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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5755))

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Abstract

In this paper, we propose a new approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) to perform clustering via minimum sum-of-squares Euclidean distance. The so called Minimum Sum-of-Squares Clustering (MSSC in short) is first formulated in the form of a hard combinatorial optimization problem. It is afterwards recast as a (continuous) DC program with the help of exact penalty in DC programming. A DCA scheme is then investigated. The related DCA is original and very inexpensive because it amounts to computing, at each iteration, the projection of points onto a simplex and/or onto a ball, that all are given in the explicit form. Numerical results on real word data sets show the efficiency of DCA and its great superiority with respect to K-means, a standard method of clustering.

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© 2009 Springer-Verlag Berlin Heidelberg

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Hoai An, L.T., Tao, P.D. (2009). Minimum Sum-of-Squares Clustering by DC Programming and DCA. In: Huang, DS., Jo, KH., Lee, HH., Kang, HJ., Bevilacqua, V. (eds) Emerging Intelligent Computing Technology and Applications. With Aspects of Artificial Intelligence. ICIC 2009. Lecture Notes in Computer Science(), vol 5755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04020-7_35

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  • DOI: https://doi.org/10.1007/978-3-642-04020-7_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04019-1

  • Online ISBN: 978-3-642-04020-7

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