Time series data analysis with sample entropy

Abstract

Entropy in relation to dynamic systems could be expressed as the rate of information production. It proved to be an indispensable tool in studying and understanding the underlying complexity of physiological systems encountered in cardiovascular and other biological studies. Joshua S. Richman and J. Randall Moorman introduced sample entropy (SampEn(m, r, N) ), a new method of analyzing given system complexity, which is closely related to entropy. It was successfully applied to several clinical cardiovascular and other time series. Although methods employed in estimating sample entropy are well suited for short data sets, their efficiency drops dramatically as the data of interests gets longer. This is due to the fact that SampEn(m, r, N) algorithm is of N2 order.

The focus of this project is on optimizing SampEn(m, r, N) for analyzing continuous data, performing real-time on-the-go evaluations of sample entropy. The main scope is to reduce some parts of algorithm to an order of N. The process is simulated using the Matlab software.

Further, the real-life applications of SampEn(m, r, N) are discussed using an example of blood flow assessment in diffuse correlation spectroscopy (DCS).