Abstract
In this paper, we investigate two general methods of modeling and prediction which have been applied to neurobiological systems, the orthogonal search (OS) method and the canonical variate analysis (CVA) approach. In these methods, nonlinear autoregressive moving average with observed inputs (ARX) and state affine models are developed as one step predictors by minimizing the mean-squared-error. An unknown nonlinear time-invariant system is assumed to have the Markov property of finite order so that the one step predictors are finite dimensional. No special assumptions are made about model terms, model order or state dimensions. Three examples are presented. The first is a numerical example which demonstrates the differences between the two methods, while the last two examples are computer simulations for a bilinear system and the Lorenz attractor which can serve as a model for the EEG. These two methods produce comparable results in terms of minimizing the mean-square-error; however, the OS method produces an ARX model with fewer terms, while the CVA method produces a state model with fewer state dimensions. © 1999 Biomedical Engineering Society.
PAC99: 8719La, 8719Nn, 8718Bb, 8710+e
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Akaike, H. Canonical Correlation Analysis of Time Series and the Use of an Information Criterion. System Identification: Advances and Case Studies, edited by R. K. Mehra and D. G. Lainiotis. New York: Academic, 1976.
Bodenstein, G., and M. H. Praetorius. Feature extraction from the electroencephalogram by adaptive segmentation. Proc. IEEE 65:642–652, 1977.
Bohlin, T. Analysis of EEG signals with changing spectra using a short-word Kalman estimator. Math. Biosci. 35:221–259, 1977.
Brenner, R., R. J. Sclabassi, D. G. Spiker, R. Ulrich, C. F. Reynolds, F. Boller, P. Lordeon, R. Marin, and S. Pearlman. Computerized spectral analysis in elderly normal, demented and depressed subjects. Electroencephalogr. Clin. Neurophysiol. 64:483–492, 1986.
Diaz, H. Modeling of Nonlinear Systems from Input-Output Data. Troy, NY: Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, PhD Thesis, 1986.
Fliess, M., and D. Normand-Cyrot. On the approximation of nonlinear systems by some simple state-space model. Identi-fication and system parameter estimation. In: Sixth IFAC Symposium, edited by G. A. Bekey. Washington, DC, 1982, Vol. 1, pp. 433–436.
Gersch, W. Spectral analysis of EEGs by autoregression decomposition of time series. Math. Biosci. 7:205–222, 1970.
Isaksson, A., and A. Wennberg. Spectral properties of nonstationary EEG signals, evaluated by means of Kalman filtering: Application examples from a vigilance test. In: Quantitative Analysis Studies in Epilepsy, edited by P. Kellaway and I. Petersen. New York: Raven, 1976.
Isaksson, A., A. Wennberg, and L. H. Zetterberg Computer analysis of EEG signals with parametric models. Proc. IEEE 69:451–461, 1981.
Korenberg, M. J. Identifying nonlinear difference equation and functional expansion representations: The fast orthogonal algorithm. Ann. Biomed. Eng. 16:123–142, 1988.
Korenberg, M. J., S. B. Bruder, and P. J. H. McIlroy. Exact orthogonal kernel estimation from finite data records: Expanding Wiener's identification of nonlinear systems. Ann. Biomed. Eng. 16:201–214, 1988.
Korenberg, M. J., and L. D. Paarmann. An orthogonal ARMA identifier with automatic order estimation for biological modeling. Ann. Biomed. Eng. 17:571–592, 1989.
Korenberg, M. J. A robust orthogonal algorithm for system identification and time-series analysis. Biol. Cybern. 60:267–276, 1989.
Korenberg, M. J., and L. D. Paarmann. Orthogonal approach to time-series analysis and system identification. IEEE Signal Process. Mag. 8:29–43, 1991.
Krieger, D. R., R. Nakamura, R. Coppola, and R. J. Sclabassi. Resonant neuroelectric patterns evoked by a cognitive task. In: IEEE Conf. Decision Control. New York: IEEE, 1990, Vol. 1, pp. 629–634.
