By Hà Quang Minh,Vittorio Murino
This ebook offers a variety of the latest algorithmic advances in Riemannian geometry within the context of computer studying, records, optimization, computer vision, and comparable fields. The unifying subject of the several chapters within the book is the exploitation of the geometry of information utilizing the mathematical equipment of Riemannian geometry. As established via the entire chapters within the booklet, whilst the data is intrinsically non-Euclidean, the usage of this geometrical info can lead to greater algorithms that may trap extra competently the constructions inherent in the data, major eventually to raised empirical functionality. This booklet isn't meant to be an encyclopedic compilation of the purposes of Riemannian geometry. as a substitute, it focuses on numerous vital learn instructions which are at present 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 combination 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