By Hà Quang Minh,Vittorio Murino
This e-book offers a range of the newest algorithmic advances in Riemannian geometry within the context of desktop studying, information, optimization, computer vision, and similar fields. The unifying subject of the various chapters within the book is the exploitation of the geometry of information utilizing the mathematical equipment of Riemannian geometry. As confirmed via all of the chapters within the e-book, while the data is intrinsically non-Euclidean, the usage of this geometrical info can lead to higher algorithms which may trap extra appropriately the constructions inherent in the data, prime finally to higher empirical functionality. This booklet isn't really meant to be an encyclopedic compilation of the functions of Riemannian geometry. as a substitute, it focuses on a number of vital study 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 contain novel algorithms for Monte Carlo sampling and Gaussian mix version becoming, 3D mind photograph analysis,image class, motion attractiveness, 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