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Optimal Combination of Nested Clusters by a Greedy Approximation Algorithm

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5 Author(s)
Edward K. F. Dang ; The Hong Kong Polytechnic University, Hong Kong ; Robert W. P. Luk ; Dik Lun Lee ; Kei-Shiu Ho
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Given a set of clusters, we consider an optimization problem which seeks a subset of clusters that maximizes the microaverage F-measure. This optimal value can be used as an evaluation measure of the goodness of clustering. For arbitrarily overlapping clusters, finding the optimal value is NP-hard. We claim that a greedy approximation algorithm yields the global optimal solution for clusters that overlap only by nesting. We present a mathematical proof of this claim by induction. For a family of n clusters containing a total of N objects, this algorithm has an O(n2) time complexity and O(N) space complexity.

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IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:31 ,  Issue: 11 )