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Correlation Clustering

  • Reference work entry
Encyclopedia of Machine Learning

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Synonyms

Clustering with advice; Clustering with constraints; Clustering with qualitative information; Clustering with side information

Definition

In its rawest form, correlation clustering is graph optimization problem. Consider a clustering C to be a mapping from the elements to be clustered, V , to the set {1, …, | V | }, so that u and v are in the same cluster if and only if C[u] = C[v]. Given a collection of items in which each pair (u, v) has two weights w uv + and w uv − , we must find a clustering C that minimizes

$$\sum \limits_{C[u]=C[v]}{w}_{uv}^{-} + \sum \limits_{C[u]\neq C[v]}{w}_{uv}^{+}\,,$$
(1)

or, equivalently, maximizes

$$\sum \limits_{C[u]=C[v]}{w}_{uv}^{+} + \sum \limits_{C[u]\neq C[v]}{w}_{uv}^{-}\,.$$
(2)

Note that although w uv + and w uv − may be thought of as positive and negative evidence towards coassociation, the actual weights are nonnegative.

Motivation and Background

The notion of clustering with advice, that is nonmetric-driven relations between items,...

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Authors and Affiliations

    Authors
    1. Anthony Wirth
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    Editor information

    Editors and Affiliations

    1. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia, 2052

      Claude Sammut

    2. Faculty of Information Technology, Clayton School of Information Technology, Monash University, P.O. Box 63, Victoria, Australia, 3800

      Geoffrey I. Webb

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    © 2011 Springer Science+Business Media, LLC

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    Wirth, A. (2011). Correlation Clustering. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30164-8_176

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