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A framework for semi-supervised and unsupervised optimal extraction of clusters from hierarchies

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Abstract

We introduce a framework for the optimal extraction of flat clusterings from local cuts through cluster hierarchies. The extraction of a flat clustering from a cluster tree is formulated as an optimization problem and a linear complexity algorithm is presented that provides the globally optimal solution to this problem in semi-supervised as well as in unsupervised scenarios. A collection of experiments is presented involving clustering hierarchies of different natures, a variety of real data sets, and comparisons with specialized methods from the literature.

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Notes

  1. These methods should be distinguished from those that use hierarchical clustering and partially labeled data to categorize unlabeled data into predefined categories (semi-supervised categorization; e.g., see Skarmeta et al. 2000; Benkhalifa et al. 2001).

  2. Note that such a reduction may be even more noticeable for higher values of \(m_{ clSize }\).

  3. In the example of Fig. 3b–d, these nodes would be virtual children of \(\mathbf{C}_1\) and \(\mathbf{C}_2\), which have been omitted for the sake of clarity.

  4. An alternative setting, in which both objectives in Eqs. (1) and (3) are combined into a single, mixed one, will be discussed further, in Sect. 3.2.

  5. Notice that \(\varGamma \) has the same properties as \(S\) discussed in Sect. 2.3: it can be computed locally for each node and it is additive w.r.t. the objects in the node, so it is compatible with the aggregation operator (sum) used in the objective function in Eqs. (1) and (5).

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Acknowledgments

This study was supported by Fapesp / CNPq (Brazil) and NSERC (Canada).

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Authors and Affiliations

  1. Department of Computing Sciences, University of Alberta, Edmonton, AB, Canada

    R. J. G. B. Campello, D. Moulavi, A. Zimek & J. Sander

  2. Department of Computer Sciences, University of São Paulo, São Carlos, Brazil

    R. J. G. B. Campello

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  1. R. J. G. B. Campello
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  2. D. Moulavi
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  3. A. Zimek
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  4. J. Sander
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Correspondence to R. J. G. B. Campello.

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Responsible editor: Hendrik Blockeel, Kristian Kersting, Siegfried Nijssen, Filip Zelezny.

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Campello, R.J.G.B., Moulavi, D., Zimek, A. et al. A framework for semi-supervised and unsupervised optimal extraction of clusters from hierarchies. Data Min Knowl Disc 27, 344–371 (2013). https://doi.org/10.1007/s10618-013-0311-4

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