By Hà Quang Minh,Vittorio Murino
This ebook provides a variety of the latest algorithmic advances in Riemannian geometry within the context of computer studying, records, 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 proven through the entire chapters within the booklet, whilst the data is intrinsically non-Euclidean, the usage of this geometrical info can lead to larger algorithms which may trap extra appropriately the constructions inherent in the data, top finally to raised empirical functionality. This booklet isn't really meant to be an encyclopedic compilation of the functions of Riemannian geometry. in its place, it focuses on numerous very important learn instructions which are presently actively pursued by researchers within the box. those contain 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 mix version becoming, 3D mind picture 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