By Hà Quang Minh,Vittorio Murino
This e-book offers a range of the latest algorithmic advances in Riemannian geometry within the context of laptop studying, statistics, optimization, computer vision, and similar fields. The unifying subject matter of different chapters within the book is the exploitation of the geometry of information utilizing the mathematical equipment of Riemannian geometry. As proven through all of the chapters within the ebook, while the data is intrinsically non-Euclidean, the usage of this geometrical info can lead to larger algorithms that may seize extra thoroughly the constructions inherent in the data, best finally to raised empirical functionality. This publication isn't meant to be an encyclopedic compilation of the functions of Riemannian geometry. in its place, it focuses on a number of very important examine instructions which are at the moment actively pursued by researchers within the box. those comprise statistical modeling and research on manifolds,optimization on manifolds, Riemannian manifolds and kernel tools, and dictionary learning and sparse coding on manifolds. Examples of functions comprise novel algorithms for Monte Carlo sampling and Gaussian mix version becoming, 3D mind picture analysis,image class, motion reputation, and movement tracking.
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