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Encyclopedia of Machine Learning
pp 766766
Partitional Clustering
 Xin JinAffiliated withUniversity of Illinois at UrbanaChampaign
 , Jiawei HanAffiliated withUniversity of Illinois at UrbanaChampaign
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 (N ≥ K) 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 Kmeans and Kmedoids the function (also referred to as the distortion function) is where  C_{i}  is the number of points in cluster i, Dist(x_{j}, center(i)) is the distance between point x_{j} and center i. Many distance functions can be used, such as Euclidean distance and L
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$${\sum \limits _{i=1}^{K}}{\sum \limits _{j=1}^{\vert {C}_{i}\vert }}\mathrm{Dist}({x}_{ j},\mathrm{center}(i)),$$
(1)
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 Title
 Partitional Clustering
 Reference Work Title
 Encyclopedia of Machine Learning
 Pages
 p 766
 Copyright
 2010
 DOI
 10.1007/9780387301648_631
 Print ISBN
 9780387307688
 Online ISBN
 9780387301648
 Publisher
 Springer US
 Copyright Holder
 Springer Science+Business Media, LLC
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 Editors

 Claude Sammut ^{(221)}
 Geoffrey I. Webb ^{(222)}
 Editor Affiliations

 221. School of Computer Science and Engineering, University of New South Wales
 222. Faculty of Information Technology, Clayton School of Information Technology, Monash University
 Authors

 Xin Jin ^{(1)}
 Jiawei Han ^{(1)}
 Author Affiliations

 1. University of Illinois at UrbanaChampaign, Urbana, IL, USA
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