PhD Scientific Days 2022

Neurosciences II.

Real-time Algorithm for Detrended Cross-correlation Analysis of Long-range Coupled Processes

Text of the abstract

Examining long-range cross-correlations between processes is of great significance in many fields, including neuroscience. Such analyses are computationally expensive and thus mostly carried out offline. However, many applications such as mental state monitoring require methods providing estimates in real-time. Despite this, no algorithms have been proposed yet to assess long-range coupling online.

We introduce a real-time formula for detrended cross-correlation analysis (DCCA), a well-established and widely used method for assessing long-range cross-correlations. We show that the formula can also be expressed in matrix operations, which allows for performing DCCA between multiple processes simultaneously, as well as online derivation of the detrended cross-correlation coefficients (DCCCs), a standardized version of DCCA. Execution time (ET) and precision of the online methods (pairwise and matrix) was compared with their offline counterparts in a simulation environment using multiple realizations of time series ranging from 28 to 217 datapoints in length. The ETs of online methods were also contrasted in case of increasing number of time series. Finally, to evaluate real-world applicability of the algorithm, we analysed electroencephalography (EEG) recordings. Data was obtained from 22 young, healthy volunteers (12 female, aged 23.9±2.3) in eyes-open (EO) and eyes-closed (EC) resting conditions (14 cortical regions, 256 Hz sampling rate). DCCC analysis was carried out and a linear classifier was trained to see if mental state (EO vs. EC) could be identified online automatically.

ET was reduced on average by three orders of magnitude when comparing the online to the offline implementation, while precision remained unaffected. Simulations indicated that the matrix formula should be preferred over sequential pairwise evaluation when the number of time series exceeds 8. Classification of mental state could be achieved with an accuracy surpassing 79%.

Our novel real-time DCCA formula vastly outperformed the offline implementation in execution time, while maintaining precision. The introduced matrix formula provided additional benefits as the number of time series pairs increased. Based on our results regarding real-world applicability, our real-time formula carries future potential e.g. in automated mental-state monitoring.