On Hölder fields clustering

Test

Volumn 21, Issue 2, 2012, Pages 301-316

  Cadre, Benoît ^a   Paris, Quentin ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Clustering; Empirical risk minimization; Hilbert space; k means; Random fields; Unsupervised learning

Indexed keywords

EID: 85027917874     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11749-011-0244-4     Document Type: Article

References (37)

1. Abaya EA, Wise GL (1984) Convergence of vector quantizers with applications to optimal quantization. SIAM J Appl Math 183-189.
2. Adamczak R (2008) A tail inequality for suprema of unbounded empirical processes with applications to Markov chains. Electron J Probab 1000-1034.
3. Antos A (2005) Improved minimax bounds on the test and training distortion of empirically designed vector quantizers. IEEE Trans Inf Theory 4022-4032.
4. Antos A, Györfi L, György A (2005) Improved convergence rates in empirical vector quantizer design. IEEE Trans Inf Theory 4013-4022.
5. Bartlett PL, Linder T, Lugosi G (1998) The minimax distorsion redundancy in empirical quantizer design. IEEE Trans Inf Theory 1802-1813.
6. Biau G, Devroye L, Lugosi G (2008) On the performance of clustering in Hilbert spaces. IEEE Trans Inf Theory 781-790.
7. Breton JC, Nourdin I, Peccati G (2009). Exact confidence intervals for the Hurst parameter of a fractional Brownian motion. Electron J Stat 416-425.
8. P(1/n). IEEE Trans Inf Theory 457.
9. Coeurjolly J-F (2008). Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles. Ann Stat 1404-1434.
10. Cont R, Tankov P (2003) Financial modelling with jump processes, 2nd edn. Chapmann and Hall, CRC Press, London.
11. Devroye L, Györfi L, Lugosi G (1996) A probabilistic theory of pattern-recognition. Springer, New York.
12. Duda RO, Hart PE, Stork DG (2000) Pattern classification, 2nd edn. Wiley-Interscience, New York.
13. Frisch U (1995) Turbulences. Cambridge University Press, Cambridge.
14. Gersho A, Gray RM (1992) Vector quantization and signal compression. Kluwer Academic, Boston.
15. Graf S, Luschgy H (2000) Foundations of quantization for probability distributions. Lectures notes in mathematics, vol 1730. Springer, New York.
16. Gray RM, Neuhoff DL (1998) Quantization. IEEE Trans Inf Theory 2325-2384.
17. Hartigan JA (1975) Clustering algorithms. Wiley, New York.
18. Hartigan JA (1978) Asymptotic distributions for clustering criteria. Ann Stat 117-131.
19. Huang W (2009) Exponential integrability of Itô's processes. J Math Anal Appl 427-433.
20. Kärner O (2001) Comments on Hurst exponent. Geophys Res Lett 3825-3826.
21. Kimmel M, Axelrod DE (2002) Branching processes in biology. Springer, Berlin.
22. Lacaux C, Loubès J-M (2007) Hurst exponent estimation of fractional Lévy motions. Alea 143-164.
23. Lamberton D, Lapeyre B (1996) Introduction to stochastic calculus applied to finance. Chapman and Hall, CRC Press, London.
24. Linder T (2000) On the training distortion of vector quantizers. IEEE Trans Inf Theory 1617-1623.
25. Linder T (2001) Learning-theoretic methods in vector quantization. Lecture notes for the advanced school on the principle of nonparametric learning, Udine, Italy, July 9-13.
26. Linder T, Lugosi G, Zeger K (1994) Rates of convergence in the source coding theorem, in empirical quantizer design, and in universal lossy source coding. IEEE Trans Inf Theory 1728-1740.
27. Lindstrøm T (1993). Fractional Brownian fields as integrals of white noise. Bull Lond Math Soc 83-88.
28. Mandelbrot B (1997) Fractals and scaling in finance. Selected works of Benoit B. Mandelbrot. Discontinuity, concentration, risk, selecta vol E, with a forward by RE Gomory. Springer, New York.
29. Mandelbrot B, van Ness J (1968) Fractional Brownian motion, fractional noises and applications. SIAM Rev 422-437.
30. Maurer A, Pontil M (2010). K-dimensional coding schemes in Hilbert spaces. IEEE Trans Inf Theory 5839-5846.
31. Pipiras V, Taqqu MS (2003) Fractional calculus and its connection to fractional Brownian motion. In: Long range dependence. Birkhäuser, Basel, pp 166-201.
32. Pisier G (1983) Some applications of the metric entropy condition to harmonic analysis. In: Banach spaces, harmonic analysis, and probability theory. Lecture notes in math, vol 995. Springer, Berlin, pp 123-154.
33. Pollard D (1981) Strong consistency of k-means clustering. Ann Stat 135-140.
34. Pollard D (1982a) A central limit theorem for k-means clustering. Ann Probab 199-205.
35. Pollard D (1982b) Quantization and the method of k-means. IEEE Trans Inf Theory 1728-1740.
36. Revuz D, Yor M (1999) Continuous martingales and Brownian motion. Springer, New York.
37. van Kampen NG (2007) Stochastic processes in physics and chemistry, 3rd edn. Elsevier, New York.