Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Partitional Clustering

  • Xin Jin
  • Jiawei Han
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_631

Definition

Partitional clustering decomposes a data set into a set of disjoint clusters. Given a data set of N points, a partitioning method constructs K (NK) partitions of the data, with each partition representing a cluster. That is, it classifies the data into K groups by satisfying the following requirements: (1) each group contains at least one point, and (2) each point belongs to exactly one group. Notice that for fuzzy partitioning, a point can belong to more than one group.

Many partitional clustering algorithms try to minimize an objective function. For example, in K-means and K-medoids the function (also referred to as the distortion function) is
$${\sum \limits _{i=1}^{K}}{\sum \limits _{j=1}^{\vert {C}_{i}\vert }}\mathrm{Dist}({x}_{ j},\mathrm{center}(i)),$$
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Recommended Reading

  1. Han, J., & Kamber, M. (2006). Data mining: Concepts and techniques (2nd ed.). San Francisco: Morgan Kaufmann Publishers.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Xin Jin
    • 1
  • Jiawei Han
    • 1
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA