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Affine-Invariant Riemannian Distance Between Infinite-Dimensional Covariance Operators

  • Hà Quang MinhEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

Abstract

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.

Keywords

Covariance Operator Separable Hilbert Space Reproduce Kernel Hilbert Space Scalar Perturbation Positive Definite Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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