming from the analystical result performs better than many famous classifiers in the mass, including Parzen window method with Gaussian kernel, the k-nearest neighbor rule, BP, and SVM.