Testing stationarity with surrogates: A time-frequency approach

IEEE Transactions on Signal Processing

Volumn 58, Issue 7, 2010, Pages 3459-3470

  Borgnat, Pierre ^a   Flandrin, Patrick ^a   Honeine, Paul ^b   Richard, Cédric ^b   Xiao, Jun ^a  

^a UNIVERSITÉ DE LYON   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE TROYES   (France)

Author keywords

One class classification; Stationarity test; Support vector machines; Time frequency analysis

Indexed keywords

LOCAL TIME; NONSTATIONARY; NULL HYPOTHESIS; ONE-CLASS CLASSIFICATION; ONE-CLASS CLASSIFIER; STATIONARITY; STATIONARITY TEST; TIME FREQUENCY ANALYSIS; TIME FREQUENCY FEATURES; TIME-FREQUENCY APPROACH; TYPICAL MODEL;

SUPPORT VECTOR MACHINES;

STATISTICAL TESTS;

EID: 77953759601     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2043971     Document Type: Article

References (36)

1. J. Xiao, P. Borgnat, and P. Flandrin, "Testing stationarity with timefrequency surrogates," in Proc. EUSIPCO, Poznan, Poland, 2007, pp. 2020-2024.
2. J. Xiao, P. Borgnat, P. Flandrin, and C. Richard, "Testing stationarity with surrogates-A one-class SVM approach," in Proc. IEEE Stat. Signal Process. Workshop (SSP), Madison, WI, 2007, pp. 720-724.
3. S. Mallat, G. Papanicolaou, and Z. Zhang, "Adaptive covariance estimation of locally stationary processes," Ann. Stat., vol.24, no.1, pp. 1-47, 1998.
4. W. Martin and P. Flandrin, "Detection of changes of signal structure by using the Wigner-Ville spectrum," Signal Process., vol.8, pp. 215-233, 1985.
5. R. Silverman, "Locally stationary random processes," IRE Trans. Inf. Theory, vol.3, pp. 182-187, 1957.
6. M. Davy and S. Godsill, "Detection of abrupt signal changes using support vector machines: An application to audio signal segmentation," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Orlando, FL, 2002, pp. 1313-1316.
7. H. Laurent and C. Doncarli, "Stationarity index for abrupt changes detection in the time-frequency plane," IEEE Signal Process. Lett., vol.5, no.2, pp. 43-45, 1998.
8. W. Martin, "Measuring the degree of non-stationarity by using the Wigner-Ville spectrum," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), San Diego, CA, 1984, pp. 41B.3.1-41B.3.4.
9. S. Kay, "A new nonstationarity detector," IEEE Trans. Signal Process., vol.56, no.4, pp. 1440-1451, Apr. 2008.
10. P. Basu, D. Rudoy, and P. Wolfe, "A nonparametric test for stationarity based on local Fourier analysis," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Taiwan, R.O.C., 2009, pp. 3005-3008.
11. M. B. Priestley and T. S. Rao, "A test for non-stationarity of timeseries," J. Roy. Stat. Soc. B (Methodologic.), vol.31, no.1, pp. 140-149, 1969.
12. M. B. Priestley, Non-Linear and Non-Stationary Time Series Analysis. London, U.K.: Academic, 1988.
13. M. B. Priestley, "Evolutionary spectra and non-stationary processes," J. Roy. Stat. Soc. B (Methodologic.), vol.27, no.2, pp. 204-237, 1965.
14. P. Flandrin, Time-Frequency/Time-Scale Analysis. San Diego, CA: Academic, 1999.
15. M. Bayram and R. Baraniuk, "Multiple window time-varying spectrum estimation," in Nonlinear and Nonstationary Signal Processing, W. J. Fitzgerald, et al., Ed. Cambridge, U.K.: Cambridge Univ. Press, 2000.
16. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, "Testing for nonlinearity in time series: The method of surrogate data," Physica D, vol.58, no.1-4, pp. 77-94, 1992.
17. C. Keylock, "Constrained surrogate time series with preservation of the mean and variance structure," Phys. Rev. E, vol.73, pp. 030 767.1-030 767.4, 2006.
18. M. Basseville, "Distances measures for signal processing and pattern recognition," Signal Process., vol.18, no.4, pp. 349-369, 1989.
19. J. Xiao, P. Borgnat, and P. Flandrin, "Sur un test temps-fréquence de stationnarité," (in French, with extended English summary) Traitement du Signal, vol.25, no.4, pp. 357-366, 2008.
20. E. Serpedin, F. Panduru, I. Sari, and G. Giannakis, "Bibliography on cyclostationarity," Signal Process., vol.85, no.12, pp. 2233-2303, 2005.
21. P. J. Brockwell and R. A. Davies, Time Series: Theory and Methods, ser. Springer Series in Statistics, 2nd ed. New York: Springer, 1991.
22. Y. Dwivedi and S. S. Rao, "A test for second order stationarity of a time series based on the discrete Fourier transform," 2009, arXiv:0911.4744.
23. J. Huillery, F. Millioz, and N. Martin, "On the description of spectrogram probabilities with a Chi-squared law," IEEE Trans. Signal Process., vol.56, no.6, pp. 2249-2258, Jun. 2008.
24. E. Parzen, "On estimation of a probability density function and mode," Ann. Math. Stat., vol.33, no.3, pp. 1065-1076, 1962.
25. T. W. Sager, "An iterative method for estimating a multivariate mode and isopleth," J. Amer. Stat. Assoc., vol.74, no.366, pp. 329-339, 1979.
26. M. Moya, M.Koch, and L. Hostetler, "One-class classifier networks for target recognition applications," in Proc. World Congr. Neural Netw., 1993, pp. 797-801.
27. M. Moya and D. Hush, "Network constraints and multi-objective optimization for one-class classification," Neural Netw., vol.9, no.3, pp. 463-474, 1996.
28. D. M. J. Tax and R. P. W. Duin, "Support vector data description," Mach. Learn., vol.54, no.1, pp. 45-66, 2004.
29. B. Schölkopf, J. C. Platt, J. Shawe-Taylor, A. J. Smola, and R. C. Williamson, "Estimating the support of a high-dimensional distribution," Neural Comput., vol.13, no.7, pp. 1443-1471, 2001.
30. J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis. Cambridge, U.K.: Cambridge Univ. Press, 2004.
31. R. Vert, "Theoretical insights on density level set estimation, application to anomaly detection," Ph.D. dissertation, Paris 11-Paris Sud, Paris, France, 2006.
32. P. Honeiné, C. Richard, and P. Flandrin, "Time-frequency learning machines," IEEE Trans. Signal Process., vol.55, no.7, pt. 2, pp. 3930-3936, Jul. 2007.
33. H. Amoud, P. Honeine, C. Richard, P. Borgnat, and P. Flandrin, "Timefrequency learning machines for nonstationarity detection using surrogates," in Proc. IEEE Stat. Signal Process. Workshop (SSP), Cardiff, U.K., 2009, pp. 565-568.
34. C. Richard, A. Ferrari, H. Amoud, P. Honeine, P. Flandrin, and P. Borgnat, "Statistical hypothesis testing with time-frequency surrogates to check signal stationarity," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Dallas, TX, 2010, pp. 3666-3669.
35. J. Xiao and P. Flandrin, "Multitaper time-frequency reassignment for nonstationary spectrum estimation and chirp enhancement," IEEE Trans. Signal Process., vol.55, no.6, pt. 2, pp. 2851-2860, Jun. 2007.
36. P. Borgnat and P. Flandrin, "Revisiting and testing stationarity," J. Phys.: Conf. Series, vol.139, p. 012004, 2008.