Optimality tests for fixed points of the fuzzy c-means algorithm

摘要

The Fuzzy c-Means(FCM) clustering algorithms are known to converge to either local minima or saddle points of the objective function which defines the FCM method. The object of this paper is to derive efficient numerical tests for local extrema of the FCM functional that enable one to identify each candidate as a local minimum or saddle point. Numerical examples of the theory derived illustrate that the tests proposed cover all possible cases.