國立虎尾科技大學 |

Regression and fitting on manifold-valued data

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Regression and fitting on manifold-valued data/ by 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:	Engineering Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-031-61712-6
ISBN:	9783031617126

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

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

1203947
Engineering Mathematics.

LC Class. No.: QA613

Dewey Class. No.: 516.07

Regression and fitting on manifold-valued data
LDR:02672nam a2200325 a 4500 001 1134272
003 DE-He213
005 20240724125324.0
006 m d
007 cr nn 008maaau
008 241213s2024 sz s 0 eng d
020 $a 9783031617126 $q (electronic bk.)
020 $a 9783031617119 $q (paper)
024 7 $a 10.1007/978-3-031-61712-6 $2 doi
035 $a 978-3-031-61712-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA613
072 7 $a PBKS $2 bicssc
072 7 $a MAT041000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 516.07 $2 23
090 $a QA613 $b .A241 2024
100 1 $a Adouani, Ines. $3 1455656
245 1 0 $a Regression and fitting on manifold-valued data $h [electronic resource] / $c by Ines Adouani, Chafik Samir.
260 $a Cham : $c 2024. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a vii, 181 p. : $b ill. (some col.), digital ; $c 24 cm.
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.
650 2 4 $a Engineering Mathematics. $3 1203947
650 2 4 $a Computer Imaging, Vision, Pattern Recognition and Graphics. $3 671334
650 1 4 $a Computational Mathematics and Numerical Analysis. $3 669338
650 0 $a Regression analysis. $3 569541
650 0 $a Manifolds (Mathematics) $3 672402
700 1 $a Samir, Chafik. $3 1455657
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-61712-6
950 $a Mathematics and Statistics (SpringerNature-11649)