Abstract
Fuzzy C-means (FCM) is an important clustering algorithm with broad applications such as retail market data analysis, network monitoring, web usage mining, and stock market prediction. Especially, parameters in FCM have influence on clustering results. However, a lot of FCM algorithm did not solve the problem, that is, how to set parameters. In this study, we present a kind of method for computing parameters values according to role of parameters in the clustering process. New parameters are assigned to membership and typicality so as to modify objective function, on the basis of which Lagrange equation is constructed and iterative equation of membership is acquired, so does the typicality and center equation. At last, a new possibilistic fuzzy C-means based on the weight parameter algorithm (WPFCM) was proposed. In order to test the efficiency of the algorithm, some experiments on different datasets are conducted to compare WPFCM with FCM, possibilistic C-means (PCM), and possibilistic fuzzy C-means (PFCM). Experimental results show that iterative times of WPFCM are less than FCM about 25% and PFCM about 65% on dataset X12. Resubstitution errors of WPFCM are less than FCM about 19% and PCM about 74% and PFCM about 10% on the IRIS dataset.
Highlights
Clustering is a method of unsupervised learning and had been applied in various fields, including data mining, pattern recognition, computer vision, and bioinformatics
fuzzy possibilistic C-means (FPCM) reduced sensitivity to noise in fuzzy C-means (FCM) and resolved coincident problem in possibilistic C-means (PCM); typicality value became very small as dataset scale increasing for the reason of row sum constraints
A new possibilistic fuzzy C-mean based on weight parameters was proposed according to the importance of membership and typicality in the clustering process
Summary
Fuzzy C-means (FCM) is an important clustering algorithm with broad applications such as retail market data analysis, network monitoring, web usage mining, and stock market prediction. Parameters in FCM have influence on clustering results. A lot of FCM algorithm did not solve the problem, that is, how to set parameters. A new possibilistic fuzzy C-means based on the weight parameter algorithm (WPFCM) was proposed. In order to test the efficiency of the algorithm, some experiments on different datasets are conducted to compare WPFCM with FCM, possibilistic C-means (PCM), and possibilistic fuzzy C-means (PFCM). Experimental results show that iterative times of WPFCM are less than FCM about 25% and PFCM about 65% on dataset X12. Resubstitution errors of WPFCM are less than FCM about 19% and PCM about 74% and PFCM about 10% on the IRIS dataset
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