Analytical Analysis of Multiscale Entropy of Time Series: White Noise and 1/f Noise

DOI

10.2991/msbda-19.2019.32How to use a DOI?

Keywords

Multiscale entropy, Time series, White noise, 1/f noise

Abstract

Multiscale entropy (MSE) has attracted many applications in revealing the complexity of bio-signals since its introduction in early 2000. To better understand the MSE method, a lot of researchers have been working on its analytical solution. The existing analytical solutions are limited either to bulky double integrals, or to a proportional relation. This study intends to solve the double integrals and further approximate the analytical formula of MSE. Combining Costa’s method with Briggs’ integral and Taylor series expansion, we approximated the analytical formula of MSE for uncorrelated (white) noise. With the additional help of the eigenvalue of a fractal Brownian motion process, we approximated the analytical formula of MSE for correlated noise (1/f noise). The analytical formulae were verified on simulated power noise with known scaling exponent. The proposed analytical solution may shed some light on the understanding of MSE in analyzing biological time series.

Copyright

© 2019, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Wei Han
AU  - Yanwen Zhuo
AU  - Chi Tang
AU  - Wenbo Liu
AU  - Shengyi Zhou
AU  - Shuo Liu
AU  - Zhou Fei
AU  - Kangning Xie
PY  - 2019/08
DA  - 2019/08
TI  - Analytical Analysis of Multiscale Entropy of Time Series: White Noise and 1/f Noise
BT  - Proceedings of the 2019 International Conference on Modeling, Simulation and Big Data Analysis (MSBDA 2019)
PB  - Atlantis Press
SP  - 202
EP  - 209
SN  - 2352-538X
UR  - https://doi.org/10.2991/msbda-19.2019.32
DO  - 10.2991/msbda-19.2019.32
ID  - Han2019/08
ER  -