Kaposzta Zalan, Czoch Akos, Stylianou Orestis, Kim Keumbi, Mukli Peter, Eke Andras, Racz Frigyes Samuel
Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary.
Institute of Translational Medicine, Semmelweis University, Budapest, Hungary.
Front Physiol. 2022 Mar 11;13:817268. doi: 10.3389/fphys.2022.817268. eCollection 2022.
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.
评估一对或一组过程之间的幂律互相关在从神经科学到金融市场等不同分析领域具有重要意义。在大多数情况下，此类分析计算成本高昂，因此一旦获得整个信号就会离线进行。然而，许多应用——如精神状态监测或金融预测——需要能够实时估计无标度耦合的快速算法。去趋势互相关分析（DCCA）是去趋势波动分析（DFA）在双变量领域的推广，已被引入作为一种旨在量化一对非平稳信号之间幂律互相关的方法。后来，类似于皮尔逊互相关系数，DCCA被改编为去趋势互相关系数（DCCC），但截至目前，这些分析技术都没有提供在线算法。在这里，我们引入了一个新公式，用于实时获取DCCA的标度函数。此外，该公式可以通过矩阵表示法进行推广，以同时获得不仅一对信号之间，而且一组信号中所有可能对之间的标度关系。这还包括对每个单独过程的DFA标度函数的并行估计，从而也允许实时获取DCCC。所提出的算法在精度上与离线变体相匹配，同时在执行时间方面效率更高。我们证明了该方法可用于在闭眼和睁眼静息条件下获得的多通道脑电图记录的精神状态监测。
