新的基于数据几何结构的聚类有效性函数  

Novel clustering validity function based on the geometry structure of data

作　　者：赵恒[1] 张高煜[1] 胡海虹[1] 

机构地区：[1]西安电子科技大学电子工程学院,陕西西安710071

出　　处：《系统工程与电子技术》2007年第1期96-98,共3页Systems Engineering and Electronics

基　　金：国家自然科学基金(60402038);武器装备预研基金(5141707304DZ0167)资助课题

摘　　要：以Xie-Beni指标作为聚类有效性函数取得了良好的效果,但当聚类个数很大时,Xie-Beni指标将单调递减。针对此问题,分别考察改进的HubertΓ统计量和聚类分离度,导出一个新的基于数据几何结构的聚类有效性函数,使得它有惟一的最大值,函数值随聚类个数增大而递减的趋势并不影响最优聚类个数的判定。实验表明,该有效性函数能够发现最优的聚类个数,对于分类结构比较明确的数据,有良好的性能,而且对模糊因子m有良好的鲁棒性。Many clustering validity functions have been proposed, especially those based on the geometrical structure of data set, such as Dunn＇s index and Xie-Beni index. Xie-Beni index decreases with the number of partitions increasing. It is difficult to choose the optimal partition of data when the number of clusters is large. From the point of view of the compactness and the separation of clustering, a novel clustering validity function is proposed, which is based on the improved Huber P statistic combined with the separation of clustering. The function has the only maximum with the number of clusters increasing. The experiment indicates that the function is simply, precise and robust, can be used as the optimal index for choosing the optimal partition of data.

关 键 词：聚类有效性 聚类分离度 聚类紧致度 统计量 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]