结合多目标优化算法的模糊聚类有效性指标及应用  

Fuzzy Clustering Validity Index Combined with Multi-objective Optimization Algorithm and Its Application

作　　者：崔国楠 王立松[1] 康介祥 高忠杰 王辉 尹伟 CUI Guo-nan;WANG Li-song;KANG Jie-xiang;GAO Zhong-jie;WANG Hui;YIN Wei(School of Computer Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210000,China;Software Department of China Aeronautical Radio Electronics Research Institute,Shanghai 200233,China)

机构地区：[1]南京航空航天大学计算机科学与技术学院,南京210000 [2]中国航空无线电电子研究院软件部,上海200233

出　　处：《计算机科学》2021年第10期197-203,共7页Computer Science

摘　　要：模糊聚类方法可以更有效地对复杂数据集进行分析,由于模糊聚类算法的种类繁多且聚类结果会随着输入的聚类个数的不同而改变,使得模糊聚类算法产生的结果不准确,因此,要获得准确的聚类结果必须确定模糊聚类个数k。目前已有的研究主要是利用多种模糊聚类有效性指标来确定最优聚类个数k,但是诸如SSD,PBM等模糊聚类指标会随着划分的聚类个数k的增加而单调递减,导致聚类个数k不准确。为此,文中提出了一种结合多目标优化算法的模糊聚类有效性指标(A Validity Index of Fuzzy Clustering Combined with Multi-objective Optimization Algorithm,OSACF),将模糊聚类度量指标与多目标优化算法(Multi-Objective Optimization Algorithm,MOEA)相结合来解决聚类最优个数k的问题。与使用聚类有效性指标不同,OSACF通过建立聚类个数k与聚类度量指标之间的双目标模型并使用MOEA优化该双目标模型来确定最优聚类个数k,避免了聚类有效性指标趋于单调递减的影响。另一方面,OSACF使用形态形似距离替代传统的欧氏距离度量,避免了聚类形状对计算聚类k值的影响。实验结果表明,OSACF结合MOEA得到的最优模糊聚类个数k比已有的聚类有效性指标获得的结果更准确。Fuzzy clustering method can analyze complex data sets more effectively.Because there are many kinds of fuzzy clustering algorithms and the clustering results will change with the number of input clusters,the results of fuzzy clustering algorithm are not accurate,so the number of fuzzy clustering k must be determined in order to obtain certain clustering results.At present,the existing research mainly uses a variety of fuzzy clustering effectiveness indexes to determine the optimal number of clusters k.However,fuzzy clustering indexes such as SSD,PBM will decrease monotonically with the increase of clustering number k,which makes it impossible to determine the optimal number of clusters k.Therefore,this paper proposes a fuzzy clustering validity index(OSACF)combined with a multi-objective optimization algorithm,which combines fuzzy clustering validity with a multi-objective optimization algorithm(MOEA)to solve the optimal number of clusters k problem.Different from using clustering validity index,OSACF establishes a bi-objective model between cluster number k and clustering validity index,and uses MOEA to optimize the bi-objective model to determine the optimal cluster number k,so as to avoid the influence of monotonous decreasing of clustering validity index.On the other hand,OSACF uses morphological similarity distance to replace the traditional Euclidean distance metric,which avoids the influence of cluster shape on the calculation of cluster k.The experimental results show that the optimal fuzzy cluster number k obtained by OSACF combined with MOEA is more accurate than the results obtained by the existing clustering effectiveness indicators.

关 键 词：聚类有效性指标 模糊聚类 多目标优化算法 模糊聚类个数k 

分 类 号：TP302[自动化与计算机技术—计算机系统结构]