Abstract
We are interested in the greedy method to compute an hierarchical complete linkage clustering. There are two known methods for this problem, one having a running time of \({\mathcal O}(n^3)\) with a space requirement of \({\mathcal O}(n)\) and one having a running time of \({\mathcal O}(n^2 \log n)\) with a space requirement of Θ(n 2), where n is the number of points to be clustered. Both methods are not capable to handle large point sets. In this paper, we give an algorithm with a space requirement of \({\mathcal O}(n)\) which is able to cluster one million points in a day on current commodity hardware.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bao, E., Jiang, T., Kaloshian, I., Girke, T.: Seed: Efficient clustering of next-generation sequences. Bioinformatics 27(18), 2502–2509 (2011), http://bioinformatics.oxfordjournals.org/content/27/18/2502.abstract
Bu, D., Li, S.C., Li, M.: Clustering 100,000 protein structure decoys in minutes. IEEE/ACM Transactions on Computational Biology and Bioinformatics 9(3), 765–773 (2012)
Chong, Z., Ruan, J., Wu, C.I.: Rainbow: An integrated tool for efficient clustering and assembling rad-seq reads. Bioinformatics 28(21), 2732–2737 (2012), http://bioinformatics.oxfordjournals.org/content/28/21/2732.abstract
Cormack, R.: A review of classification. Journal of the Royal Statistical Society, Series A 134(3), 321–367 (1971)
Day, W.H., Edelsbrunner, H.: Efficient algorithms for agglomerative hierarchical clustering methods. Journal of Classification 1, 1–24 (1984)
Defays, D.: An efficient algorithm for a complete link method. Computer Journal 20, 364–366 (1977)
Ernst, J., Nau, G.J., Bar-Joseph, Z.: Clustering short time series gene expression data. Bioinformatics 21(suppl. 1), i159–i168 (2005), http://bioinformatics.oxfordjournals.org/content/21/suppl_1/i159.abstract
Feliu, E., Oliva, B.: How different from random are docking predictions when ranked by scoring functions? Proteins: Structure, Function, and Bioinformatics 78(16), 3376–3385 (2010)
Gray, J., Moughan, S., Wang, C., Schueler-Furman, O., Kuhlman, B., Rohl, C., Baker, D.: Protein-protein docking with simultaneous optimization of rigid-body displacement and side-chain conformations. J. Mol. Biol. 331(1), 281–299 (2003)
Hildebrandt, A., Dehof, A.K., Rurainski, A., Bertsch, A., Schumann, M., Toussaint, N., Moll, A., Stockel, D., Nickels, S., Mueller, S., Lenhof, H.P., Kohlbacher, O.: BALL - Biochemical Algorithms Library 1.3. BMC Bioinformatics 11(1), 531 (2010)
Hildebrandt, A.K., Diezen, M., Lengauer, T., Lenhof, H.P., Althaus, E., Hildebrandt, A.: Efficient computation of root mean square deviations under rigid transformations (submitted)
Jamroz, M., Kolinski, A.: Clusco: Clustering and comparison of protein models. BMC Bioinformatics 14(1), 62 (2013)
Miele, V., Penel, S., Duret, L.: Ultra-fast sequence clustering from similarity networks with silix. BMC Bioinformatics 12(1), 116 (2011), http://www.biomedcentral.com/1471-2105/12/116
Murtagh, F.: Complexities of hierarchic clustering algorithms: The state of the art. Computational Statistics Quarterly 1, 101–113 (1984)
Shortle, D., Simons, K.T., Baker, D.: Clustering of low-energy conformations near the native structures of small proteins. Proceedings of the National Academy of Sciences 95(19), 11158–11162 (1998), http://www.pnas.org/content/95/19/11158.abstract
Sibson, R.: SLINK: An optimally efficient algorithm for the single-link cluster method. The Computer Journal 16(1), 30–34 (1973)
Sivriver, J., Habib, N., Friedman, N.: An integrative clustering and modeling algorithm for dynamical gene expression data. Bioinformatics 27(13), i392–i400 (2011), http://bioinformatics.oxfordjournals.org/content/27/13/i392.abstract
Torda, A.E., van Gunsteren, W.F.: Algorithms for clustering molecular dynamics configurations. J. Comput. Chem. 15(12), 1331–1340 (1994), http://dx.doi.org/10.1002/jcc.540151203
Wang, Y., Xu, M., Wang, Z., Tao, M., Zhu, J., Wang, L., Li, R., Berceli, S.A., Wu, R.: How to cluster gene expression dynamics in response to environmental signals. Briefings in Bioinformatics 13(2), 162–174 (2012), http://bib.oxfordjournals.org/content/13/2/162.abstract
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Althaus, E., Hildebrandt, A., Hildebrandt, A.K. (2014). A Greedy Algorithm for Hierarchical Complete Linkage Clustering. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Algorithms for Computational Biology. AlCoB 2014. Lecture Notes in Computer Science(), vol 8542. Springer, Cham. https://doi.org/10.1007/978-3-319-07953-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-07953-0_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07952-3
Online ISBN: 978-3-319-07953-0
eBook Packages: Computer ScienceComputer Science (R0)