Statistical models of reconstructed phase spaces for signal classification

IEEE Transactions on Signal Processing

Volumn 54, Issue 6 I, 2006, Pages 2178-2186

  Povinelli, Richard J ^a   Johnson, Michael T ^a   Lindgren, Andrew C ^b   Roberts, Felice M ^a   Ye, Jinjin ^c  

^a Marquette University   (United States)

^b NORTHROP GRUMMAN CORPORATION   (United States)

^c University of California   (United States)

Author keywords

Reconstructed phase spaces (RPSs); Signal classification; Statistical models

Indexed keywords

MAXIMUM LIKELIHOOD ESTIMATION; NEURAL NETWORKS; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; SIGNAL FILTERING AND PREDICTION; STATISTICAL METHODS; TIME SERIES ANALYSIS;

RECONSTRUCTION PHASE SPACES; SIGNAL CLASSIFICATION; STATISTICAL MODELS;

SIGNAL RECONSTRUCTION;

EID: 33744520854     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2006.873479     Document Type: Article

References (38)

1. 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, pp. 77-94, 1992.
2. T. Sauer, J. A. Yorke, and M. Casdagli, "Embedology," J. Stat. Phys., vol. 65, pp. 579-616, 1991.
3. F. Takens, "Detecting strange attractors in turbulence," in Proc. Dynam. Syst. Turbulence, Warwick, 1980, pp. 366-381.
4. G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control, Rev. ed. San Francisco, CA: Holden-Day, 1976.
5. B. Gold and N. Morgan, Speech and Audio Signal Processing. New York: Wiley, 2000.
6. J. G. Proakis, Digital Communications, 4th ed. Boston, MA: McGraw-Hill, 2001.
7. E. Ott, Chaos in Dynamical Systems. Cambridge, U.K.: Cambridge Univ. Press, 1993.
8. P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D, vol. 9, pp. 189-208, 1983.
9. H. Leung, "System identification using chaos with application to equalization of a chaotic modulation system," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, pp. 314-320, 1998.
10. R. J. Povinelli, F. M. Roberts, K. M. Ropella, and M. T. Johnson, "Are nonlinear ventricular arrhythmia characteristics lost, as signal duration decreases?," in Proc. Comput. Cardiol., Memphis, TN, 2002, pp. 221-224.
11. D. M. Tumey, P. E. Morton, D. F. Ingle, C. W. Downey, and J. H. Schnurer, "Neural network classification of EEG using chaotic preprocessing and phase space reconstruction," in Proc. 1991 IEEE 17th Ann. Northeast Bioeng. Conf., 1991, pp. 51-52.
12. R. J. Povinelli, M. T. Johnson, A. C. Lindgren, and J. Ye, "Time series classification using Gaussian mixture models of reconstructed phase spaces," IEEE Trans. Knowl. Data Eng., vol. 16, pp. 779-783, 2004.
13. D. Sciamarella and G. B. Mindlin, "Unveiling the topological structure of chaotic flows from data," Phys. Rev. E, vol. 64, pp. 036 209:1-7,2001.
14. R. Brown, "Calculating Lyapunov exponents for short and/or noisy data sets," Phys. Rev. E, vol. 47, pp. 3962-3969, 1993.
15. A. Petry, D. Augusto, and C. Barone, "Speaker identification using nonlinear dynamical features," Chaos Solitons Fractals, vol. 13, pp. 221-231, 2002.
16. P. E. Rapp, T. A. A. Watanabe, P. Faure, and C. J. Cellucci, "Nonlinear signal classification," Int. J. Bifurc. Chaos in Appl. Sci. Eng., vol. 12, pp. 1273-93, 2002.
17. N. Tishby, "A dynamical systems approach to speech processing," in Proc. Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), 1990, pp. 365-368.
18. Y. Ashkenazy, P. C. Ivanov, S. Havlin, C.-K. Peng, A. L. Goldberger, and H. E. Stanley, "Magnitude and sign correlations in heartbeat fluctuations," Phys. Rev. Lett., vol. 86, pp. 1900-3, 2001.
19. M. Banbrook, S. McLaughlin, and I. Mann, "Speech characterization and synthesis by nonlinear methods," IEEE Trans. Speech Audio Process., vol. 7, pp. 1-17, 1999.
20. H. D. I. Abarbanel, T. A. Carroll, L. M. Pecora, J. J. Sidorowich, and L. S. Tsimring, "Predicting physical variables in time-delay embedding," Phys. Rev. E, vol. 49, pp. 1840-1853, 1994.
21. T. Sauer, "Time series prediction using delay coordinate embedding," in Time Series Prediction: Forecasting the Future and Understanding the Past, A. S. Weigend and N. A. Gershenfeld, Eds. Reading, MA: Addison-Wesley, 1994, pp. 175-194.
22. J. Kadtke, "Classification of highly noisy signals using global dynamical models," Phys. Lett. A, vol. 203, pp. 196-202, 1995.
23. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, "Geometry from a time series," Phys. Rev. Lett., vol. 45, pp. 712-716, 1980.
24. H. Whitney, "Differentiable manifolds," Ann. Math., ser. 2nd, vol. 37, pp. 645-680, 1936.
25. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1997.
26. H. D. I. Abarbanel, Analysis of Observed Chaotic Data. New York: Springer, 1996.
27. L. Cao, "Practical method for determining the minimum embedding dimension of a scalar time series," Physica D, vol. 110, pp. 43-50, 1997.
28. T. Gautama, D. P. Mandic, and M. M. V. Hulle, "A differential entropy based method for determining the optimal embedding parameters of a signal," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Hong Kong, 2003, pp. 29-32.
29. J. B. Vitrano and R. J. Povinelli, "Selecting dimensions and delay values for time-delay embedding using a genetic algorithm," in Proc. Genetic Evolut. Computat. Conf., San Francisco, CA, 2001, pp. 1423-1430.
30. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Royal Statist. Soc., ser. B, vol. 39, pp. 1-38, 1977.
31. T. M. Mitchell, Machine Learning. New York: McGraw-Hill, 1997.
32. I. Singer, Implantable Cardioverter-Defibrillator. Amonk, NY: Futura, 1994.
33. C. Cabo and D. S. Rosenbaum, Quantitative Cardiac Electrophysiology. New York: Marcel Dekker, 2002.
34. I. Romero and L. Serrano, "ECG frequency domain features extraction: A new characteristic for arrhythmias classification," in Proc. 23rd Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., Istanbul, Turkey, 2001, pp. 2006-2008.
35. M. T. Johnson, R. J. Povinelli, A. C. Lindgren, J. Ye, X. Liu, and K. M. Indrebo, "Time-domain isolated phoneme classification using reconstructed phase spaces," IEEE Trans. Speech Audio Process., vol. 13, no. 4, pp. 458-466, Jul. 2005.
36. J. S. Garofolo, L. F. Lamel, W. M. Fisher, J. G. Fiscus, D. S. Pallett, N. Dahlgren, and N. L. Dahlgren. Darpa timit acoustic-phonetic continuous speech corpus. [CD-ROM], 1993.
37. K.-F. Lee and H.-W. Hon, "Speaker-independent phone recognition using hidden Markov models," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, pp. 1641-1648, 1989.
38. L. D. Alsteris and K. K. Paliwal, "Importance of window shape for phase-only reconstruction of speech," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Montreal, QC, Canada, 2004, pp. 1573-1576.