Multiscale analysis of biological data by scale-dependent Lyapunov exponent - Jianbo eGao (Frontiers in Physiology, 2012)
Physiological signals often are highly nonstationary and multiscaled--- depending upon the scale at which they are examined, they mayexhibit different behaviors, such asnonlinearity, sensitive dependence on small disturbances, longmemory, and extreme variations. Such data have been accumulatingrapidly in all areas ofhealth sciences.It is very desirable to characterize the differentbehaviors of such signals on a wide range of scales simultaneously.The scale-dependent Lyapunov exponent (SDLE) is capable of such afundamental task. In particular, SDLE can readilycharacterize all known types of data, includingdeterministic chaos, noisy chaos,random $1/f^{alpha}$processes, stochastic limit cycles, among others. It can alsoreadily deal with many types of nonstationarity anddetect intermittent chaos.To illustrate its effectiveness in analyzing physiological data,we consider detection of epileptic seizures from EEG and certaincardiac disease from heart rate variability (HRV) data.In particular, we show that commonlyused complexity measures for physiological data, including thosefrom information theory, chaos theory, and random fractal theory, can all be related to thevalues of the SDLE at specific scales, and therefore,SDLE can act as the basis for a unified theory ofmultiscale analysis of complex data.