Abstract
This article presents a novel, nonlinear, data-driven signal processing method, which can help neuroscience researchers visualize and understand complex dynamical patterns in both time and space. Specifically, we present applications of a Koopman operator approach for eigendecomposition of electrophysiological signals into orthogonal, coherent components and examine their associated spatiotemporal dynamics. This approach thus provides enhanced capabilities over conventional computational neuroscience tools restricted to analyzing signals in either the time or space domains. This is achieved via machine learning and kernel methods for data-driven approximation of skew-product dynamical systems. The approximations successfully converge to theoretical values in the limit of long embedding windows. First, we describe the method, then using electrocorticographic (ECoG) data from a mismatch negativity experiment, we extract time-separable frequencies without bandpass filtering or prior selection of wavelet features. Finally, we discuss in detail two of the extracted components, Beta ( sim 13 Hz) and high Gamma ( sim 50 Hz) frequencies, and explore the spatiotemporal dynamics of high- and low- frequency components.
Highlights
Mammalian brains exhibit different oscillations of electrical current
Another challenge in analyzing EEG and ECoG data is the limitation faced by variance-based approaches (e.g., principal component analysis (PCA)) when capturing low-amplitude signals
We previously found that the data-driven Koopman operator approach is a robust tool for identifying low-amplitude events that are masked by larger-amplitude events [27, 48]
Summary
Mammalian brains exhibit different oscillations of electrical current. These oscillations are commonly divided into 5–8 bands based on their frequency. By their construction, PCA patterns are linear functions of the input data, which constrain the generality of patterns that the method can recover, when the observations do not provide access to all states of the system (typically the case in neuroscience applications) Another class of techniques takes advantage of various wavelets (e.g., Hilbert-Huang, Morlet wavelets) to transform the signal into frequency domain (e.g., [11]) and select dominant modes. While EEG and ECoG records patterns that evolve in space and time, most available computational methods study temporal and spatial changes separately [6] Despite their shortcomings, these approaches have been widely used to study one of the central questions of contemporary neuroscience: What mechanisms underlie spatial and temporal coordination of neural activities across various brain areas and during different steps of cognitive processing?
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
