Data-driven Koopman operator approach for computational neuroscience

Abstract

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 $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo></mml:math> 13 Hz) and high Gamma ( $ \sim $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo></mml:math> 50 Hz) frequencies, and explore the spatiotemporal dynamics of high- and low- frequency components.