Geodesic Distance Kernels

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Published: Jan 5, 2018
Keywords:
Finsler metrics, Hilbert spaces, non-symmetric kernels, weighted quasi-metric spaces

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Uraiwan Somboon*
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
Praiboon Pantaragphong
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
Sorin V. Sabau
School of Biological Science, Department of Biology, Tokai University, Sapporo Campus, Sapporo, Japan

Abstract

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


*Corresponding author:       Tel.: +66 91 7300313


E-mail: uraiwan.somboon@gmail.com

Article Details

Issue
Vol. 17 No. 1 (2017)
Section
Original Research Articles

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References

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