International Journal of Bifurcation and Chaos, Vol. 12, No. 6 (2002) 1273–1293 c  World Scientific Publishing Company NONLINEAR SIGNAL CLASSIFICATION P. E. RAPP ∗,† and T. A. A. WATANABE † Department of Pharmacology and Physiology, Medical College of Pennsylvania–Hahnemann University, PA, USA ∗ Paul.E.Rapp@drexel.edu P. FAURE Institut Pasteur, Paris C. J. CELLUCCI † Department of Physics, Ursinus College, Collegeville, PA, USA † The Arthur P. Noyes Research Foundation, Norristown, PA, USA Received July 26, 2001; Revised August 28, 2001 In this contribution, we show that the incorporation of nonlinear dynamical measures into a multivariate discrimination provides a signal classification system that is robust to additive noise. The signal library was composed of nine groups of signals. Four groups were generated computationally from deterministic systems (van der Pol, Lorenz, R¨ ossler and H´ enon). Four groups were generated computationally from different stochastic systems. The ninth group contained inter-decay interval sequences from radioactive cobalt. Two classification criteria (minimum Mahalanobis distance and maximum Bayesian likelihood) were tested. In the absence of additive noise, no errors occurred in a within-library classification. Normally distributed random numbers were added to produce signal to noise ratios of 10, 5 and 0 dB. When the minimum Mahalanobis distance was used as the classification criterion, the corresponding error rates were 2.2%, 4.4% and 20% (Expected Error Rate = 89%). When Bayesian maximum likelihood was the criterion, the error rates were 1.1%, 4.4% and 21% respectively. Using nonlinear measures an effective discrimination can be achieved in cases where spectral measures are known to fail. Most classification errors occurred at low signal to noise ratios when a stochastic signal was misclassified into a different group of stochastic signals. When the within-library classification exercise is limited to the four groups of deterministic signals, no classification errors occurred with clean data, at SNR = 10 dB, or at SNR = 5 dB. A single classification error (Observed Error Rate = 2.5%, Expected Error Rate = 75%) occurred with both classification criteria at SNR = 0 dB. Keywords : Discriminant analysis; nonlinear dynamics; complexity; fractal dimension; time series analysis; chaos. * Author for correspondence. Clinical Research Center, Building 52, Norristown State Hospital, 1001 Sterigere St. Norristown, PA 19401, USA. 1273