Measuring the Complexity of a Physiological Time Series: a Review

Abstract

Research background and hypothesis. Complex Systems Theory indeed is a solid basis for a scientific approach
in the analysis of living, learning, and evolving systems. A number of different entropy estimators have been applied
to physiological time series attempting to quantify its complexity.
Research aim. The aim of the paper is to review most popular complexity estimators (entropies) applied in
biological, medical, sport and exercise sciences and their performances.
Research results. Various measures of complexity were developed by scientists to compare time series and
distinguish regular  (e.  g.  periodic),  chaotic, and random behavior. In this paper a brief review of most popular
complexity  estimators  –  Sample  Entropy,  Control  Entropy,  Spectral  Entropy,  Wavelet  Entropy,  Singular-Value
Decomposition Entropy, Permutation Entropy, Base-Scale Entropy, Entropy based on Lempel-Ziv algorithm – and
their performances is presented. In biological applications they are used to distinguish peculiarities in behavior of
biological systems or may serve as non-invasive, objective means of determining physiological changes under steady
or non-steady state conditions.
Discussion and conclusions. The choice of a particular entropy estimator is determined by the goal type, the
capability  of  estimators  in  characterizing  the  constraints  on  a  physiological  time  series,  its  robustness  to  noise
considering  the  above-mentioned  advantages  and  disadvantages  of  particular  algorithms.  It  is  difficult  to  apply
analytical solutions in the analysis of behavior of living, learning, and evolving systems and new approaches and
solutions remain on the agenda.

Keywords: physiological time series, complexity, entropy.