title: K-means-type algorithms: a generalized convergence theorem and characterization of local optimality.
abstract: The K-means algorithm is a commonly used technique in cluster analysis. In this paper, several questions about the algorithm are addressed. The clustering problem is first cast as a nonconvex mathematical program. Then, a rigorous proof of the finite convergence of the K-means-type algorithm is given for any metric. It is shown that under certain conditions the algorithm may fail to converge to a local minimum, and that it converges under differentiability conditions to a Kuhn-Tucker point. Finally, a method for obtaining a local-minimum solution is given.
authors.affiliation: Department of Systems Engineering, University of Petroleum and Minerals, Dhahran, Saudi Arabia.
authors.forename: S Z
authors.initials: SZ
authors.lastname: Selim
authors.forename: M A
authors.initials: MA
authors.lastname: Ismail