Regression and Fitting on Manifold-Valued Data
暫譯: 流形值數據的回歸與擬合
Adouani, Ines, Samir, Chafik
- 出版商: Springer
- 出版日期: 2025-07-24
- 售價: $2,030
- 貴賓價: 9.5 折 $1,929
- 語言: 英文
- 頁數: 181
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031617142
- ISBN-13: 9783031617140
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相關分類:
Machine Learning
海外代購書籍(需單獨結帳)
商品描述
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.
商品描述(中文翻譯)
本書以建設性的方式介紹了一個通用框架，用於回歸和擬合方法，適用於涉及流形數據的多種應用和任務。這種方法論在機器學習、醫學、機器人技術、生物學、計算機視覺、人類生物識別、奈米製造、信號處理和圖像分析等領域具有重要且多樣的應用。
第一章提供了動機範例、廣泛的應用、所面臨的挑戰以及一些關注點。第二章對歐幾里得情況進行了全面的探索和逐步的說明。另一個專門的章節涵蓋了每個流形所需的幾何工具，並提供了針對流形值數據的任何應用的表達式和關鍵概念。
所有損失函數和優化方法均以算法形式給出，並且可以輕鬆實現。特別是，考慮了許多流行的流形，並提供了推導和具體的公式。所有章節都遵循相同的理念，所有新穎之處均以直觀的範例進行說明。此外，每章還包括針對現實世界問題的模擬和實驗，以便理解和潛在擴展，適用於廣泛的應用。
作者簡介
Ines ADOUANI received her PhD in complex analysis and Finsler geometry from the University of Pierre and Marie Curie, France, in 2015. Since then, she has been serving as an Assistant Professor at the Institute of Applied Sciences and Technology of Sousse, Tunisia. Additionally, from 2020 to 2021, she held a position as an Assistant Professor at King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Her main research interests encompass complex geometry (including Finsler and Kähler geometry), optimization on Riemannian manifolds, regression, and fitting on Riemannian manifolds, as well as their applications to computer vision and medical imaging problems.
Chafik SAMIR received his PhD on learning and analysis of shapes and patterns in 2007 at the University of Lille, France. After spending two years as a postdoc working on manifolds and related applications at UCL, he joined UCA in 2009. His main research interests are machine learning for manifold-valued data, such as functional and medical observations, optimization of loss functions, statistical shape analysis, spatio-temporal patterns and fusion, regression and fitting on Riemannian manifolds, and their applications to real-world problems.
作者簡介(中文翻譯)
Ines ADOUANI於2015年在法國皮埃爾與瑪麗居里大學獲得複雜分析和芬斯勒幾何的博士學位。自那時起，她一直擔任突尼西亞蘇斯應用科學與技術研究所的助理教授。此外，從2020年到2021年，她在沙烏地阿拉伯達蘭的法赫德石油與礦業大學擔任助理教授。她的主要研究興趣包括複雜幾何（包括芬斯勒和卡勒幾何）、黎曼流形上的優化、回歸分析以及在黎曼流形上的擬合，並將其應用於計算機視覺和醫學影像問題。
Chafik SAMIR於2007年在法國里爾大學獲得形狀和模式學習與分析的博士學位。在UCL擔任兩年的博士後研究員，專注於流形及相關應用後，他於2009年加入UCA。他的主要研究興趣是針對流形值數據的機器學習，例如功能性和醫學觀察、損失函數的優化、統計形狀分析、時空模式與融合、在黎曼流形上的回歸和擬合，以及這些技術在現實問題中的應用。
