Reference Work Entry

Encyclopedia of Machine Learning

pp 766-766

Partitional Clustering

  • Xin JinAffiliated withUniversity of Illinois at Urbana-Champaign
  • , Jiawei HanAffiliated withUniversity of Illinois at Urbana-Champaign

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
$${\sum \limits _{i=1}^{K}}{\sum \limits _{j=1}^{\vert {C}_{i}\vert }}\mathrm{Dist}({x}_{ j},\mathrm{center}(i)),$$
(1)
where | Ci | is the number of points in cluster i, Dist(xj, center(i)) is the distance between point xj and center i. Many distance functions can be used, such as Euclidean distance and L ...
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