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Dynamic Programming in Clustering

  • Reference work entry
Encyclopedia of Optimization

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Article Outline

Keywords

The GDPP

Partitioning

  Admissibility Restrictions on Partitions

Hierarchical Clustering

  Constrained Hierarchical Clustering

Optimal Sequencing of an Object Set

  Optimal Sequencing Based on the Construction of Optimal Paths

Optimal Ordered Partitions

Heuristic Applications of the GDPP

See also

References

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References

  1. Alpert CJ, Kahng AB (1995) Multiway partitioning via geometric embeddings, orderings, and dynamic programming. IEEE Trans Computer-Aided Design Integr Circuits and Syst 14:1342–1357

    Article  Google Scholar 

  2. Alpert CJ, Kahng AB (1997) Splitting an ordering into a partition to minimize diameter. J Class 14:51–74

    Article  MATH  MathSciNet  Google Scholar 

  3. Batagelj V, Korenjak-Černe S, Klavžar S (1994) Dynamic programming and convex clustering. Algorithmica 11:93–103

    Article  MATH  MathSciNet  Google Scholar 

  4. Bellman R (1962) Dynamic programming treatment of the traveling salesman problem. J ACM 9:61–63

    Article  MATH  Google Scholar 

  5. Defays D (1978) A short note on a method of seriation. British J Math Statist Psych 31:49–53

    Google Scholar 

  6. Fisher WD (1958) On grouping for maximum heterogeneity. J Amer Statist Assoc 53:789–798

    Article  MATH  MathSciNet  Google Scholar 

  7. Hansen P, Jaumard B (1997) Cluster analysis and mathematical programming. Math Program 79:191–215

    MathSciNet  Google Scholar 

  8. Hartigan JA (1975) Clustering algorithms. Wiley, New York

    MATH  Google Scholar 

  9. Held M, Karp RM (1962) A dynamic programming approach to sequencing problems. J Soc Indus Appl Math 10:196–210

    Article  MATH  MathSciNet  Google Scholar 

  10. Hubert LJ, Arabie P, Meulman J (1997) The construction of globally optimal ordered partitions. In: Mirkin B, McMorris FR, Roberts FS, Rzhetsky A (eds) Mathematical hierarchies and biology. DIMACS, Amer. Math. Soc., Providence, RI, pp 299–312

    Google Scholar 

  11. Hubert LJ, Arabie P, Meulman J (1997) Hierarchical clustering and the construction of (optimal) ultrametrics using L p -norms. In: Dodge Y (ed) L 1-statistical procedures and related topics. vol 31 of Lecture Notes. Inst. Math. Statist., Berkley, U.S., pp 457–472

    Google Scholar 

  12. Hubert LJ, Arabie P, Meulman J (2001) Combinatorial data analysis: Optimization by dynamic programming. SIAM, Philadelphia

    MATH  Google Scholar 

  13. Hubert LJ, Baker FB (1978) Applications of combinatorial programming to data analysis: The traveling salesman and related problems. Psychometrika 43:81–91

    Article  MathSciNet  Google Scholar 

  14. Jensen RE (1969) A dynamic programming algorithm for cluster analysis. J Oper Res Soc Amer 7:1034–1057

    Google Scholar 

  15. Robinson WS (1951) A method for chronologically ordering archaeological deposits. Amer Antiq 16:293–301

    Article  Google Scholar 

  16. Späth H (1980) Cluster analysis algorithms. Horwood, Westergate

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University Illinois, Champaign, USA

    L. J. Hubert

  2. Rutgers University, Newark, USA

    P. Arabie

  3. Leiden University, Leiden, The Netherlands

    J. Meulman

Authors
  1. L. J. Hubert
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  2. P. Arabie
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  3. J. Meulman
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Hubert, L.J., Arabie, P., Meulman, J. (2008). Dynamic Programming in Clustering . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_145

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