On ultrametricity, data coding, and computation

Journal of Classification

Volumn 21, Issue 2, 2004, Pages 167-184

  Murtagh, Fionn ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Binary tree; Classification; Clustering; Dendrogram; Hierarchy; Isosceles; Metric; Non Archimedean; p Adic; Ultrametric; Unsupervised

Indexed keywords

EID: 17544364135     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00357-004-0015-y     Document Type: Article

References (35)

1. BELLMAN, R. (1961). Adaptive Control Processes: A Guided Tour, Princeton, New Jersey: Princeton University Press.
2. BENZÉCRI, J.P. (1979). La Taxinomie, 2nd ed., Paris: Dunod.
3. BENZÉCRI, J.P. (1992). Transl. T.K. Gopalan. Correspondence Analysis Handbook, Basel: Marcel Dekker.
4. BUSTOS, D., NAVARRO, G., and CHÁVEZ, E. (2003). "Pivot Selection Techniques for Proximity Searching in Metric Spaces", Pattern Recognition Letters, 24, 2357-2366.
5. CAILLIEZ, F., and PAGÈS, J.-P. (1976). Introduction à l'Analyse des Données, Paris: SMASH (Société de Mathématiques Appliquées et de Sciences Humaines).
6. CHÁVEZ, E., and NAVARRO, G. (2000). "Measuring the Dimensionality of General Metric Spaces", Technical Report TR/DCC-00-1, Department of Computer Science, University of Chile.
7. CHÁVEZ, E., NAVARRO, G., BAEZA-YATES, R., and MARROQUíN, J.L. (2001). "Proximity Searching in Metric Spaces", ACM Computing Surveys, 33, 273-321.
8. CHÁVEZ, E., and NAVARRO, G. (2003). "Probabilistic Proximity Search: Fighting the Curse of Dimensionality in Metric Spaces", Information Processing Letters, 85, 39-46.
9. DAY, W.H.E. (1996). "Complexity Theory: An Introduction for Practitioners of Classification", in P. Arabie, L.J. Hubert and G. De Soete, Eds., Clustering and Classification, Singapore: World Scientific, 199-233.
10. FISHER, R.A. (1936). "The Use of Multiple Measurements in Taxonomic Problems", The Annals of Eugenics, 1, 179-188.
11. FUKUNAGA, K., and NARENDRA, P.M. (1975). "A Branch and Bound Algorithm for Computing k-Nearest Neighbors", IEEE Transactions on Computers, C-24, 750-753.
12. GOUVÊA, F.Q. 2003, P-Adic Numbers, New York: Springer-Verlag, 2nd edn., 3rd printing.
13. HARTMANN, A.K. (1998). "Are Ground States of 3D ±J Spin Glasses Ultrametric?", Europhysics Letters, 44, 249-254.
14. HJALTASON, G.R., and SAMET, H. (2003). "Properties of Embedding Methods for Similarity Searching in Metric Spaces", IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 530-549.
15. JOHNSON, S.C. (1967). "Hierarchical Clustering Schemes", Psychometrika, 32, 241-254.
16. KRASNER, M. (1944). "Nombres semi-réels et espaces ultramétriques", Comptes-Rendus de l'Académie des Sciences, Tome II, 219, 433.
17. KŘIVÁNEK, M., and MORÁVEK, J. (1986). "NP-Hard Problems in Hierarchical-Tree Clustering", Acta Informatica, 23, 311-323.
18. KŘIVÁNEK, M., and MORÁVEK, J. (1984). "On NP-Hardness in Hierarchical Clustering", in T. Havránek, Z. Sidák and M. Novák, Eds., Compstat 1984: Proceedings in Computational Statistics, 189-194, Vienna: Physica-Verlag.
19. LERMAN, I.C. (1981). Classification et Analyse Ordinale des Données, Paris: Dunod.
20. MAHLER, M. (1981). P-adic Numbers and Their Functions, 2nd edn., Cambridge: Cambridge University Press.
21. MÉZARD, M., PARISI, G., SOURLAS, N., TOULOUSE, G., and VIRASORO, M.A. (1984). "Nature of the Spin-Glass Phase", Physical Review Letters, 52, 1156-1159.
22. MURTAGH, F. (1983). "A Survey of Recent Advances in Hierarchical Clustering Algorithms", The Computer Journal, 26, 354-359.
23. MURTAGH, F. (1984a). "Counting Dendrograms: a Survey", Discrete Applied Mathematics, 1, 191-199.
24. MURTAGH, F. (1984b). "Structures of Hierarchic Clusterings: Implications for Information Retrieval and for Multivariate Data Analysis", Information Processing and Management, 20, 611-617.
25. MURTAGH, F. (1985). Multidimensional Clustering Algorithms, Würzburg: Physica-Verlag.
26. OGIELSKI, A.T., and STEUB, D.L. (1985). "Dynamics of Ultrametric Spaces", Physical Review Letters, 55, 1634-1637.
27. PARISI, G., and RICCI-TERSENGHI, F. (2000). "On the Origin of Ultrametricity", Journal of Physics A: Mathematical and General, 33, 113-129.
28. RAMMAL, R., ANGLES D'AURIAC, J.C., and DOUCOT, B. (1985). "On the Degree of Ultrametricity", Le Journal de Physique - Lettres, 46, L-945 - L-952.
29. RAMMAL, R., TOULOUSE, G., and VIRASORO, M.A. (1986). "Ultrametricity for Physicists", Reviews of Modern Physics, 58, 765-788.
30. ROBERTS, M.D. (2001). "Ultrametric Distance in Syntax", http://arXiv.org/abs/cs.CL/9810012
31. SCHIKHOF, W.H. (1984). Ultrametric Calculus, Cambridge: Cambridge University Press.
32. TREVES, A. (1997). "On the Perceptual Structure of Face Space", BioSystems, 40, 189-196.
33. WATSON, S. (2003). "The Classification of Metrics and Multivariate Statistical Analysis", preprint, York University, 27 pp.
34. WILLETT, P. (1988). "Recent Trends in Hierarchic Document Clustering: A Critical Review", Information Processing and Management, 24, 577-597.
35. YOUNG, M.P., and YAMANE, S. (1992). "Sparse Population Coding of Faces in the Inferotemporal Cortex", Science, 256, 1327-1331.