Analysis of Parameter Selection for Gustafson–Kessel Fuzzy Clustering Using Jacobian Matrix


In fuzzy clustering, the fuzzy c-suggests that (FCM) is the foremost known algorithm. Many extensions and variations of FCM had been proposed within the literature. The first vital extension to FCM was proposed by Gustafson and Kessel (GK). Within the GK fuzzy clustering, they thought-about the impact of various cluster shapes apart from spherical shapes by replacing the Euclidean distance of the FCM objective perform with the Mahalanobis distance. The GK algorithm has become one in all the foremost frequently used clustering algorithms. Just like FCM, the fuzziness index m is a parameter in that the worth can greatly influence the performance of the GK algorithm. However, there's no theoretical work on the parameter selection for the fuzziness index m of GK. During this paper, we have a tendency to reveal the relation between the stable fixed points of the GK algorithm and the datasets using Jacobian matrix analysis, and then provide a theoretical base for choosing the fuzziness index m within the GK algorithm. Some experimental results verify the effectiveness of our theoretical results.

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