Kernel methods play an important role in solving classiffication and regression problems. While usually a kernel is designed by hand, recently, Owhadi and Yoo proposed Kernel Flows as a data-driven approach to obtaining suitable kernels. A first analysis by Darcy has shown that convergence and stability of convergence depend on the initialisation of parameters. We further analyse Kernel Flows utilising the Koopman operator framework proposed by Dietrich et al. in order to better understand the behaviour of the algorithm. To this end, we formalize Kernel Flows as a dynamical system and use it to learn kernels for toy data sets and estimate the point spectrum of the Koopman operator using extended dynamic mode decomposition. Based on the spectrum, we search for eigenvalues close to one and determine the basins of attraction based on a clustering of the evaluation of the eigenfunctions to eigenvalues close to one. We show that the analysis through the Koopman operator relies on a good choice of the number of clusters used in k-means clustering which poses a problem since, to the best of our knowledge, no approach to reliably determine the number of basins of attraction exists. In our analysis of Kernel Flows through the Koopman operator, we have shown that there is a significant difference in the form of the depicted basins of attraction of the used synthetic datasets compared to real basins of attraction on real datasets. This might indicate a problem with the synthetic datasets and, thus, the analysis based on it.     «

Kernel methods play an important role in solving classiffication and regression problems. While usually a kernel is designed by hand, recently, Owhadi and Yoo proposed Kernel Flows as a data-driven approach to obtaining suitable kernels. A first analysis by Darcy has shown that convergence and stability of convergence depend on the initialisation of parameters. We further analyse Kernel Flows utilising the Koopman operator framework proposed by Dietrich et al. in order to better understand the b...     »