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Time Series Classification Using Gaussian Mixture Models of Reconstructed Phase Spaces
June 2004 (vol. 16 no. 6)
pp. 779-783

Abstract—A new signal classification approach is presented that is based upon modeling the dynamics of a system as they are captured in a reconstructed phase space. The modeling is done using full covariance Gaussian Mixture Models of time domain signatures, in contrast with current and previous work in signal classification that is typically focused on either linear systems analysis using frequency content or simple nonlinear machine learning models such as artificial neural networks. The proposed approach has strong theoretical foundations based on dynamical systems and topological theorems, resulting in a signal reconstruction, which is asymptotically guaranteed to be a complete representation of the underlying system, given properly chosen parameters. The algorithm automatically calculates these parameters to form appropriate reconstructed phase spaces, requiring only the number of mixtures, the signals, and their class labels as input. Three separate data sets are used for validation, including motor current simulations, electrocardiogram recordings, and speech waveforms. The results show that the proposed method is robust across these diverse domains, significantly outperforming the time delay neural network used as a baseline.

[1] J.G. Proakis, Digital Comm., fourth ed. Boston: McGraw-Hill, 2001.
[2] E. Keogh and S. Kasetty, On the Need for Time Series Data Mining Benchmarks: A Survey and Empirical Demonstration Proc. Eighth ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining, 2002.
[3] J.R. Buchler, Z. Kollath, T. Serre, and J. Mattei, Nonlinear Analysis of the Lightcurve of the Variable Star R Scuti Astrophysical J., pp. 462-489, 1996.
[4] Q. Ding, Z. Zhuang, L. Zhu, and Q. Zhang, Application of the Chaos, Fractal and Wavelet Theories to the Feature Extraction of Passive Acoustic Signal Acta Acustica, vol. 24, pp. 197-203, 1999.
[5] A. Petry, D. Augusto, and C. Barone, Speaker Identification Using Nonlinear Dynamical Features Chaos, Solitons, and Fractals, vol. 13, pp. 221-231, 2002.
[6] M.E.H. Benbouzid, Bibliography on Induction Motors Faults Detection and Diagnosis IEEE Trans. Energy Conversion, vol. 14, pp. 1065-1074, 1999.
[7] E. Manios, G. Fenelon, T. Malacky, A.L. Fo, and P. Brugada, Life Threatening Ventricular Arrhythmias in Patients with Minimal or No Structural Heart Disease: Experience with the Implantable Cardioverter Defibrillator available at , 1997, cited Dec. 2000.
[8] F. Takens, Detecting Strange Attractors in Turbulence Proc. Dynamical Systems and Turbulence, pp. 366-381, 1980.
[9] T. Sauer, J.A. Yorke, and M. Casdagli, Embedology J. Statistical Physics, vol. 65, pp. 579-616, 1991.
[10] H. Kantz and T. Schreiber, Nonlinear Time Series Analysis. Cambridge: Cambridge Univ. Press, 1997.
[11] H.F.V. Boshoff and M. Grotepass, The Fractal Dimension of Fricative Speech Sounds Proc. South African Symp. Comm. and Signal Processing, pp. 12-61, 1991.
[12] Y. Ashkenazy, P.C. Ivanov, S. Havlin, C.-K. Peng, A.L. Goldberger, and H.E. Stanley, Magnitude and Sign Correlations in Heartbeat Fluctuations Physical Rev. Letters, vol. 86, pp. 1900-1903, 2001.
[13] V. Schulte-Frohlinde, Y. Ashkenazy, P.C. Ivanov, L. Glass, A.L. Goldberger, and H.E. Stanley, Noise Effects on the Complex Patterns of Abnormal Heartbeats Physical Rev. Letters, vol. 87, pp. 068104/1-4, 2001.
[14] D. Sciamarella and G.B. Mindlin, Topological Structure of Chaotic Flows from Human Speech Chaotic Data Physical Rev. Letters, vol. 82, p. 1450, 1999.
[15] C. Casdagli, Nonlinear Prediction of Chaotic Time Series Physica D, vol. 35, pp. 335-356, 1989.
[16] H.D.I. Abarbanel, T.A. Carroll, L.M. Pecora, J.J. Sidorowich, and L.S. Tsimring, Predicting Physical Variables in Time-Delay Embedding Physical Rev. E, vol. 49, pp. 1840-1853, 1994.
[17] J.D. Farmer and J.J. Sidorowich, Exploiting Chaos to Predict the Future and Reduce Noise Evolution, Learning, and Cognition, Y.C. Lee, ed., pp. 277-330, World Scientific, 1988.
[18] J. Kadtke, Classification of Highly Noisy Signals Using Global Dynamical Models Physics Letters A, vol. 203, pp. 196-202, 1995.
[19] T.K. Moon, The Expectation-Maximization Algorithm in Signal Processing IEEE Signal Processing Magazine, vol. 13, no. 6, pp. 47-60, 1996.
[20] J. Garofolo, L. Lamel, W. Fisher, J. Fiscus, D. Pallett, N. Dahlgren, and V. Zue, TIMIT Acoustic-Phonetic Continuous Speech Corpus Linguistic Data Consortium, 1993.
[21] N.A. Demerdash and J.F. Bangura, A Time-Stepping Coupled Finite Element-State Space Modeling for Analysis and Performance Quality Assessment of Induction Motors in Adjustable Speed Drives Applications Proc. Naval Symp. Electric Machines, pp. 235-242, 1997.
[22] C.T. Lin and C.S.G. Lee, Neural Fuzzy Systems a Neuro-Fuzzy Synergism to Intelligent Systems. Upper Saddle River, N.J.: Prentice-Hall, 1996.

Index Terms:
Signal classification, reconstructed phase spaces, Gaussian mixture models.
Richard J. Povinelli, Michael T. Johnson, Andrew C. Lindgren, Jinjin Ye, "Time Series Classification Using Gaussian Mixture Models of Reconstructed Phase Spaces," IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 6, pp. 779-783, June 2004, doi:10.1109/TKDE.2004.17
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