Affine-Invariant Riemannian Distance Between Infinite-Dimensional Covariance Operators

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)


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.


Covariance Operator Separable Hilbert Space Reproduce Kernel Hilbert Space Scalar Perturbation Positive Definite Matrice 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Pattern Analysis and Computer Vision (PAVIS), Istituto Italiano di Tecnologia (IIT)GenovaItaly

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