核密度估计及其在聚类算法构造中的应用  

Kernel Density Estimation and Its Application to Clustering Algorithm Construction

作　　者：李存华[1] 孙志挥[1] 陈耿[1] 胡云[1] 

机构地区：[1]东南大学计算机科学与工程系

出　　处：《计算机研究与发展》2004年第10期1712-1719,共8页Journal of Computer Research and Development

基　　金：国家自然科学基金项目 ( 70 3 710 15 );国家科技部中小型企业创新基金项目 ( 0 2C2 62 13 2 10 0 70 );江苏省教育厅自然科学基金项目( 0 2KJB5 2 0 0 12 )

摘　　要：经典数理统计学中的核密度估计理论是构造基于数据集密度函数聚类算法的理论基础 ,采用分箱近似的快速核密度函数估计方法同样为构造高效的聚类算法提供了依据 通过对核密度估计理论及其快速分箱核近似方法的讨论 ,给出分箱近似密度估计相对于核密度估计的均方误差界 ,提出基于网格数据重心的分箱核近似方法 在不改变计算复杂度的条件下 ,基于网格数据重心的分箱核近似密度函数计算可以有效地降低近似误差 ,这一思想方法对于构造高效大规模数据聚类分析算法具有指导意义Kernel density estimation provides solid foundation for density based clustering algorithm construction While binned approximation is shown to be an efficient mechanism for fast kernel density computation, it is also proven to be a promising approach to construct robust clustering algorithms This paper deals with formation and accuracy of the binned kernel density estimators, presents mean squared error bounds for the closeness of such estimators to the unbinned kernel density estimators To improve the accuracy of the binning method, a nave grid level approximated density estimator is constructed, followed by a detailed proof of its mean squared error bounds The improved approach constructs binned density estimator by substituting the center of a grid with the gravity center of the data points, which results in better estimation accuracy without loss of computation efficiency As a main concern, the close relation between the density based clustering algorithms and the kernel estimation methods is revealed

关 键 词：核密度估计 分箱规则 聚类算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]