Fuzzy clustering is a widely applied method for obtaining fuzzy models from data. It has been applied successfully in various fields including finance and marketing. Despite the successful applications, there are a number of issues that must be dealt with in practical applications of fuzzy clustering algorithms. This technical report proposes two extensions to the objective function based fuzzy clustering for dealing with these issues. First, the (point) prototypes are extended to hypervolumes whose size is determined automatically from the data being clustered. These prototypes are shown to be less sensitive to a bias in the distribution of the data. Second, cluster merging by assessing the similarity among the clusters during optimization is introduced. Starting with an over-estimated number of clusters in the data, similar clusters are merged during clustering in order to obtain a suitable partitioning of the data. An adaptive threshold for merging is introduced. The proposed extensions are applied to Gustafson-Kessel and fuzzy c-means algorithms, and the resulting extended algorithms are given. The properties of the new algorithms are illustrated in various examples.

cluster merging, fuzzy clustering, similarity, volume prototypes
Data Collection and Data Estimation Methodology; Computer Programs (jel C8), Business Administration and Business Economics; Marketing; Accounting (jel M), Production Management (jel M11), Transportation Systems (jel R4)
Erasmus Research Institute of Management
ERIM Report Series Research in Management
Copyright 2000, U. Kaymak, M. Setnes, This report in the ERIM Report Series Research in Management is intended as a means to communicate the results of recent research to academic colleagues and other interested parties. All reports are considered as preliminary and subject to possibly major revisions. This applies equally to opinions expressed, theories developed, and data used. Therefore, comments and suggestions are welcome and should be directed to the authors.
Erasmus Research Institute of Management

Kaymak, U, & Setnes, M. (2000). Extended Fuzzy Clustering Algorithms (No. ERS-2000-51-LIS). ERIM Report Series Research in Management. Erasmus Research Institute of Management. Retrieved from http://hdl.handle.net/1765/57