TY - GEN
T1 - Sparse Learning of Kernel Transfer Operators
AU - Hou, Boya
AU - Bose, Subhonmesh
AU - Vaidya, Umesh
N1 - Funding Information:
B. Hou and S. Bose are with the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, Urbana, IL 61801. U. Vaidya is with the Department of Mechanical Engineering in Clemson University, Clemson, SC 29634. This work was partially supported by the NSF-EPCN-2031570 grant.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - Transfer operators such as the Koopman and the Perron-Frobenius operators provide valuable insights into the properties of nonlinear dynamical systems. Recent work has shown that non-parametric approximations of these operators can be constructed over reproducing kernel Hilbert space (RKHS) with data. These kernel transfer operators can then be written as functions of covariance and cross-covariance operators associated with the data generated by the dynamical system. In this paper, we study sparse kernel learning methods for kernel transfer operators. Specifically, we study sample complexity guarantees for coherency-based sparsification and demonstrate its efficacy over an example dynamical system.
AB - Transfer operators such as the Koopman and the Perron-Frobenius operators provide valuable insights into the properties of nonlinear dynamical systems. Recent work has shown that non-parametric approximations of these operators can be constructed over reproducing kernel Hilbert space (RKHS) with data. These kernel transfer operators can then be written as functions of covariance and cross-covariance operators associated with the data generated by the dynamical system. In this paper, we study sparse kernel learning methods for kernel transfer operators. Specifically, we study sample complexity guarantees for coherency-based sparsification and demonstrate its efficacy over an example dynamical system.
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U2 - 10.1109/IEEECONF53345.2021.9723412
DO - 10.1109/IEEECONF53345.2021.9723412
M3 - Conference contribution
AN - SCOPUS:85127047552
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 130
EP - 134
BT - 55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
A2 - Matthews, Michael B.
PB - IEEE Computer Society
T2 - 55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
Y2 - 31 October 2021 through 3 November 2021
ER -