Regression and Fitting on Manifold-valued Data

• Verfasst von: Adouani, Ines [VerfasserIn]
• Verfasst von: Samir, Chafik [VerfasserIn]
• Titel: Regression and Fitting on Manifold-valued Data
• Verf.angabe: by Ines Adouani, Chafik Samir
• Ausgabe: 1st ed. 2024.
• Verlagsort: Cham
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Verlag: Imprint: Springer
• E-Jahr: 2024
• Jahr: 2024.
• Jahr: 2024.
• Umfang: 1 Online-Ressource(VII, 181 p. 47 illus., 45 illus. in color.)
• ISBN: 978-3-031-61712-6
• DOI: doi:10.1007/978-3-031-61712-6
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Adouani, Ines: Regression and fitting on manifold-valued data. - Cham : Springer Nature Switzerland, 2024. - vii, 181 Seiten
• K10plus-PPN: 1896933343
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.

Abstract

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.