一种基于调和均值的模糊聚类算法

k调和均值算法用数据点与所有聚类中心的距离的调和平均替代了数据点与聚类中心的最小距离，是一种减小初始值影响聚类结果的有效的聚类方法。本文对k调和均值算法进行扩展，考虑到数据点同时对不同聚类的隶属关系，将模糊的概念应用到聚类中，提出了模糊k调和均值-Fuzzv K—Harmonic Means(FKHM)算法。在中心迭代聚类算法的统一框架的基础上，推导出FKHM算法聚类中心的条件概率表达式以及在迭代过程中的数据点加权函数表达式。以划分相似度作为聚类结果的评价准则，实验表明，FKHM算法在聚类对于初值不敏感的同时提高了聚类结果的精确度，达到较好的聚类效果。

A Fuzzy Clustering Algorithm Based on K-Harmonic Means

The k-harmonic means clustering algorithm is an effective method to avoid the dependency of the performance of clustering on the initialization of the clustering centers. Considering the fact that the same data may belong to several clusters to some extent at the same time, the fuzzy membership concept of data is used in the process of clustering, the fuzzy k-harmonic means clustering algorithm is thus proposed. Unified expression for the iterative of centers is described as to deduce the conditional probability expression of the centers and data weight functions for FKHM. Finally, the partition similitude is used to evaluate the result of clustering. Experiment result indicates that not only the fuzzy k-harmonic means algorithm is less sensitive to the initialization of centers, but also the quality of clustering results can be improved compared with k-harmonic means.