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Optimal Combination of Nested Clusters by a Greedy Approximation Algorithm

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5 Author(s)
Dang, E.K.F. ; Dept. of Comput., Hong Kong Polytech. Univ., Hong Kong, China ; Luk, R.W.P. ; 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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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:31 ,  Issue: 11 )