【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 揭示了基于网格上密度函数近似的聚类算法与核密度估计理论之间的关系更多还原

【Abstract】 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更多还原