On Some Incremental Algorithms for the Minimum Sum-of-Squares Clustering Problem. Part 1: Ordin and Bagirov's Incremental Algorithm

TL;DR

This paper analyzes and improves incremental algorithms for the minimum sum-of-squares clustering problem using DC programming, providing convergence properties and preliminary numerical results on real data.

Contribution

It introduces enhancements to Ordin and Bagirov's incremental clustering algorithm, establishing convergence and rate of convergence properties for the first time.

Findings

Finite convergence of the algorithms is demonstrated.

Convergence and rate of convergence are established.

Preliminary numerical tests show promising results.

Abstract

Solution methods for the minimum sum-of-squares clustering (MSSC) problem are analyzed and developed in this paper. Based on the DCA (Difference-of-Convex functions Algorithms) in DC programming and recently established qualitative properties of the MSSC problem, we suggest several improvements of the incremental algorithms of Ordin and Bagirov and of Bagirov. Properties of the new algorithms are obtained and preliminary numerical tests of those on real-world databases are shown. Finite convergence, convergence, and the rate of convergence of solution methods for the MSSC problem are presented for the first time in our paper. This Part 1 is devoted to the incremental heuristic clustering algorithm of Ordin and Bagirov and the modified version proposed herein.