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cs.LG2023
Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approach
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter. To achieve this…
cs.LG2023
Geometric Learning with Positively Decomposable Kernels
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces…
cs.LG2023
The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle
Nathaël Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega
On Euclidean spaces, the Gaussian kernel is one of the most widely used kernels in applications. It has also been used on non-Euclidean spaces, where it is known that there may be…