基于样本模糊隶属度归n化约束的松弛模糊C均值聚类算法  

Relaxed Fuzzy C-means Clustering Algorithm Based on the Normalization n Constraint of Fuzzy Membership Degree of Sample

作　　者：文传军[1] 詹永照[2] WEN Chuan-jun;ZHAN Yong-zhao(School of Mathematical Sciences and Chemical Engineering, Changzhou Institute of Technology, Changzhou 213002, P.R.China;School of Computer Science and Communication Engineering, Jiangsu University, Zhenjiang 212013, P.R.China)

机构地区：[1]常州工学院数理与化工学院,常州213002 [2]江苏大学计算机科学与通信工程学院,镇江212013

出　　处：《科学技术与工程》2017年第36期96-104,共9页Science Technology and Engineering

基　　金：国家自然科学基金(61170126);常州工学院校级课题(YN1305)资助

摘　　要：模糊C均值聚类算法(FCM)由于样本模糊隶属度归一性的约束,导致FCM算法对噪声数据敏感。提出松弛模糊C均值聚类算法(RFCM),RFCM算法在可能性C均值聚类算法(PCM)目标函数的基础上,放弃了FCM算法单个样本模糊隶属度归一化约束,转为n个样本模糊隶属度之和为n的约束;并利用粒子群算法对样本模糊隶属度进行优化估计,使得模糊指标可拓展为m>0的情况,同时采用梯度法得到RFCM算法聚类中心迭代公式。RFCM理论分析了算法对噪声数据抗噪的原理,解释了RFCM算法模糊指标m>0的合理性,讨论了RFCM算法的收敛性。基于Gauss数据集和UCI数据集的仿真测试验证了所提出算法的有效性。The FCM algorithm is sensitive to noise data due to the normalized constraint of fuzzy membership.A novel clustering algorithm is proposed and named as relaxed fuzzy C means clustering(RFCM),the objective function of PCM is utilized as the objective function of RFCM,and RFCM loosens the normalized constraint and only requests the whole summation of n samples'fuzzy memberships equal to n,particle swarm optimization algorithms(PSO)are optimally used to select the fuzzy memberships of RFCM,and the value scope of fuzzy index m is extended to m>0,The iterative formula of clustering centers are derived by gradient method for RFCM.The anti noise performance of RFCM is analysed theoretically,and the rationality of new value scope of m>0is explained for RFCM,and the convergence of RFCM is discussed simultaneously.The effectiveness of RFCM are proved through simulation experiments.

关 键 词：模糊聚类 归一化约束 模糊指标 粒子群算法 噪声数据 

分 类 号：TP391.45[自动化与计算机技术—计算机应用技术]