By Hà Quang Minh,Vittorio Murino
This booklet provides a range of the newest algorithmic advances in Riemannian geometry within the context of desktop studying, statistics, optimization, computer vision, and similar fields. The unifying subject matter of the several chapters within the book is the exploitation of the geometry of information utilizing the mathematical equipment of Riemannian geometry. As tested via all of the chapters within the publication, whilst the data is intrinsically non-Euclidean, the usage of this geometrical details can lead to greater algorithms that could seize extra competently the buildings inherent in the data, top finally to raised empirical functionality. This e-book isn't meant to be an encyclopedic compilation of the purposes of Riemannian geometry. as a substitute, it focuses on a number of vital 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 equipment, and dictionary learning and sparse coding on manifolds. Examples of purposes comprise novel algorithms for Monte Carlo sampling and Gaussian blend version becoming, 3D mind photograph analysis,image type, motion popularity, and movement tracking.
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Algorithmic Advances in Riemannian Geometry and Applications: For Machine Learning, Computer Vision, Statistics, and Optimization (Advances in Computer Vision and Pattern Recognition) by Hà Quang Minh,Vittorio Murino