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Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes

Assessing power-law cross-correlations between a pair – or among a set – of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal i...

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Autores principales: Kaposzta, Zalan, Czoch, Akos, Stylianou, Orestis, Kim, Keumbi, Mukli, Peter, Eke, Andras, Racz, Frigyes Samuel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8963246/
https://www.ncbi.nlm.nih.gov/pubmed/35360238
http://dx.doi.org/10.3389/fphys.2022.817268
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author Kaposzta, Zalan
Czoch, Akos
Stylianou, Orestis
Kim, Keumbi
Mukli, Peter
Eke, Andras
Racz, Frigyes Samuel
author_facet Kaposzta, Zalan
Czoch, Akos
Stylianou, Orestis
Kim, Keumbi
Mukli, Peter
Eke, Andras
Racz, Frigyes Samuel
author_sort Kaposzta, Zalan
collection PubMed
description Assessing power-law cross-correlations between a pair – or among a set – of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal is obtained. However, many applications – such as mental state monitoring or financial forecasting – call for fast algorithms capable of estimating scale-free coupling in real time. Detrended cross-correlation analysis (DCCA), a generalization of the detrended fluctuation analysis (DFA) to the bivariate domain, has been introduced as a method designed to quantify power-law cross-correlations between a pair of non-stationary signals. Later, in analogy with the Pearson cross-correlation coefficient, DCCA was adapted to the detrended cross-correlation coefficient (DCCC), however as of now no online algorithms were provided for either of these analysis techniques. Here we introduce a new formula for obtaining the scaling functions in real time for DCCA. Moreover, the formula can be generalized via matrix notation to obtain the scaling relationship between not only a pair of signals, but also all possible pairs among a set of signals at the same time. This includes parallel estimation of the DFA scaling function of each individual process as well, thus allowing also for real-time acquisition of DCCC. The proposed algorithm matches its offline variants in precision, while being substantially more efficient in terms of execution time. We demonstrate that the method can be utilized for mental state monitoring on multi-channel electroencephalographic recordings obtained in eyes-closed and eyes-open resting conditions.
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spelling pubmed-89632462022-03-30 Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes Kaposzta, Zalan Czoch, Akos Stylianou, Orestis Kim, Keumbi Mukli, Peter Eke, Andras Racz, Frigyes Samuel Front Physiol Physiology Assessing power-law cross-correlations between a pair – or among a set – of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal is obtained. However, many applications – such as mental state monitoring or financial forecasting – call for fast algorithms capable of estimating scale-free coupling in real time. Detrended cross-correlation analysis (DCCA), a generalization of the detrended fluctuation analysis (DFA) to the bivariate domain, has been introduced as a method designed to quantify power-law cross-correlations between a pair of non-stationary signals. Later, in analogy with the Pearson cross-correlation coefficient, DCCA was adapted to the detrended cross-correlation coefficient (DCCC), however as of now no online algorithms were provided for either of these analysis techniques. Here we introduce a new formula for obtaining the scaling functions in real time for DCCA. Moreover, the formula can be generalized via matrix notation to obtain the scaling relationship between not only a pair of signals, but also all possible pairs among a set of signals at the same time. This includes parallel estimation of the DFA scaling function of each individual process as well, thus allowing also for real-time acquisition of DCCC. The proposed algorithm matches its offline variants in precision, while being substantially more efficient in terms of execution time. We demonstrate that the method can be utilized for mental state monitoring on multi-channel electroencephalographic recordings obtained in eyes-closed and eyes-open resting conditions. Frontiers Media S.A. 2022-03-11 /pmc/articles/PMC8963246/ /pubmed/35360238 http://dx.doi.org/10.3389/fphys.2022.817268 Text en Copyright © 2022 Kaposzta, Czoch, Stylianou, Kim, Mukli, Eke and Racz. https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Physiology
Kaposzta, Zalan
Czoch, Akos
Stylianou, Orestis
Kim, Keumbi
Mukli, Peter
Eke, Andras
Racz, Frigyes Samuel
Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes
title Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes
title_full Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes
title_fullStr Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes
title_full_unstemmed Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes
title_short Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes
title_sort real-time algorithm for detrended cross-correlation analysis of long-range coupled processes
topic Physiology
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8963246/
https://www.ncbi.nlm.nih.gov/pubmed/35360238
http://dx.doi.org/10.3389/fphys.2022.817268
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