Approximate entropy: a complexity measure for biological time series data

Abstract

Difficulties with, and the possible inappropriateness of, applications of dimension and entropy algorithms to biological data, such as heart rate and electroencephalography (EEG) data, are indicated. A recently developed family of statistics, ApEn, can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The ability to discern changing complexity from such a relatively small amount of data holds substantial promise for diverse applications. ApEn can potentially distinguish low-dimensional deterministic systems, periodic and multiply periodic systems, high-dimensional chaotic systems, and stochastic and mixed (stochastic and deterministic) systems. Variance estimates for ApEn yield rigorous error bars for appropriate statistical interpretation results; no such valid statistics have been established for dimension and entropy algorithms in the general setting.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>