Similarity Based Fuzzy Possibilistic C-Means with Constraints

Data analysis is recognized as a very essential science in the real world. Cluster analysis is an approach for categorizing data and it is a method for finding clusters of a data set with most relationship in the similar cluster and most variation between different clusters. It is extensively used in pattern recognition, image processing, and data analysis. The Fuzzy-Possibilistic C-Means (FPCM) approach is the effective clustering algorithm for clustering unlabeled data that produces both membership and typicality values during clustering process. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint constructs unrealistic typicality values for large data sets. A Modification on fuzzy possibilistic clustering algorithm based on a prototype-driven learning of parameters was previously performed to obtain better quality clustering results. A similarity based fuzzy and possibilistic c-means algorithm is presented in this paper. The major purpose of the similarity based approach is to differentiate between the domain terms and the noisy terms. The efficiency of the Similarity based Fuzzy Possibilistic C-means clustering approach is enhanced by using the penalized and compensated constraints. Penalized and Compensated terms are embedded with the Modified fuzzy possibilistic clustering method’s objective function to construct the Similarity based Penalized and Compensated constraints based Modified FPCM (SPCMFPCM). Several numerical examples are given that compare MFPCM and SPCMFPCM. The experimental observations illustrate that SPCMFPCM clusters the data more accurately than the MFPCM. Since the proposed approach is less sensitive to outliers and can avoid coincident clusters, it is a strong candidate for fuzzy rule-based system identification.