一种新的模糊聚类有效性指标  

A novel validity index for fuzzy clustering

作　　者：梁鲜[1] 曲福恒[1] 才华[2] 杨勇[1] 

机构地区：[1]长春理工大学计算机科学技术学院,吉林长春130022 [2]长春理工大学电子信息工程学院,吉林长春130022

出　　处：《微型机与应用》2015年第8期74-75,79,共3页Microcomputer & Its Applications

基　　金：吉林省自然科学基金(20130101179JC-13;201215145)

摘　　要：针对模糊C均值(FCM)算法聚类数需要预先设定的问题,提出了一种新的模糊聚类有效性指标。首先,计算簇中每个属性的方差,给方差较小的属性赋予较大的权值,给方差较大的属性赋予较小的权值,得到一种基于属性加权的FCM算法;然后,根据FCM改进算法得到的隶属度矩阵计算类内紧致性和类间分离性;最后,利用类内紧致性和类间分离性定义一个新的聚类有效性指标。实验结果表明,该指标可以找到符合数据自然分布的类的数目。基于属性加权的FCM算法可以识别不同属性的重要程度,增加聚类结果的准确率,使用FCM改进算法得到的隶属度矩阵定义的有效性指标,能够发现正确的聚类个数,实现聚类无监督的学习过程。Aiming at the problem that the number of clustering of Fuzzy C-means（FCM） algorithm needs setting in advance, a new fuzzy cluster validity index was presented. Firstly, through the calculation of variance of each attribute in the cluster, giving the big weight to the attributes of small variance, while giving the small weight to the attributes of big variance, to get a FCM algorithm based on weighted attribute. Secondly, the inter class compactness and the inter class separability were computed by using the membership matrix which was calculated by the improved algorithm of FCM. Finally, a new cluster validity index was defined by using the inter class compactness and separability. Experimental results show that the optimal cluster number can be effectively found by the proposed index. The FCM algorithm based on weighted attribute can identify the degree of importance of different attributes, increase the accuracy of clustering results. The new cluster validity index defined by the membership matrix which was calculated by the improved algorithm of FCM, can find the correct number of clusters, and realize the learning process of unsupervised clustering.

关 键 词：模糊聚类 模糊C均值算法 有效性指标 最佳聚类数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]