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Combinatoral Optimization in Clustering

In: Handbook of Combinatorial Optimization

Author

Listed:
  • Boris Mirkin

    (Rutgers University, Center for Discrete Mathematics & Theoretical Computer Science (DIMACS)
    Central Economics-Mathematics Institute (CEMI))

  • Ilya Muchnik

    (Rutgers University, RUTCOR and DIMACS)

Abstract

Clustering is a mathematical technique designed for revealing classification structures in the data collected on real-world phenomena. A cluster is a piece of data (usually, a subset of the objects considered, or a subset of the variables, or both) consisting of the entities which are much “alike”, in terms of the data, versus the other part of the data. The term itself was coined in psychology back in thirties when a heuristical technique was suggested for clustering psychological variables based on pair-wise coefficients of correlation. However, two more disciplines also should be credited for the outburst of clustering occurred in the sixties: numerical taxonomy in biology and pattern recognition in machine learning. Among relevant sources are Hartigan (1975), Jain and Dubes (1988), Mirkin (1996). Simultaneously, industrial and computational applications gave rise to graph partitioning problems which are touched below in 6.2.4.

Suggested Citation

  • Boris Mirkin & Ilya Muchnik, 1998. "Combinatoral Optimization in Clustering," Springer Books, in: Ding-Zhu Du & Panos M. Pardalos (ed.), Handbook of Combinatorial Optimization, pages 1007-1075, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0303-9_15
    DOI: 10.1007/978-1-4613-0303-9_15
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