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Regression and fitting on manifold-valued data

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Regression and fitting on manifold-valued databy Ines Adouani, Chafik Samir.
作者:	Adouani, Ines.
其他作者:	Samir, Chafik.
出版者:	Cham :Springer Nature Switzerland :2024.
面頁冊數:	vii, 181 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Manifolds (Mathematics)
電子資源:	https://doi.org/10.1007/978-3-031-61712-6
ISBN:	9783031617126$q(electronic bk.)

Regression and fitting on manifold-valued data
Adouani, Ines.

Regression and fitting on manifold-valued data[electronic resource] /by Ines Adouani, Chafik Samir. - Cham :Springer Nature Switzerland :2024. - vii, 181 p. :ill. (some col.), digital ;24 cm.

Introduction -- Spline Interpolation and Fitting in R�� -- Spline Interpolation on the Sphere S�� -- Spline Interpolation on the Special Orthogonal Group ��(��) -- Spline Interpolation on Stiefel and Grassmann manifolds -- Spline Interpolation on the Manifold of Probability Measures -- Spline Interpolation on the Manifold of Probability Density Functions -- Spline Interpolation on Shape Space -- Spline Interpolation on Other Riemannian Manifolds.

This book introduces in a constructive manner a general framework for regression and fitting methods for many applications and tasks involving data on manifolds. The methodology has important and varied applications in machine learning, medicine, robotics, biology, computer vision, human biometrics, nanomanufacturing, signal processing, and image analysis, etc. The first chapter gives motivation examples, a wide range of applications, raised challenges, raised challenges, and some concerns. The second chapter gives a comprehensive exploration and step-by-step illustrations for Euclidean cases. Another dedicated chapter covers the geometric tools needed for each manifold and provides expressions and key notions for any application for manifold-valued data. All loss functions and optimization methods are given as algorithms and can be easily implemented. In particular, many popular manifolds are considered with derived and specific formulations. The same philosophy is used in all chapters and all novelties are illustrated with intuitive examples. Additionally, each chapter includes simulations and experiments on real-world problems for understanding and potential extensions for a wide range of applications.

ISBN: 9783031617126$q(electronic bk.)

Standard No.: 10.1007/978-3-031-61712-6doiSubjects--Topical Terms:

198996
Manifolds (Mathematics)

LC Class. No.: QA613

Dewey Class. No.: 516.07

Regression and fitting on manifold-valued data
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505 0 $a Introduction -- Spline Interpolation and Fitting in R𝒏 -- Spline Interpolation on the Sphere S𝒏 -- Spline Interpolation on the Special Orthogonal Group 𝑺𝑶(𝒏) -- Spline Interpolation on Stiefel and Grassmann manifolds -- Spline Interpolation on the Manifold of Probability Measures -- Spline Interpolation on the Manifold of Probability Density Functions -- Spline Interpolation on Shape Space -- Spline Interpolation on Other Riemannian Manifolds.
520 $a This book introduces in a constructive manner a general framework for regression and fitting methods for many applications and tasks involving data on manifolds. The methodology has important and varied applications in machine learning, medicine, robotics, biology, computer vision, human biometrics, nanomanufacturing, signal processing, and image analysis, etc. The first chapter gives motivation examples, a wide range of applications, raised challenges, raised challenges, and some concerns. The second chapter gives a comprehensive exploration and step-by-step illustrations for Euclidean cases. Another dedicated chapter covers the geometric tools needed for each manifold and provides expressions and key notions for any application for manifold-valued data. All loss functions and optimization methods are given as algorithms and can be easily implemented. In particular, many popular manifolds are considered with derived and specific formulations. The same philosophy is used in all chapters and all novelties are illustrated with intuitive examples. Additionally, each chapter includes simulations and experiments on real-world problems for understanding and potential extensions for a wide range of applications.
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650 2 4 $a Engineering Mathematics. $3 806481
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