Affine-Invariant Riemannian Distance Between Infinite-Dimensional Covariance Operators

This paper studies the affine-invariant Riemannian distance on the Riemann-Hilbert manifold of positive definite operators on a separable Hilbert space. This is the generalization of the Riemannian manifold of symmetric, positive definite matrices to the infinite-dimensional setting. In particular, in the case of covariance operators in a Reproducing Kernel Hilbert Space (RKHS), we provide a closed form solution, expressed via the corresponding Gram matrices.

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