The haar wavelet transform of a dendrogram

Journal of Classification

Volumn 24, Issue 1, 2007, Pages 3-32

  Murtagh, Fionn ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Compression; Computability; Data approximation; Data summarization; Hierarchical clustering; Multivariate data analysis; Wavelet transform

Indexed keywords

EID: 34250832748     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-007-0007-9     Document Type: Article

References (42)

1. ALTAISKY, M.V. (2004), "p-Adic Wavelet Transform and Quantum Physics", Proceedings of the Steklov Institute of Mathematics, 245, 34-39.
2. ALTAISKY, M.V. (2005), Wavelets: Theory, Applications, Implementation, Hyderabad: Universities Press.
3. ARISTOTLE (350 BC), The Categories, translated by E.M. Edghill, Project Gutenberg e-text, www.gutenberg.net
4. BENEDETTO, R.L. (2004), "Examples of Wavelets for Local Fields", in Eds. C. Heil, P. Jorgensen, D. Larson, Wavelets, Frames, and Operator Theory, Contemporary Mathematics 345, 21-47.
5. BENEDETTO, J.J. and BENEDETTO, R.L. (2004), "A Wavelet Theory for Local Fields and Related Groups", The Journal, of Geometric Analysis, 14, 423-456.
6. BENZÉCRI, J.P. (1979), La Taxinomie (2nd ed.), Paris: Dunod.
7. CHAKRABARTI, K., GAROFALAKIS, M., RASTOGI, R., and SHIM, K. (2001), "Approximate Query Processing using Wavelets", VLDB Journal, International Journal on Very Large Databases, 10, 199-223.
8. SHUI-LUNG CHUANG, and LEE-FENG CHIEN (2005), "Taxonomy Generation for Text Segments: A Practical Web-Based Approach", ACM Transactions on Information Systems, 23, 363-396.
9. DEBNATH, L., and MIKUSINSKI, P. (1999), Introduction to Hilbert Spaces with Applications (2nd ed.), San Diego: Academic Press.
10. EDALAT, A. (1997), "Domains for Computation in Mathematics, Physics and Exact Real Arithmetic", Bulletin of Symbolic Logic, 3, 401-452.
11. EDALAT, A. (2003), "Domain Theory and Continuous Data Types", lecture notes, www.doc.ic.ac.uk/~ae/teaching.html
12. FISHER, R.A. (1936), "The Use of Multiple Measurements in Taxonomic Problems", The Annals of Eugenics, 7, 179-188.
13. FOOTE, R., MIRCHANDANI, G., ROCKMORE, D., HEALY, D., and OLSON, T. (2000a), "A Wreath Product Group Approach to Signal and Image Processing: Part I - Multiresolution Analysis", IEEE Transactions on Signal Processing, 48, 102-132.
14. FOOTE, R., MIRCHANDANI, G., ROCKMORE, D., HEALY, D., and OLSON, T. (2000b), "A Wreath Product Group Approach to Signal and Image Processing: Part II - Convolution, Correlations and Applications", IEEE Transactions on Signal Processing, 48, 749-767.
15. FOOTE, R. (2005), "An Algebraic Approach to Multiresolution Analysis", Transactions of the American Mathematical Society, 357, 5031-5050.
16. FRAZIER, M.W. (1999), An Introduction to Wavelets through Linear Algebra, New York: Springer.
17. HÄRDLE, W. (2000), Wavelets, Approximation, and Statistical Applications, Berlin: Springer.
18. HARTIGAN, J.A., and WONG, M.A. (1979), "A K-Means Clustering Algorithm", Applied Statistics, 28, 100-108.
19. HEISER, W.J. (2004), "Geometric Representation of Association Between Categories", Psychametrika, 69, 513-545.
20. 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.
21. JOE, M.J., WANG, K.-Y., and KIM, S.-W. (2001), "Wavelet Transformation-Based Management of Integrated Summary Data for Distributed Query Processing", Data and Knowledge Engineering, 39, 293-312.
22. JOHNSON, S.C. (1967), "Hierarchical Clustering Schemes", Psychometrika, 32, 241-254.
23. KARGUPTA, H., and PARK, B.-H. (2004), "A Fourier Spectrum-Based Approach to Represent Decision Trees for Mining Data Streams in Mobile Environments", IEEE Transactions on Knowledge and Data Engineering, 16, 216-229.
24. KHRENNIKOV, A.Yu., and KOZYREV, S.V. (2006), "Ultrametric Random Field", http://arxiv.org/abs/math.PR/0603584
25. KOZYREV, S.V. (2002), "Wavelet Analysis as a p-Adic Spectral Analysis", Math. Izv., 66, 367-376. http://arxiv.org/abs/math-ph/ 0012019
26. KOZYREV, S.V. (2004), "P-Adic Pseudo-differential Operators and p-Adic Wavelets", Theoretical and Mathematical Physics, 138, 322-332.
27. LERMAN, I.C. (1981), Classification et Analyse Ordinale des Données, Paris: Dunod.
28. MURTAGH, F. (1985), Multidimensional Clustering Algorithms, Würzburg: Physica-Verlag.
29. MURTAGH, F. (1998), "Wedding the Wavelet Transform and Multivariate Data Analysis", Journal of Classification, 15, 161-183.
30. MURTAGH, F. (2004), "On Ultrametricity, Data Coding, and Computation", Journal of Classification, 21, 167-184.
31. MURTAGH, F. (2005), Correspondence Analysis and Data Coding with Java and R, Boca Raton, Florida: Chapman and Hall.
32. MURTAGH, F. (2006), "Haar Wavelet Transform of a Dendrogram: Additional Notes", http://arxiv.org/pdf/cs.IR/0702067
33. MURTAGH, F. (2007), "On Ultrametric Algorithmic Information", in preparation.
34. MURTAGH, F., STARCK, J.-L., and BERRY, M. (2000), "Overcoming the Curse of Dimensionality in Clustering by Means of the Wavelet Transform", The Computer Journal, 43, 107-120.
35. NABBEN, R., and VARGA, R.S. (1994), "A Linear Algebra Proof that the Inverse of a Strictly Ultrametric Matrix is a Strictly Diagonal Dominant Stieltjes Matrix", SIAM Journal on Matrix Analysis and Applications, 15, 107-113.
36. OCKERBLOOM, J.M. (2003), Grimms' Fairy Tales, http://www.cs.cmu. edu/~spok/grimmtmp
37. SCHIKHOF, W.M. (1984), Ultrametric Calculus, Cambridge: Cambridge University Press.
38. SPÄTH, H. (1985), Cluster Dissection and Analysis, Chichester, England: Ellis Horwood.
39. STARCK. J.-L., and MURTAGH, F. (2006), Astronomical Image and Data Analysis, Heidelberg: Springer, Chapter 9: "Multiple Resolution in Data Storage and Retrieval" (1st ed. 2002.)
40. STRANG, G., and NGUYEN, T. (1996), Wavelets and Filter Banks, Wellesley, Massachusetts: Wellesley-Cambridge Press.
41. TAO LI, QI LI, SHENGHUO ZHU, and MITSUNORI OGIHARA (2002), "A Survey on Wavelet Applications in Data Mining", SIGKDD Explorations, 4, 49-68.
42. VITTER, J.S., and WANG, M. (1999), "Approximate Computation of Multidimensional Aggregates of Sparse Data using Wavelets", Proceedings of the ACM SIGMOD International Conference on Management of Data, 193-204.