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Regression and Fitting on Manifold-valued Data : Mathematics and Statistics (R0) - Ines Adouani

Regression and Fitting on Manifold-valued Data

By: Ines Adouani, Chafik Samir

eText | 23 July 2024

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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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Non-FictionMathematicsCalculus & Mathematical AnalysisNumerical AnalysisComputing & I.T.Computer ScienceArtificial IntelligenceComputer VisionApplied MathematicsEngineering & TechnologyTechnology in GeneralEngineering in General
Image ProcessingMaths for Engineers

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