Interpretation and optimization of the k-means algorithm |
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Authors: | Kristian Sabo Rudolf Scitovski |
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Institution: | 1. Department of Mathematics, University of Osijek, Osijek, Croatia
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Abstract: | The paper gives a new interpretation and a possible optimization of the wellknown k-means algorithm for searching for a locally optimal partition of the set A = {a i ∈ ? n : i = 1, …, m} which consists of k disjoint nonempty subsets π1, …, π k , 1 ? k ? m. For this purpose, a new divided k-means algorithm was constructed as a limit case of the known smoothed k-means algorithm. It is shown that the algorithm constructed in this way coincides with the k-means algorithm if during the iterative procedure no data points appear in the Voronoi diagram. If in the partition obtained by applying the divided k-means algorithm there are data points lying in the Voronoi diagram, it is shown that the obtained result can be improved further. |
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