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Cluster Definition by the Optimization of Simple Measures
May 1984 (vol. 6 no. 5)
pp. 645-652
Thomas Bailey, Department of Computer Science, University of Wyoming, Laramie, WY 82071.
John Cowles, Department of Computer Science, University of Wyoming, Laramie, WY 82071.
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.
Citation:
Thomas Bailey, John Cowles, "Cluster Definition by the Optimization of Simple Measures," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 5, pp. 645-652, May 1984, doi:10.1109/TPAMI.1984.4767579
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