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Titlebook: Geometric Science of Information; Third International Frank Nielsen,Frédéric Barbaresco Conference proceedings 2017 Springer International

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https://doi.org/10.1057/9780230597488., implicitly defined as the locus of points which are weighted means of . reference points [., .]. Barycentric subspaces can naturally be nested and allow the construction of inductive forward or backward nested subspaces approximating data points. We can also consider the whole hierarchy of embedd
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Brian Fahy,Veronica Walker Vadillopace. One approach to find such a manifold is to estimate a Riemannian metric that locally models the given data. Data distributions with respect to this metric will then tend to follow the nonlinear structure of the data. In practice, the learned metric rely on parameters that are hand-tuned for a
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Firoz Miyanji MD,Stefan Parent MDensional manifold and compared using a Riemannian metric that is invariant under the action of the reparameterization group. This group induces a quotient structure classically interpreted as the “shape space”. We introduce a simple algorithm allowing to compute geodesics of the quotient shape space
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Three Perspectives on a Projecttional least-squares norm. We revisit the convexity and insensitivity to noise of the Wasserstein metric which demonstrate the robustness of the metric in seismic inversion. Numerical results illustrate that full waveform inversion with quadratic Wasserstein metric can often effectively overcome the
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