Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

K-Means and K-Medoids

Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_545

Synonyms

CLARA (Clustering LARge Applications); CLARANS (Clustering large applications based upon randomized search); K-means partition; PAM (Partitioning Around Medoids)

Definitions

K-Means

Given an integer k and a set of objects S = {p1, p2,…,pn} in Euclidian space, the problem of k-means clustering is to find a set of centre points (means) P = {c1, c2,…,ck}, |P| = k in the space, such that S can be partitioned into k corresponding clusters C1, C2,…,Ck, by assigning each object in S to the closest centre ci. The sum of square error criterion (SEC) measure, defined as \( {\displaystyle {\sum}_{i=1}^k{\displaystyle \sum_{p\in {C}_i}\Big|p-{c}_i}}\Big|{}^2 \)

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Recommended Reading

  1. 1.
    Kaufman L, Rousseeuw PJ. Finding groups in data: an introduction to cluster analysis. New York: Wiley; 1990.CrossRefGoogle Scholar
  2. 2.
    MacQueen J. Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematics, Statistics and Probabilities; 1967. p. 281–97.Google Scholar
  3. 3.
    Ng RT, Han J. Efficient and effective clustering methods for spatial data mining. In: Proceedings of the 20th International Conference on Very Large Databases; 1994. p. 144–55.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The University of QueenslandBrisbaneAustralia

Section editors and affiliations

  • Xiaofang Zhou
    • 1
  1. 1.School of Inf. Tech. & Elec. Eng.Univ. of QueenslandBrisbaneAustralia