A Scaled-Correlation Based Approach for Defining and Analyzing Functional Networks
Many natural systems can be described as networks of interacting elements, forming a graph of interactions. This is the case for climate models, coupled chemical systems, computer or social networks, or the brain. For many of these cases, dynamical networks emerge whose structure changes in time. Estimating the structure of such networks from the time series that describe the activity of their nodes is a serious challenge. Here, we devise a new method that is based on the Scaled Correlation function to estimate interactions between nodes that occur on fast timescales. We apply the method on EEG measurements from human volunteers to evaluate neuronal functional connectivity associated with a visual perception task. We compare the statistics of networks extracted with the new method with those that are extracted using traditional techniques, like the Pearson correlation coefficient or the cross-correlation function. Results indicate that the new method is superior in identifying networks whose structure correlates to the cognitive processes engaged during visual perception. The method is general enough to be applied on any data that describes dynamical interactions evolving on multiple timescales, as is the case in climate modeling, chemical networks, or complex biological systems.
KeywordsEEG Functional brain networks Metrics Cross-Correlation Scaled-Correlation Pearson correlation coefficient Directed weighted network
This work was supported by two grants from Consiliul National al Cercetării Ştiinţifice (CNCS) - Unitatea Executivă pentru Finanţarea Învăţământului Superior, a Cercetării Dezvoltării şi Inovării (UEFISCDI): PNII-RU-TE-2014-4- 13 0406/2015 contract no. 169/2015 and PN-III-P4-ID-PCE-2016-0010 contract no. 78/2017.
- 2.Koniaris, M., Anagnostopoulos, I., Vassiliou, Y.: Network analysis in the legal domain: a complex model for European Union legal sources, CoRR (2015)Google Scholar
- 7.Bracewell, R.: Pentagram notation for cross correlation. In: The Fourier Transform and Its Applications, pp. 46 and 243. McGraw-Hill, New York (1965)Google Scholar
- 12.Finc, K., Bonna, K., Lewandowska, M., Wolak, T., Nikadon, J., Dreszer, J., Duch, W., Khn, S.: Transition of the functional brain network related to increasing cognitive demands. Hum. Brain Mapp. 38, 3659–3674 (2017)Google Scholar