General Fuzzy C-Means Clustering Strategy: Using Objective Function to Control Fuzziness of Clustering Results
Kaixin Zhao, Yaping Dai, Zhiyang Jia, Ye Ji
Abstract
As one of the most commonly used clustering methods, the fuzzy C-means (FCM) clustering strategy extends the notion of hard clustering to associate each pattern with every cluster using a membership function. Although a lot of efforts have been made by the clustering community, it is still unclear how to evaluate the fuzziness of different versions of FCM. To fill this theoretical blank, by observing a family of objective functions, a definition of fuzzy degree is provided to quantify the fuzziness of different versions of FCM according to their dedicated objective functions. Then, a general fuzzy C-means (GFCM) clustering algorithm is proposed to solve the clustering problem of using FCM under different distance metrics and fuzzy degrees. From the perspective of fuzzy attribute, the using of this fuzzy degree can be used to reveal the essential difference among a group of FCM-based clustering algorithms, and the proposed GFCM achieves the aim of using objective functions to control the fuzziness of clustering results. Additionally, some properties and relations of these FCM-based clustering algorithms under different fuzzy degrees are discussed and the convergence and stability of the proposed GFCM are proved. Finally, extensive experiments have been performed to demonstrate that by comparison with the effect caused by distance metric, the choices of fuzzy degree have a more significant effect and improvement on the performances of a FCM-based clustering algorithm.