On the asymptotic properties of fuzzy c-means cluster prototypes as estimators of mixture subpopulation centers

Several computational studies suggest that the fuzzy c-means (FCM) clustering scheme may be used successfully in some cases to obtain estimates for the parameters of a statistical mixture (e.g., for a mixture of normal distributions). While these (limited) simulation results for the fuzzy c-means approach support this hypothesis, we provide herein an example that shows that the FCM cluster prototypes cannot generally be statistically consistent estimators of the centers (means) of any univariate mixture having symmetric component distributions