Titlebook: Geometric Science of Information; First International Frank Nielsen,Frédéric Barbaresco Conference proceedings 2013 Springer-Verlag Berlin

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Information Geometry and Its Applications: Survey It defines a Riemannian metric uniquely, which is the Fisher information metric. Moreover, a family of dually coupled affine connections are introduced. Mathematically, this is a study of a triple (.), where . is a manifold, . is a Riemannian metric, and . is a third-order symmetric tensor. Informa

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Information-Geometric Optimization: The Interest of Information Theory for Discrete and Continuous Oe about the function. Information geometry provides a systematic method, IGO (information-geometric optimization) to easily build optimization algorithms having nice properties; in particular it minimizes the influence of arbitrary choices such as how the space of solutions is represented. In some s

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Bi-invariant Means on Lie Groups with Cartan-Schouten Connectionsvariant metric provide a nice setting as the Lie group becomes a geodesically complete Riemannian manifold, thus also metrically complete. However, this Riemannian approach is fully consistent with the group operations only if a bi-invariant metric exists.

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Parallel Transport with Pole Ladder: Application to Deformations of Time Series of Images can be modeled by using deformations resulting from the non-rigid registration of follow-up images. The comparison of longitudinal trajectories is therefore the transport of longitudinal deformations in a common reference frame. We previously showed that the Schild’s Ladder is an efficient and simp

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Horizontal Dimensionality Reduction and Iterated Frame Bundle Developmentand centered analysis distorts inter-point distances in the presence of curvature. In this paper, we define a dimensionality reduction procedure for data in Riemannian manifolds that moves the analysis from a center point to local distance measurements. . measures distances relative to lower-order h

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