Krieger, D. R., R. J. Sclabassi, R. Cappola, and R. Nakamura. Spatiotemporal cortical patterns evoked in monkeys by a discrimination task. J. Cognitive Neurosci. 3:242–251, 1991.
Larimore, W. E. System identification, reduced-order filtering and modeling via canonical variate analysis. In: Proceedings of the 1983 IEEE American Control Conference, edited by H. S. Rao and T. Dorato. New York: IEEE, 1983, Vol. 1, pp. 445–51.
Larimore, W. E. Order-recursive factorization of the pseudoinverse of a covariance matrix. IEEE Trans. Autom. Control. 35:1299–1303, 1990.
Larimore, W. E. Identification of nonlinear system using canonical variate analysis. In: 29th IEEE Conf. Decision Control. New York: IEEE, 1987, Vol. 3, pp. 1694–1699.
Larimore, W. E. Generalized canonical variate analysis of nonlinear systems. In: 27th IEEE Conf. Decision Control. New York: IEEE, 1988, Vol. 2, 1720–1725.
Larimore, W. E. Canonical variate analysis in identification, filtering, and adaptive control. In: 29th IEEE Conf. on Decision Control. New York: IEEE, 1990, Vol. 1, pp. 596–604.
Larimore, W. E., S. Mahmood, and R. K. Mehra, Multivariable adaptive model algorithmic control. In: Proceedings of the Conference on Decision and Control, edited by A. H. Haddad and M. Polis. New York: IEEE, 1984, Vol. 2, pp. 675–680.
Larimore, W. E. Identification and filtering of nonlinear systems using canonical variate analysis, nonlinear modeling and forecasting. In: SFI Studies in the Sciences of Complexity, edited by M. Casdagli and S. Eubank. Reading, MA: Addison-Wesley, 1992, Vol. XII, pp. 283–303.
Larimore, W. E. Optimal reduced bank modeling, prediction, monitoring, and control using canonical variate analysis. In: Preprints IFAC Advanced Control of Chemical Processes, Banff, Alberta, Canada, 1997, pp. 61–66.
Lieb, J., R. J. Sclabassi, P. Crandell, and R. Buchness. Comparison of the action of diazepam and phenobarbital using EEG derived power spectra obtained from temporal lobe epileptics. Neuropharmacology 13:769–783, 1974.
Lopes da Silva, F. H. Analysis of EEG Nonstationarities. In: Contemporary Clinical Neurophysiology (EEG Suppl. No. 34), edited by W. A. Cobb and H. Van Duijn. Amsterdam: Elsevier, 1978.
Lorenz, E. N. Deterministic nonperiodic flow. J. Atmos. Sci. 20:130–141, 1963.
Rogowski, Z., I. Gath, and E. Bental. On the prediction of epileptic seizures. Biol. Cybern. 42:9–15, 1981.
Scher, M. S., S. G. Dokianakis, M. Sun, D. A. Steppe, R. D. Guthrie, and R. J. Sclabassi. Computer classification of sleep in preterm and fullterm neonates at similar postconceptional term ages. Sleep 1996:18–25.
Sclabassi, R. J., M. Sun, D. N. Krieger, P. Jasiukities, and M. Scher. Time-frequency domain problems in the neurosciences. In: Time-Frequency Signal Analysis, edited by B. Boashash. New York: Wiley, 1992, pp. 498–519.
Thormundsson, T., J. R. Sveinsson, and J. A. Benediktsson. Cancellation of nonlinear intersymbol interference in voiceband communication channels. In: Proceedings of the IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing. New York: IEEE, 1997, pp. 862–865.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wu, YT., Sun, M., Krieger, D. et al. Comparison of Orthogonal Search and Canonical Variate Analysis for the Identification of Neurobiological Systems. Annals of Biomedical Engineering 27, 592–606 (1999). https://doi.org/10.1114/1.213
Issue Date:
DOI: https://doi.org/10.1114/1.213