Entropy-based fuzzy clustering and fuzzy modeling

Fuzzy clustering is capable of finding vague boundaries that crisp clustering fails to obtain. But time complexity of fuzzy clustering is usually high, and the need to specify complicated parameters hinders its use. In this paper, an entropy-based fuzzy clustering method is proposed. It automatically identifies the number and initial locations of cluster centers. It calculates the entropy at each data point and selects the data point with minimum entropy as the first cluster center. Next it removes all data points having similarity larger than a threshold with the chosen cluster center. This process is repeated till all data points are removed. Unlike previous methods of its kind, it does not need to revise entropy value for each data point after a cluster center is determined. This saves a lot of time. Also it requires just two parameters that are easy to specify. It is able to find the natural clusters in the data. The clustering method is also extended to construct a rule-based fuzzy model. A new way of estimating initial membership functions for fuzzy sets is presented. The experimental results show that the fuzzy model is good in predicting output variable values.