DYNAMICS EXTRACTION IN MULTIVARIATE BIOMEDICAL TIME-SERIES

A nonlinear analysis of the underlying dynamics of a biomedical time s eries is proposed by means of a multi-dimensional testing of nonlinear Markovian hypotheses in the observed time series. The observed dynami cs of the original N-dimensional biomedical time series is tested agai nst a hierarchy of null hypotheses corresponding to N-dimensional nonl inear Markov processes of increasing order, whose conditional probabil ity densities are estimated using neural networks. For each of the N t ime series, a measure based on higher order cumulants quantifies the i ndependence between the past of the N-dimensional time series, and its value r steps ahead. This cumulant-based measure is used as a discrim inating statistic for testing the null hypotheses. Experiments perform ed on artificial and real world examples, including autoregressive mod els, noisy chaos, and nonchaotic nonlinear processes, show the effecti veness of the proposed approach in modeling multivariate systems, pred icting multidimensional time series, and characterizing the structure of biological systems. Electroencephalogram (EEG) time series and hear t rate variability trends are tested as biomedical signal examples.