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Improved Analysis of Complete-Linkage Clustering

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Abstract

Complete-linkage clustering is a very popular method for computing hierarchical clusterings in practice, which is not fully understood theoretically. Given a finite set \(P\subseteq \mathbb {R}^d\) of points, the complete-linkage method starts with each point from P in a cluster of its own and then iteratively merges two clusters from the current clustering that have the smallest diameter when merged into a single cluster. We study the problem of partitioning P into k clusters such that the largest diameter of the clusters is minimized and we prove that the complete-linkage method computes an O(1)-approximation for this problem for any metric that is induced by a norm, assuming that the dimension d is a constant. This improves the best previously known bound of \(O(\log {k})\) due to Ackermann et al. (Algorithmica 69(1):184–215, 2014). Our improved bound also carries over to the k-center and the discrete k-center problem.

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References

  1. Ackermann, M.R., Blömer, J., Kuntze, D., Sohler, C.: Analysis of agglomerative clustering. Algorithmica 69(1), 184–215 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cole, J.R., Wang, Q., Fish, J.A., Chai, B., McGarrell, D.M., Sun, Y., Brown, C.T., Porras-Alfaro, A., Kuske, C.R., Tiedje, J.M.: Ribosomal database project: data and tools for high throughput rrna analysis. Nucl. Acids Res. 42, D633–D642 (2013)

    Article  Google Scholar 

  3. Dasgupta, S., Long, P.M.: Performance guarantees for hierarchical clustering. J. Comput. Syst. Sci. 70(4), 555–569 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Defays, D.: An efficient algorithm for a complete link method. Comput. J. 20(4), 364–366 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  5. Feder, T., Greene, D.H.: Optimal algorithms for approximate clustering. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC), pp. 434–444 (1988)

  6. Ghaemmaghami, H., Dean, D., Vogt, R., Sridharan, S.: Speaker attribution of multiple telephone conversations using a complete-linkage clustering approach. In: Proceedings of the 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4185–4188 (2012)

  7. Rieck, K., Trinius, P., Willems, C., Holz, T.: Automatic analysis of malware behavior using machine learning. J. Comput. Secur. 19(4), 639–668 (2011)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Computer Science, University of Bonn, Bonn, Germany

    Anna Großwendt & Heiko Röglin

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  1. Anna Großwendt
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  2. Heiko Röglin
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Correspondence to Heiko Röglin.

Additional information

This research was supported by ERC Starting Grant 306465 (BeyondWorstCase). A preliminary version of this work appeared in the proceedings of ESA 2015.

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Großwendt, A., Röglin, H. Improved Analysis of Complete-Linkage Clustering. Algorithmica 78, 1131–1150 (2017). https://doi.org/10.1007/s00453-017-0284-6

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  • DOI: https://doi.org/10.1007/s00453-017-0284-6

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