A 2-approximation polynomial algorithm for a clustering problem
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A 2-approximation algorithm is presented for some NP-hard data analysis problem that consists in partitioning a set of Euclidean vectors into two subsets (clusters) under the criterion of minimum sum-of-squares of distances from the elements of clusters to their centers. The center of the first cluster is the average value of vectors in the cluster, and the center of the second one is the origin.
Keywordscluster analysis search for a vector subset computational complexity approximation polynomial algorithm
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- 4.A. V. Kel’manov, “AProblemofOff-Line Detection of a Repeating Fragment in a Number Sequence,” Trudy Inst.Mat. i Mekh. Ural. Otdel. Ross. Akad. Nauk 14(2), 81–88 (2008).Google Scholar
- 8.D. Aloise, A. Deshpande, P. Hansen, and P. Popat, “NP-Hardness of Euclidean Sum-of-Squares Clustering,” Preprint G-2008-33 (Les Cahiers du GERAD, 2008).Google Scholar
- 9.D. Aloise and P. Hansen, “On the Complexity ofMinimum Sum-of-Squares Clustering,” Preprint G-2007-50 (Les Cahiers du GERAD, 2007).Google Scholar
- 14.J. B. MacQueen, “Some Methods for Classification and Analysis of Multivariate Observations,” in Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1 (Berkeley, 1967), pp. 281–297.Google Scholar
- 15.M. Mahajan, P. Nimbhorkar, and K. Varadarajan, “The Planar k-Means Problem is NP-Hard,” in Lecture Notes in Computer Science, Vol. 5431 (Springer, New York, 2009), pp. 284–285.Google Scholar