Adaptive Fuzzy Clustering Model Based on Internal Connectivity of All Data Points

Abstract

This paper proposes a new kind of fuzzy C-means clustering model (FCM),which is named as adaptive fuzzy clustering (AFCM). Different from most current fuzzy clustering methods,the AFCM considers the internal connectivity of all data points. An adaptive degree vector W and an adaptive exponent p are introduced into the model to jointly influence the clustering process. The AFCM simultaneously outputs three categories of parameters:fuzzy membership degree matrix U,adaptive degree vector W ,and cluster prototype matrix V. Two groups of numerical experiments,Group 1 and Group 2,were executed to evaluate the AFCM. Group 1 demonstrates the clustering performance of the AFCM,with FCM being its counterpart,and the results showed that the AFCM can obtain better clustering quality,meanwhile its time complexity can hold the same level as that of the FCM by choosing the available p. Group 2 checks the ability of the AFCM in mining the outliers,with the density-based LOF being its counterpart and the results showed that the AFCM has considerable advantages in computing efficiency,and that the outliers minded by the AFCM are global,and reflect the relationship between the outliers and the whole data set. It is pointed out that the AFCM possesses the unique advantages when mining the outliers of the large-scale or dynamic data sets,and clustering the data set for better clustering results,especially when it is necessary to simultaneously fulfill both tasks of clustering and mining outliers.