面向结构复杂数据集的模糊聚类有效性指标  

Fuzzy clustering validity index facing data set with complexity structure

作　　者：唐益明[1,2] 丰刚永 任福继[1,2] 胡相慧 张有成 

机构地区：[1]合肥工业大学情感计算与先进智能机器安徽省重点实验室 [2]合肥工业大学计算机与信息学院

出　　处：《电子测量与仪器学报》2018年第4期119-127,共9页Journal of Electronic Measurement and Instrumentation

基　　金：国家自然科学基金(61673156,61432004,61672202,U1613217);安徽省自然科学基金(1408085MKL15,1508085QF129);中国博士后科学基金(2014T70585);国家“八六三”高技术研究发展计划基金(2012AA011103)资助项目

摘　　要：如何有效确定聚类数是聚类领域的历史性难题之一。面向聚类的一大标志性算法——模糊C均值算法,现在聚类评价性指标普遍对数据结构复杂和集群大小差异悬殊的数据集难以做出精准判断。针对该问题,提出了一种新的基于数据集几何结构和大小集群的模糊聚类的有效性指标VGSDC（面向几何结构和大小集群的指标）。以类内平方误差和、隶属度权值得到紧致性度量策略,以聚类中心距离最小值、各聚类中心到平均聚类中心的距离和衍生出分离性测算方法,由此合成得到新的有效性指标VGSDC。进一步凭借VGSDC的极值处对应的类别数可自动得到最佳聚类数。通过在6个数据集上与11种聚类有效性指标的实验对比分析,发现所提的VGSDC指标性能最优,不仅可以处理多种类型的数据集,而且充分考虑了数据集的结构特征和复杂性,能够适用于大型、聚类中心间距离差异悬殊的数据集。How to effectively determine the clustering number is one of the historical challenges in the clustering field. A typical algorithm for clustering is the fuzzy c-means algorithm. Nowadays it is difficult for clustering validity index to make accurate judgment for complex data structure and the huge disparity of cluster size. Aiming at the problem,a new clustering validity index VGSDC( index for geometry structure and different clusters) is proposed for the geometry structure of data set and clusters with different size. The compactness strategy is obtained by square error sum within the classes as well as weights of membership degree,and then the separation computing method is gotten by minimum distance between cluster centers together with distance sum from centers to average center. And finally,the new validity index VGSDCis obtained. Furthermore,the best clustering number can be automatically obtained by the number of categories corresponding to the extreme value of VGSDC. Through the experiment in 6 data structure,it is found that the proposed VGSDC gets the better performance comparing with 11 kinds of clustering validity indexes. VGSDCcan not only handle multiple types of data sets,and also provide full consideration to the structure characteristics and complexity of the data sets. As a result,it can be applied to large data sets with huge differences of clustering center distance.

关 键 词：有效性指标 聚类分析 模糊C均值算法 紧致性 分离性 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论]