Sparse Learning of Kernel Transfer Operators

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.