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Interpretation and optimization of the k -means algorithm

Kristian Sabo, Rudolf Scitovski (2014)

Applications of Mathematics

The paper gives a new interpretation and a possible optimization of the well-known 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 π 1 , , 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....

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