Advanced Methods in Detrended Fluctuation Analysis with Applications in Computational Cardiology
Year: 2019
Type: dissertation
Abstract: Fractals are ubiquitous in nature. A defining characteristic of fractality is self-similarity; the phenomenon looks similar when observed at multiple scales, which implies the existence of a power law scaling relation. Detrended fluctuation analysis (DFA) is a popular tool for studying these fractal scaling relations. Power laws become linear relationships in logarithmic scales, and conventionally these scaling exponents are determined by simple linear regression in approximately linear regions in doubly logarithmic plots. However, in practice the scaling is hardly ever exact, and its behavior may often vary at different scales.\n\nThis thesis extends the fluctuation analysis by introducing robust tools for determining these scaling exponents. A method based on the Kalman smoother is utilized for extracting a whole spectrum of exponents as a function of the scale. The method is parameter-free and resistant to statistical noise, which distinguishes it from prior efforts for determining such local scale exponents. Additionally, an optimization scheme is presented to obtain data-adaptive segmentation of approximately linear regimes. Based on integer linear programming model, the procedure may readily be customized for various purposes. This versatility is demonstrated by applying the method to a group of data to find a common segmentation that is particularly well-suited for machine learning applications.\n\nFirst, the methods are are employed in exploring the details of the scaling by analyzing simulated data with known scaling properties. These findings provide insight into the interpretation of earlier results.\n\nSecond, the methods are applied to the study of heart rate variability. The beating of the heart follows fractal-like patterns, and deviations in these complex variations may be indicative of cardiac diseases. In this context DFA is traditionally performed by extracting two scaling exponents, for short- and long-range correlations, respectively. This has been criticized as an oversimplification, which is corroborated by the results of this thesis. The heart rate exhibits richer fractal-like variability, which becomes apparent in the full scaling spectra. The additional information provided by these methods facilitate improved classification of cardiac conditions.
Author: Molkkari, Matti
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2947218704