A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms

In this paper the convergence of a class of clustering procedures, popularly known as the fuzzy ISODATA algorithms, is established. The theory of Zangwill is used to prove that arbitrary sequences generated by these (Picard iteration) procedures always terminates at a local minimum, or at worst, always contains a subsequence which converges to a local minimum of the generalized least squares objective functional which defines the problem.