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Solution methods for the minimum sum-of-squares clustering (MSSC) problem areanalyzed and developed in this paper. Based on the DCA (Difference-of-Convexfunctions Algorithms) in DC programming and recently established qualitativeproperties of the MSSC problem, we suggest several improvements of theincremental algorithms of Ordin and Bagirov and of Bagirov. Properties of thenew algorithms are obtained and preliminary numerical tests of those onreal-world databases are shown. Finite convergence, convergence, and the rateof convergence of solution methods for the MSSC problem are presented for thefirst time in our paper. This Part 1 is devoted to the incremental heuristicclustering algorithm of Ordin and Bagirov and the modified version proposedherein.

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