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Algorithmic advances in Riemannian geometry and applications = for machine learning, computer vision, statistics, and optimization /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Algorithmic advances in Riemannian geometry and applications/ edited by Ha Quang Minh, Vittorio Murino.
Reminder of title:	for machine learning, computer vision, statistics, and optimization /
other author:	Minh, Ha Quang.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xiv, 208 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Geometry, Riemannian. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-45026-1
ISBN:	9783319450261

Algorithmic advances in Riemannian geometry and applications = for machine learning, computer vision, statistics, and optimization /
Algorithmic advances in Riemannian geometry and applicationsfor machine learning, computer vision, statistics, and optimization /[electronic resource] :edited by Ha Quang Minh, Vittorio Murino. - Cham :Springer International Publishing :2016. - xiv, 208 p. :ill., digital ;24 cm. - Advances in computer vision and pattern recognition,2191-6586. - Advances in computer vision and pattern recognition..

Introduction -- Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms -- Sampling Constrained Probability Distributions using Spherical Augmentation -- Geometric Optimization in Machine Learning -- Positive Definite Matrices: Data Representation and Applications to Computer Vision -- From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings -- Dictionary Learning on Grassmann Manifolds -- Regression on Lie Groups and its Application to Affine Motion Tracking -- An Elastic Riemannian Framework for Shape Analysis of Curves and Tree-Like Structures.

This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.

ISBN: 9783319450261

Standard No.: 10.1007/978-3-319-45026-1doiSubjects--Topical Terms:

672546
Geometry, Riemannian.

LC Class. No.: QA671

Dewey Class. No.: 516.373

Algorithmic advances in Riemannian geometry and applications = for machine learning, computer vision, statistics, and optimization /
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245 0 0 $a Algorithmic advances in Riemannian geometry and applications $h [electronic resource] : $b for machine learning, computer vision, statistics, and optimization / $c edited by Ha Quang Minh, Vittorio Murino.
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505 0 $a Introduction -- Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms -- Sampling Constrained Probability Distributions using Spherical Augmentation -- Geometric Optimization in Machine Learning -- Positive Definite Matrices: Data Representation and Applications to Computer Vision -- From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings -- Dictionary Learning on Grassmann Manifolds -- Regression on Lie Groups and its Application to Affine Motion Tracking -- An Elastic Riemannian Framework for Shape Analysis of Curves and Tree-Like Structures.
520 $a This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.
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