Regression and Fitting on Manifold-valued Data

by: Ines Adouani (Author),Chafik Samir(Author)

Publisher: Springer

Edition: 2024th

Publication Date: 2024/7/24

Language: English

Print Length: 188 pages

ISBN-10: 3031617118

ISBN-13: 9783031617119

Book Description

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 leaing, 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 conces. 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.

About the Author

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 leaing, 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 conces. 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.