Titlebook: Geometric Science of Information; Second International Frank Nielsen,Frédéric Barbaresco Conference proceedings 2015 Springer International

zonules

https://doi.org/10.1007/978-3-642-01754-4 additional properties: Lie groups, Quotient spaces, Stratified spaces etc? How can we describe the .? The structure of Quotient space in particular is widely used to model data, for example every time one deals with shape data. These can be shapes of constellations in Astronomy, shapes of human org

Atrium

百靈鳥

內(nèi)向者

Barycentric Subspaces and Affine Spans in Manifoldss (PGA) and Geodesic PCA (GPCA) minimize the distance to a “Geodesic subspace”. This allows to build sequences of nested subspaces which are consistent with a forward component analysis approach. However, these methods cannot be adapted to a backward analysis and they are not symmetric in the parame

PANEL

Dimension Reduction on Polyspheres with Application to Skeletal Representationscipal nested spheres (PNS) analysis. Applying our method to skeletal representations of simulated bodies as well as of data from real human hippocampi yields promising results in view of dimension reduction. Specifically in comparison to composite PNS (CPNS), our method of principal nested deformed

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Affine-Invariant Riemannian Distance Between Infinite-Dimensional Covariance Operatorse. 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 G

Charlatan

A Sub-Riemannian Modular Approach for Diffeomorphic Deformationsribe transformations. The method, built on a coherent sub-Riemannian framework, defines a metric on modular deformations and characterises optimal deformations as geodesics for this metric. We will present a generic way to build local affine transformations as deformation modules, and display exampl

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The Nonlinear Bernstein-Schr?dinger Equation in Economicsthat we call the “nonlinear Bernstein-Schr?dinger system”, which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.

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Some Geometric Consequences of the Schr?dinger ProblemWe stress the analogies between this entropy minimization problem and the renowned optimal transport problem, in search for a theory of lower bounded curvature for metric spaces, including discrete graphs.

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Optimal Transport, Independance Versus Indetermination Duality, Impact on a New Copula Designction with the MKP transportation problem (MKP, stands for Monge-Kantorovich Problem). Using the duality between “independance” and “indetermination” structures, shown in this former paper, we are in a position to derive a novel approach to design a copula, suitable and efficient for anomaly detecti