Generalized fuzzy c-means algorithms

Abstract

This paper presents the development, testing and evaluation of generalized fuzzy c-means (FCM) algorithms. The proposed algorithms are developed by relaxing the constraints imposed on the membership functions by the axiomatic requirements associated with fuzzy c-partitions. Clustering is formulated as a constrained minimization problem, whose solution depends on the constraints imposed on the membership functions. This minimization problem results in a broad family of Generalized FCM algorithms, which include the FCM algorithm as a special case. The Minimum FCM and Geometric FCM algorithms are also obtained as limiting cases of Generalized FCM algorithms. The proposed formulation assigns to each feature vector a parameter that can be used to measure the certainty of its assignment to various clusters. These parameters can be used to identify outliers in the feature set. The Generalized FCM algorithms are evaluated and tested by experiments involving the IRIS data set and a two-dimensional vowel data set.