Fast, Linear Time Hierarchical Clustering using the Baire Metric

Journal of Classification

Volumn 29, Issue 2, 2012, Pages 118-143

  Contreras, Pedro ^a,b   Murtagh, Fionn ^a,c  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b ThinkingSafe Ltd   (United Kingdom)

^c SCIENCE FOUNDATION IRELAND   (Ireland)

Author keywords

Baire; Hierarchical clustering; k means; Longest common prefix; m adic; p adic; Redshift; Ultrametric

Indexed keywords

EID: 84863004563     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-012-9106-3     Document Type: Article

References (31)

1. ADELMAN-MCCARTHY, J. K. et al. (2007), "The Fifth Data Release of the Sloan Digital Sky Survey", The Astrophysical Journal Supplement Series, 172(2), 634-644.
2. BENZÉCRI, J.-P. (1979), La Taxinomie (2nd ed.), Paris: Dunod.
3. BRADLEY, P. E. (2008), "Degenerating Families of Dendrograms", Journal of Classification, 25, 27-42.
4. BRADLEY, P. E. (2010), "Mumford Dendrograms", Computer Journal, 53, 393-404.
5. CONTRERAS, P. (2010), Search and Retrieval in Massive Data Collections, London: Royal Holloway, University of London.
6. CONTRERAS, P., and MURTAGH, F. (2007), "Evaluation of Hierarchies based on the Longest Common Prefix, or Baire, Metric", Classification Society of North America (CSNA) meeting, University of Illinois, Urbana-Champaign IL, USA.
7. D'ABRUSCO, R., LONGO, G., PAOLILLO, M., BRESCIA, M., DE FILIPPI, E., STAIANO, A., and TAGLIAFERRI, R. (2007a), "The Use of Neural Networks to Probe the Structure of the Nearby Universe", ArXiv, April 2007, http://arxiv. org/pdf/astroph/0701137/.
8. D'ABRUSCO, R., STAIANO, A., LONGO, G., BRESCIA, M., PAOLILLO, M., DE FILIPPIS, E., and TAGLIAFERRI, R. (2007b), "Mining the SDSS Archive. I. Photometric Redshifts in the Nearby Universe", Astrophysical Journal, 663(2), 752-764.
9. D'ABRUSCO, R., STAIANO, A., LONGO, G., PAOLILLO, M., and DE FILIPPIS, E. (2006), "Steps Toward a Classifier for the Virtual Observatory. I. Classifying the SDSS Photometric Archive", 1st Workshop of Astronomy and Astrophysics for Students-Naples, April 2006, http://arxiv. org/abs/0706. 4424.
10. DAVEY, B. A., and PRIESTLEY, H. A. (2002), Introduction to Lattices and Order (2nd ed.), Cambridge: Cambridge University Press.
11. FERNÁNDEZ-SOTO, A., LANZETTA, K. M., HSIAO-WENCHEN, PASCARELLE, S. M., and NORIAKI YAHATA (2001), "On the Compared Accuracy and Reliability of Spectroscopic and Photometric Redshift Measurements", The Astrophysical Journal Supplement Series, 135, 41-61.
12. GANTER, B., and WILLE, R. (1999), Formal Concept Analysis: Mathematical Foundations, Springer, (Formale Begriffsanalyse: Mathematische Grundlagen, Springer, 1996).
13. HARTIGAN, J. A., and WONG, M. A. (1979), "Algorithm AS 136: A k-means Clustering Algorithm", Journal of the Royal Statistical Society, Series C (Applied Statistics), 28(1), 100-108.
14. HITZLER, P., and SEDA, A. K (2002), "The Fixed-point Theorems of Priess-Crampe and Ribenboim in Logic Programming", Fields Institute Communications, 32, 219-235.
15. JANOWITZ, M. F. (1978), "An Order Theoretic Model for Cluster Analysis", SIAM Journal on Applied Mathematics, 34, 55-72.
16. JANOWITZ, M. F. (2010), Ordinal and Relational Clustering, Hackensack, NJ: World Scientific.
17. JOHNSON, S. C. (1967), "Hierarchical Clustering Schemes", Psychometrika, 32, 241-254.
18. LERMAN, I. C. (1981), Classification et Analyse Ordinale des Données, Paris: Dunod.
19. LONGO, G. (2010), "DAME. Data Mining & Exploration", http://people. na. infn. it/astroneural/.
20. MURTAGH, F. (2009), "Symmetry in Data Mining and Analysis: A Unifying View based on Hierarchy", Proceedings of Steklov Institute of Mathematics, 265, 177-198.
21. MURTAGH, F. (2004a), "Quantifying Ultrametricity", in COMPSTAT 2004 - Proceedings in Computational Statistics, ed. J. Antoch, Prague, Czech Republic: Springer, pp. 1561-1568.
22. MURTAGH, F. (2004b), "Thinking Ultrametrically", in Classification, Clustering, and Data Mining Applications. Proceedings of the Meeting of the International Federation of Classification Societies (IFCS), eds. D. Banks, L. House, F. R. McMorris, P. Arabie, and W. Gaul, Chicago: Springer, pp. 3-14.
23. MURTAGH, F. (2004c), "On Ultrametricity, Data Coding, and Computation", Journal of Classification, 21, 167-184.
24. MURTAGH, F. (2005), "Identifying the Ultrametricity of Time Series", The European Physical Journal B, 43(4), 573-579.
25. MURTAGH, F. (1985), Multidimensional Clustering Algorithms, Wuerzburg: Physica-Verlag.
26. MURTAGH, F., DOWNS, G., and CONTRERAS, P. (2008), "Hierarchical Clustering of Massive, High Dimensional Data Sets by Exploiting Ultrametric Embedding", SIAM Journal on Scientific Computing, 30(2), 707-730.
27. PEREIRA, J., SCHMIDT, F., CONTRERAS, P., MURTAGH, F., and ASTUDILLO, H. (2010), "Clustering and Semantics Preservation in Cultural Heritage Information Spaces", in RIAO'2010, 9th International Conference on Adaptivity, Personalization and Fusion of Heterogeneous Information, Paris, France, pp. 100-105.
28. SDSS (2008), Sloan Digital Sky Survey, http://www. sdss. org.
29. SEDA, A. K, and HITZLER, P. (2010), "Generalized Distance Functions in the Theory of Computation", Computer Journal, 53, 443-464.
30. VAN ROOIJ, A. C. M. (1978), Non-Archimedean Functional Analysis, New York: Marcel Dekker.
31. VEMPALA, S. S. (2004), "The Random Projection Method. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science", American Mathematical Society, 65, ISBN = 0821820184.