Efficient Implementation of the Fuzzy c-Means Clustering Algorithms

This paper reports the results of a numerical comparison of two versions of the fuzzy c-means (FCM) clustering algorithms. In particular, we propose and exemplify an approximate fuzzy c-means (AFCM) implementation based upon replacing the necessary ``exact' variates in the FCM equation with integer-valued or real-valued estimates. This approximation enables AFCM to exploit a lookup table approach for computing Euclidean distances and for exponentiation. The net effect of the proposed implementation is that CPU time during each iteration is reduced to approximately one sixth of the time required for a literal implementation of the algorithm, while apparently preserving the overall quality of terminal clusters produced. The two implementations are tested numerically on a nine-band digital image, and a pseudocode subroutine is given for the convenience of applications-oriented readers. Our results suggest that AFCM may be used to accelerate FCM processing whenever the feature space is comprised of tuples having a finite number of integer-valued coordinates.