Journal of Global Optimization

, Volume 37, Issue 4, pp 593–608 | Cite as

A new efficient algorithm based on DC programming and DCA for clustering

  • Le Thi Hoai An
  • M. Tayeb Belghiti
  • Pham Dinh Tao


In this paper, a version of K-median problem, one of the most popular and best studied clustering measures, is discussed. The model using squared Euclidean distances terms to which the K-means algorithm has been successfully applied is considered. A fast and robust algorithm based on DC (Difference of Convex functions) programming and DC Algorithms (DCA) is investigated. Preliminary numerical solutions on real-world databases show the efficiency and the superiority of the appropriate DCA with respect to the standard K-means algorithm.


Clustering K-median problem K-means algorithm DC programming DCA Nonsmooth nonconvex programming 

AMS subject classifications

65K05 65K10 90C26 90C90 15A60 90C06 


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Copyright information

© Springer Science+Business Media B.V.. 2006

Authors and Affiliations

  • Le Thi Hoai An
    • 1
  • M. Tayeb Belghiti
    • 2
  • Pham Dinh Tao
    • 3
  1. 1.Laboratory of Theoretical and Applied Computer Science, UFR MIMUniversity of PaulMetzFrance
  2. 2.Laboratory of Modelling, Optimization and Operations ResearchNational Institute for Applied Sciences - RouenMont Saint Aignan CedexFrance
  3. 3.Laboratory of Modelling, Optimization and Operations ResearchNational Institute for Applied Sciences - RouenMont Saint Aignan CedexFrance

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