Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis (Paperback)
暫譯: 流形上的非參數統計及其在物件數據分析中的應用（平裝本）

Patrangenaru, Victor, Ellingson, Leif

Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis (Paperback)
  • 出版商: CRC
  • 出版日期: 2020-12-18
  • 售價: $2,400
  • 貴賓價: 9.5 折 $2,280
  • 語言: 英文
  • 頁數: 517
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 0367737825
  • ISBN-13: 9780367737825
  • 相關分類: Data Science、機率統計學 Probability-and-statistics

    • 海外代購書籍(需單獨結帳)

買這商品的人也買了...

相關主題

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件數據的新方法》

《流形上的非參數統計及其在物件數據分析中的應用》提供了對流形上數據分析的理論和方法論的首次全面探討。它還深入介紹了在統計學、醫學影像、計算機視覺、模式識別和生物資訊學等多個領域中出現的實際問題的應用。

本書首先通過一些物件數據的示例進行調查，然後回顧數學統計、微分幾何和拓撲學的概念。接著，作者描述了在各種流形上工作的理論和方法，並提供了數學和統計概念的歷史視角。然後，他們展示了來自多個領域的問題，包括擴散張量成像、相似形狀分析、方向數據分析以及機器視覺的投影形狀分析。本書最後討論了當前相關研究和研究生級教學主題，以及與計算統計相關的考量。

來自不同領域的研究人員必須將統計方法與投影幾何、微分幾何和拓撲學的概念結合起來，以分析來自非歐幾里得物件空間的數據物件。作為這種方法的專家指導，本書涵蓋了流形上數據分析的一般非參數理論、處理特定空間的方法，以及對實際研究問題的廣泛應用。這些問題顯示了物件數據分析如何為大數據分析的領域打開一扇強大的大門。

作者簡介

Victor Patrangenaru is a professor of statistics at Florida State University. He received his first PhD from the University of Haifa; his differential geometry dissertation on locally homogeneous Riemannian and pseudo-Riemannian manifolds was conferred the Morris Pulver award. His second PhD was conferred at Indiana University for his dissertation on asymptotic statistics on manifolds and their applications. He has been a recipient of the Rothrock Mathematics Teaching Award from Indiana University.

 

 

Leif Ellingson is an assistant professor at Texas Tech University. He received his PhD in statistics from Florida State University; his dissertation "Statistical Shape Analysis on Manifolds with Applications to Planar Contours and Structural Proteomics" received the Ralph A. Bradley award. He has also been a recipient of the New Faculty Award from the Texas Tech Alumni Association. His current research interests include nonparametric statistics on manifolds, shape analysis, computational methods in statistics, and utilizing statistical methods in structural proteomics.

 

 

作者簡介(中文翻譯)

Victor Patrangenaru 是佛羅里達州立大學的統計學教授。他在海法大學獲得了他的第一個博士學位；他的論文是關於局部齊次的黎曼流形和偽黎曼流形的微分幾何，並獲得了莫里斯·普爾弗獎。他的第二個博士學位是在印第安納大學頒發的，論文主題是流形上的漸近統計及其應用。他曾獲得印第安納大學的羅斯羅克數學教學獎。

Leif Ellingson 是德克薩斯科技大學的助理教授。他在佛羅里達州立大學獲得統計學博士學位；他的論文《流形上的統計形狀分析及其在平面輪廓和結構蛋白質組學中的應用》獲得了拉爾夫·A·布拉德利獎。他還曾獲得德克薩斯科技校友會的新教員獎。他目前的研究興趣包括流形上的非參數統計、形狀分析、統計計算方法，以及在結構蛋白質組學中利用統計方法。

類似商品