By Hà Quang Minh,Vittorio Murino
This publication provides a variety of the newest algorithmic advances in Riemannian geometry within the context of laptop studying, facts, optimization, computer vision, and similar fields. The unifying topic of different chapters within the book is the exploitation of the geometry of information utilizing the mathematical equipment of Riemannian geometry. As verified through the entire chapters within the publication, whilst the data is intrinsically non-Euclidean, the usage of this geometrical details can lead to greater algorithms that may trap extra adequately the buildings inherent in the data, best eventually to raised empirical functionality. This ebook 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 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 tools, and dictionary learning and sparse coding on manifolds. Examples of functions comprise novel algorithms for Monte Carlo sampling and Gaussian blend version becoming, 3D mind snapshot analysis,image category, motion acceptance, 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