Dynamic mode decomposition (DMD) is a method for the mode decomposition of time series data based on the dynamical systems theory. Unlike conventional methods, the DMD can be applied to the time series whose dynamics is modeled as a nonlinear process. This property is very useful in practical applications, but the original DMD also has a drawback that it requires significantly high-dimensional data. In order to avoid this drawback, we extend the DMD by using the kernel method. Our kernel DMD can approximate the eigenfunctions of the Koopman operator, which characterize each oscillation mode, more accurately than the original DMD. We further propose a method for selecting kernel parameters, which makes our method more useful and robust in practical applications. We also demonstrate the validity of our kernel DMD by applying it to numerical data.
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