Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis (Chapman & Hall/Crc Monographs on Statistics & Applied Probability)

Victor Patrangenaru, Leif Ellingson

商品描述

A New Way of Analyzing Object Data from a Nonparametric Viewpoint

Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis provides one of the first thorough treatments of the theory and methodology for analyzing data on manifolds. It also presents in-depth applications to practical problems arising in a variety of fields, including statistics, medical imaging, computer vision, pattern recognition, and bioinformatics.

The book begins with a survey of illustrative examples of object data before moving to a review of concepts from mathematical statistics, differential geometry, and topology. The authors next describe theory and methods for working on various manifolds, giving a historical perspective of concepts from mathematics and statistics. They then present problems from a wide variety of areas, including diffusion tensor imaging, similarity shape analysis, directional data analysis, and projective shape analysis for machine vision. The book concludes with a discussion of current related research and graduate-level teaching topics as well as considerations related to computational statistics.

Researchers in diverse fields must combine statistical methodology with concepts from projective geometry, differential geometry, and topology to analyze data objects arising from non-Euclidean object spaces. An expert-driven guide to this approach, this book covers the general nonparametric theory for analyzing data on manifolds, methods for working with specific spaces, and extensive applications to practical research problems. These problems show how object data analysis opens a formidable door to the realm of big data analysis.

商品描述(中文翻譯)

《從非參數觀點分析物體數據的新方法》

《非參數統計在流形上及其在物體數據分析中的應用》是對在流形上分析數據的理論和方法進行全面研究的其中一本著作。它還深入應用於各個領域的實際問題,包括統計學、醫學影像學、計算機視覺、模式識別和生物信息學。

本書首先通過一系列具體的物體數據示例進行說明,然後回顧了數學統計學、微分幾何學和拓撲學的概念。接下來,作者描述了在不同流形上工作的理論和方法,並從數學和統計學的歷史角度出發。然後,他們提出了來自各個領域的問題,包括擴散張量成像、相似形狀分析、方向數據分析和機器視覺中的射影形狀分析。本書最後討論了當前相關研究和研究生級別的教學主題,以及與計算統計學相關的考慮因素。

不同領域的研究人員必須將統計方法與射影幾何學、微分幾何學和拓撲學的概念相結合,以分析來自非歐幾里得物體空間的數據對象。作為專家指導的指南,本書涵蓋了在流形上分析數據的一般非參數理論、處理特定空間的方法以及廣泛應用於實際研究問題的案例。這些問題展示了物體數據分析如何打開大數據分析的巨大門戶。