Nonlinear classification of biologic signals
using global dynamical models
James Kadtke and Michael Kremliovsky
Institute for Pure and Applied Physical Sciences
University of California at San Diego, MS-0360
9500 Gilman Dr.
La Jolla, CA 92093
Time series analysis methods derived from the theory of Nonlinear Dynamics have resulted in several new signal processing techniques in the last decade, with applications to prediction, noise reduction, and signal separation. Recently, many efforts have been directed towards applications to the detection and classification (D/C) of signals, or alternately, classification of the generating physical system. Although these techniques make the ansatz that the signal is generated by a dynamical system, and typically are interested in detecting determinism (esp. chaotic behavior), these techniques can be considered more general, in the sense that we quantify nonlinear correlations in the signal. These methods may be particularly relevant to the analysis of biologic signals, with e.g. applications to the automated classification of physiological signals, as well as being of fundamental interest.
Recently, we have presented a method for the D/C of noisy signals which performs D/C by assuming a dynamical systems hypothesis [Kadtke,1995]. In practice, we develop a D/C processing chain which uses global dynamical models (systems of ODEs) to extract signal correlations. In this paper, we will discuss the extraction of the dynamical models from arbitrary data sets, the use of a coefficient space to provide a classification metric, and the generation of classification probabilities from the statistics of the coefficient ensembles. We indicate how non-autonomous models can be used for the classification of transient (pulse-like) data in a natural way, and demonstrate classification in noisy simulated data examples, even down to -10 dB.
In particular, we show that this method may be valuable for the classification of biologic and medical data, which often presents significant problems because of high noise levels, short observations, or the lack of any a priori system model. Since this method performs relative classification of short observations, and relies on the statistics of the observations in the coefficient feature space to estimate classification probabilities, many of the difficulties inherent in real-world data processing are reduced. Here, we will demonstrate the performance of these methods by presenting results of the analysis of several real-world data sets, including acoustic recordings of marine mammals, and medical observations of human patients. Eventual applications include voice/speech classification, remote sensing, and automated physiological monitoring.