By Frank Nielsen, Frederic Barbaresco
This ebook constitutes the refereed court cases of the second one foreign convention on Geometric technology of data, GSI 2015, held in Palaiseau, France, in October 2015.
The eighty complete papers offered have been rigorously reviewed and chosen from a hundred and ten submissions and are equipped into the next thematic classes:
Dimension aid on Riemannian manifolds; optimum shipping; optimum shipping and functions in imagery/statistics; form area and diffeomorphic mappings; random geometry/homology; Hessian details geometry; topological varieties and knowledge; details geometry optimization; details geometry in photograph research; divergence geometry; optimization on manifold; Lie teams and geometric mechanics/thermodynamics; computational info geometry; Lie teams: novel statistical and computational frontiers; geometry of time sequence and linear dynamical platforms; and Bayesian and data geometry for inverse problems.
Read or Download Geometric Science of Information: Second International Conference, GSI 2015, Palaiseau, France, October 28–30, 2015, Proceedings PDF
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Additional info for Geometric Science of Information: Second International Conference, GSI 2015, Palaiseau, France, October 28–30, 2015, Proceedings
A set of normal coordinate systems at each point of the manifold realize an atlas which allows to work very easily on the manifold. The implementation of exp and log maps is the basis of programming on Riemannian manifolds, and most the geometric operations needed for statistics or image processing can be rephrased based on them [12,13]. 2 Taylor Expansions in Normal Coordinate Systems We consider a normal coordinate system centered at x and xv = expx (v) a i (x) the coeﬃcients of the Riemannian variation of the point x.
Adv. Comput. Math. 40(2), 283–313 (2013) 17. : Medians of probability measures in Riemannian manifolds and applications to radar target detection. D. de Department of Statistics, University of Pittsburgh, Pittsburgh, USA Abstract. We present a novel method that adaptively deforms a polysphere (a product of spheres) into a single high dimensional sphere which then allows for principal 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.
BS are deﬁned as the locus of points which are weighted means of k + 1 reference points. Depending on the generalization of the mean that we use on manifolds, Fr´echet mean, Karcher mean or exponential barycenter, we obtain the Fr´echet/Karcher barycentric subspaces (FBS/KBS) or the aﬃne span. We show that these deﬁnition are related and locally deﬁne a submanifold of dimension k, and that they generalize in some sense the geodesic subspaces. Like PGA, Barycentric Subspace Analysis (BSA) allows the construction of forward nested subspaces which contains the Fr´echet mean.