Geodesic Distance Kernels

In this paper, the authors deals with non-symmetric kernels induced by weighted quasi-metrics on Hilbert spaces and they study their fundamental properties. These are new and original. Such kind of metrics is obtained from Finsler metrics for example. We show that the use of such kernels may provide a solution to the conflict between positive definiteness of the kernel and the curvature of the underlying space.

 Keywords:Finsler metrics, Hilbert spaces, non-symmetric kernels, weighted quasi-metric spaces

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