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Combinatoral Optimization in Clustering

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Handbook of Combinatorial Optimization

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.

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Author information

Authors and Affiliations

  1. Center for Discrete Mathematics & Theoretical Computer Science (DIMACS), Rutgers University, P.O.Box 1179, Piscataway, NJ, 08855, USA

    Boris Mirkin

  2. Central Economics-Mathematics Institute (CEMI), Moscow, Russia

    Boris Mirkin

  3. RUTCOR and DIMACS, Rutgers University, P.O.Box 1179, Piscataway, NJ, 08855, USA

    Ilya Muchnik

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  1. Boris Mirkin
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Editors and Affiliations

  1. University of Minnesota, Minneapolis, USA

    Ding-Zhu Du

  2. University of Florida, Gainesville, USA

    Panos M. Pardalos

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Mirkin, B., Muchnik, I. (1998). Combinatoral Optimization in Clustering. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_15

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  • DOI: https://doi.org/10.1007/978-1-4613-0303-9_15

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