基于核密度估计的层次聚类算法

聚类分析是统计、模式识别和数据挖掘等领域中一个非常基础且非常重要的研究课题，具有广泛的应用前景。在众多的聚类方法中，基于密度的方法是一种相当有效的聚类方法，能够发现任意形状的聚类，对噪声数据不敏感，但是聚类结果严重依赖于用户参数的合理选择。以DENCLUE算法为基础，一种基于核密度估计的层次聚类算法被提出，该算法首先优选窗宽σ产生较好的核密度估计结果，然后以密度函数的局部极大值点为聚类中心形成数据的初始划分，最后根据密度函数的鞍点递归合并初始聚类产生不同层次的划分模式。理论分析和仿真实验结果显示，该算法能够发现任意形状、大小和密度的聚类，能够有效处理噪声数据，而且聚类结果不依赖于用户参数的仔细选择。

Hierarchical Clustering based on Kernel Density Estimation

Clustering is a promising application area for many fields including statistics, pattern recognition, data mining, etc. Among many clustering techniques, density-based method is one of the effective and efficient clustering methods that can discover clusters with arbitrary shape and is insensitive to noise data. According to the DENCLUE algorithm, we present a new hierarchical clustering approach based on kernel density estimation. In our approach, the window-width s is optimized to obtain good density estimation, then the density attractors are chosen to generate the center-defined data partition, and finally the center-defined clusters are iteratively merged into a hierarchy of clusters according to the saddles of density function. Theory analysis and experimental results show that this approach not only keeps the good features of DENCLUE, but also requires no input parameters and can discover clusters with arbitrary shapes and densities at different levels.