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 - Funding Information:
37M10 37M25 58C40 30C40 37N25 47A35 92C55 National Science Foundation https://doi.org/10.13039/100000001 1551489 Slawinska Joanna Office of Naval Research https://doi.org/10.13039/100000006 N00014-16-1-2649 Giannakis Dimitrios National Science Foundation https://doi.org/10.13039/100000001 DMS-1521775 Giannakis Dimitrios Defense Sciences Office, DARPA https://doi.org/10.13039/100006502 HR0011-16- C-0116 Giannakis Dimitrios National Science Foundation https://doi.org/10.13039/100000001 1355065 Read Heather L. National Institutes of Health https://doi.org/10.13039/100000002 DC015138 01 Read Heather L. National Science Foundation https://doi.org/10.13039/501100008982 1842538 Slawinska Joanna publisher-imprint-name Springer article-contains-esm No article-numbering-style ContentOnly article-registration-date-year 2019 article-registration-date-month 8 article-registration-date-day 2 article-toc-levels 0 journal-product NonStandardArchiveJournal numbering-style ContentOnly article-grants-type OpenChoice metadata-grant OpenAccess abstract-grant OpenAccess bodypdf-grant OpenAccess bodyhtml-grant OpenAccess bibliography-grant OpenAccess esm-grant OpenAccess online-first true pdf-file-reference BodyRef/PDF/10472_2019_Article_9666.pdf target-type OnlinePDF article-type OriginalPaper journal-subject-primary Computer Science journal-subject-secondary Artificial Intelligence journal-subject-secondary Mathematics, general journal-subject-secondary Computer Science, general journal-subject-secondary Complex Systems journal-subject-collection Computer Science open-access true This article is an expanded version of research presented at the 2018 International Joint Conference on Neural Networks in Rio de Janeiro, Brazil. N. M. acknowledges support from the CT Institute for the Brain and Cognitive Sciences Graduate Summer Fellowship and the University of Connecticut Department of Psychological Sciences’ Maurice L. Farber Endowment. J. S. acknowledges support from NSF grants 1551489 and 1842538. D. G. acknowledges support from ONR YIP grant N00014-16-1-2649, NSF grant DMS-1521775, and DARPA grant HR0011-16-C-0116. H. R. acknowledges support from NSF grant 1355065, NIH DC015138 01, and the University of Connecticut Brain Computer Interface Core.
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 -