Skip to main content
SpringerLink
Log in

Improved Analysis of Complete-Linkage Clustering

  • Published:
Algorithmica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

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

Author information

Authors and Affiliations

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

    Anna Großwendt & Heiko Röglin

Authors
  1. Anna Großwendt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heiko Röglin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

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

Keywords

Search

Navigation