By Hà Quang Minh,Vittorio Murino
This publication offers a range of the newest algorithmic advances in Riemannian geometry within the context of computer 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 validated via the entire chapters within the booklet, whilst the data is intrinsically non-Euclidean, the usage of this geometrical details can lead to greater algorithms which can seize extra correctly the buildings inherent in the data, major eventually to raised empirical functionality. This publication isn't really meant to be an encyclopedic compilation of the functions of Riemannian geometry. as an alternative, it focuses on numerous vital learn instructions which are at the moment actively pursued by researchers within the box. those contain 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 contain novel algorithms for Monte Carlo sampling and Gaussian blend 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