Generalized fuzzy c-means algorithms

This paper proposes generalized fuzzy c-means (FCM) algorithms. The clustering problem is formulated as a constrained minimization problem, whose solution depends on the selection of a constraint function that satisfies certain conditions. If the constraint function is proportional to the generalized mean of the membership values, the solution of this minimization problem results in a broad family of generalized FCM algorithms. The existing FCM algorithm can be obtained as a special case of the proposed formulation if the generalized mean coincides with the arithmetic mean. Other special cases include the minimum FCM and the geometric FCM. The proposed formulation also assigns to each feature vector a parameter that can be used to measure the certainty of its assignment into various clusters. The reliability of this certainty measure is verified by experiments involving an artificial data set containing outliers