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Cluster Definition by the Optimization of Simple Measures

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2 Author(s)
Bailey, Thomas ; Department of Computer Science, University of Wyoming, Laramie, WY 82071. ; Cowles, J.

We adopt the following measures of clustering based on simple edge counts in an undirected loop-free graph. Let S be a subset of the points of the graph. The compactness of S is measured by the number of edges connecting points in S to other points in S. The isolation or separation of S is measured by the negative of the number of edges connecting points in S to points not in S. The subset S is a cluster if it is compact and isolated. We study the cluster search problem: find a subset S which maximizes a linear combination of the compactness and (negative) isolation edge counts. We show that a closely related decision problem is NP-complete. We develop a pruned search tree algorithm which is much faster than complete search, especially for graphs which are derived from points embedded in a space of low dimensionality.

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-6 ,  Issue: 5 )