COMPREHENSIVE ANALYSIS OF FUZZY C - MEANS CLUSTERING AND ITS VARIANTS

Fuzzy clustering algorithms are one of the most important techniques for analysing and extracting information from data when working with datasets containing overlapping clusters. Fuzzy clustering provides a more precise representation of complex data structures compared to conventional crisp (hard) clustering approaches. It accomplishes this by allowing data points to be assigned to multiple clusters with different degrees of membership. This paper provides an extensive review of various fuzzy clustering algorithms, such as Fuzzy C - Means (FCM) and its variations including Gustafson - Kessel (GK), Noise Clustering (NC), Possibilistic C - Means (PCM), Possibilistic Fuzzy C - Means (PFCM), Credibilistic Fuzzy C - Means (CFCM), and Kernel Fuzzy C - Means (KFCM). Their underlying mathematical theories, pseudocodes and applicability to different types of data are reviewed. Furthermore, the time complexity of these algorithms are analysed and a detailed comparison is presented to clarify their performance and scalability. By examining both theoretical aspects and empirical results, this study aims to provide a comprehensive knowledge of the trade-offs between computational efficiency and clustering accuracy. This analysis is intended to serve as a resource for researchers and practitioners in selecting appropriate fuzzy clustering techniques for their specific applications.