Multiscale Analysis of Biological Data by Scale-Dependent Lyapunov Exponent - Gao, Jianbo (Frontiers in Physiology, 2012)
Physiological signals often are highly nonstationary and multiscaled --- depending upon the scale at which they are examined, they may exhibit different behaviors, such as nonlinearity, sensitive dependence on small disturbances, long memory, and extreme variations. Such data have been accumulating rapidly in all areas of health sciences. It is very desirable to characterize the different behaviors of such signals on a wide range of scales simultaneously. The scale-dependent Lyapunov exponent (SDLE) is capable of such a fundamental task. In particular, SDLE can readily characterize all known types of data, including deterministic chaos, noisy chaos, random $1/f^{α}$ processes, stochastic limit cycles, among others. It can also readily deal with many types of nonstationarity and detect intermittent chaos. To illustrate its effectiveness in analyzing physiological data, we consider detection of epileptic seizures from EEG and certain cardiac disease from heart rate variability (HRV) data. In particular, we show that commonly used complexity measures for physiological data, including those from information theory, chaos theory, and random fractal theory, can all be related to the values of the SDLE at specific scales, and therefore, SDLE can act as the basis for a unified theory of multiscale analysis of complex data.