By Hà Quang Minh,Vittorio Murino
This ebook offers a variety of the newest algorithmic advances in Riemannian geometry within the context of desktop studying, information, optimization, computer vision, and similar fields. The unifying topic of the several chapters within the book is the exploitation of the geometry of information utilizing the mathematical equipment of Riemannian geometry. As validated by way of the entire chapters within the booklet, whilst the data is intrinsically non-Euclidean, the usage of this geometrical details can lead to larger algorithms that could seize extra safely the constructions inherent in the data, prime finally to higher 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 study instructions which are presently actively pursued by researchers within the box. those comprise 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 mix version becoming, 3D mind snapshot analysis,image type, motion attractiveness, and movement tracking.
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