Liang Zhao

Date of Award


Degree Type


Embargo Date


Degree Name

Doctor of Philosophy (PhD)




Yuesheng Xu


Entropy, Filter-based, Multiscale

Subject Categories

Applied Mathematics | Bioinformatics


The multiscale entropy (MSE) has been widely and successfully used in analyzing the complexity of physiologic time series. In this thesis, we re-interpret the averaging process in MSE as filtering a time series by a filter of a piecewise constant type. From this viewpoint, we introduce the {\it filter-based multiscale entropy} (FME) which filters a time series by filters to generate its multiple frequency components and then compute the {\it blockwise} entropy of the resulting components. By choosing filters adapted to the feature of a given time series, FME is able to better capture its multiscale information and to provide more flexibility for studying its complexity. Motivated by the heart rate turbulence theory which suggests that the human heartbeat interval time series (HHITS) can be described in piecewise linear patterns, we propose the piecewise linear filter multiscale entropy (PLFME) for the complexity analysis of the time series. Numerical results from PLFME are more robust to data of various lengths than those from MSE. We then propose wavelet packet transform entropy (WPTE) analysis. We apply WPTE analysis to HHITS using lower and higher piecewise linear filters. Numerical results show that WPTE using piecewise linear filters gives us the highest classification rates discriminating different cardiac systems among other multiscale entropy analysis. At the end, we discuss the application of FME on discrete time series. We introduce an `eliminating' algorithm to examine and compare the complexity of coding and noncoding DNA sequences.


Open Access