TY - JOUR
T1 - Data-driven Koopman operator approach for computational neuroscience
AU - Marrouch, Natasza
AU - Slawinska, Joanna
AU - Giannakis, Dimitrios
AU - Read, Heather L.
N1 - Publisher Copyright:
© 2019, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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 (∼ 13 Hz) and high Gamma (∼ 50 Hz) frequencies, and explore the spatiotemporal dynamics of high- and low- frequency components.
AB - 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 (∼ 13 Hz) and high Gamma (∼ 50 Hz) frequencies, and explore the spatiotemporal dynamics of high- and low- frequency components.
KW - Brain
KW - ECoG
KW - Koopman operator
KW - Mismatch negativity
KW - Nonlinear
KW - Spatiotemporal dynamics
KW - Spectral decomposition
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U2 - 10.1007/s10472-019-09666-2
DO - 10.1007/s10472-019-09666-2
M3 - Article
AN - SCOPUS:85075154446
SN - 1012-2443
VL - 88
SP - 1155
EP - 1173
JO - Annals of Mathematics and Artificial Intelligence
JF - Annals of Mathematics and Artificial Intelligence
IS - 11-12
ER -