Correlation Clustering Task

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A Correlation Clustering Task is a clustering task that requires use of cluster correlation measure.



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/correlation_clustering Retrieved:2015-11-8.
    • Clustering is the problem of partitioning data points into groups based on their similarity. Correlation clustering provides a method for clustering a set of objects into the optimum number of clusters without specifying that number in advance. [1]
  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/correlation_clustering#Correlation_clustering Retrieved:2015-11-8.
    • Correlation clustering also relates to a different task, where correlations among attributes of feature vectors in a high-dimensional space are assumed to exist guiding the clustering process. These correlations may be different in different clusters, thus a global decorrelation cannot reduce this to traditional (uncorrelated) clustering.

      Correlations among subsets of attributes result in different spatial shapes of clusters. Hence, the similarity between cluster objects is defined by taking into account the local correlation patterns. With this notion, the term has been introduced in simultaneously with the notion discussed above. Different methods for correlation clustering of this type are discussed in, the relationship to different types of clustering is discussed in, see also Clustering high-dimensional data.

      Correlation clustering (according to this definition) can be shown to be closely related to biclustering. As in biclustering, the goal is to identify groups of objects that share a correlation in some of their attributes; where the correlation is usually typical for the individual clusters.

2011

  • (Wirth, 2011) ⇒ Anthony Wirth. (2011). “Correlation Clustering.” In: (Sammut & Webb, 2011) p.227
    • QUOTE: 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 wuv+ and wuv− , we must find a clustering C that minimizes :[math]\displaystyle{ ∑C[u]=C[v]w−uv+∑C[u]≠C[v]w+uv, \ (1) }[/math] or, equivalently, maximizes :[math]\displaystyle{ ∑C[u]=C[v]w+uv+∑C[u]≠C[v]w−uv. \ (2) }[/math] Note that although wuv+ and wuv− may be thought of as positive and negative evidence towards coassociation, the actual weights are nonnegative.

2006

2004