منابع مشابه
The Wasserstein-Fisher-Rao metric
This note gives a summary of the presentation that I gave at the workshop on shape analysis. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to measures that have different total masses. This generalization enjoys most of the properties of standard optimal transport but we will focus on the geometric formulation of the model. We expect this new metric to have interes...
متن کاملRegistration of Functional Data Using Fisher-Rao Metric
We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a proper distance on the quotient space of functions modulo the time-warping group. A convenient square-root velocity function (SRVF) representation transforms th...
متن کاملFisher-Rao Metric, Geometry, and Complexity of Neural Networks
Abstract. We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity — the Fisher-Rao norm — that possesses desirable invariance properties and is motivated by Information Geometry. We discover an analytical characterization of the new capacity measure, through which we establish norm-comparison i...
متن کاملApproximation to the Fisher-Rao metric for the focus of expansion
The Fisher-Rao metric for the focus of expansion is approximated, under the assumption that the focus is estimated from correspondences between two images taken by a translating camera. The approximation is accurate if the errors in the image correspondences are small. The parameter space for the focus of expansion is sampled at a finite set of points chosen such that every point in the space i...
متن کاملUniqueness of the Fisher–rao Metric on the Space of Smooth Densities
On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher–Rao metric. Introduction. The Fisher–Rao metric on the space Prob(M) of probability densities is of importance in the field of information geometry. Restricted to...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2009
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.7085