Functional and Shape Data Analysis. 1st ed. 2016

種類:

電子ブック

責任表示:

by Anuj Srivastava, Eric P. Klassen

出版情報:

New York, NY : Springer New York : Imprint: Springer, 2016

著者名:

• Srivastava, Anuj.
• Klassen, Eric P.
• SpringerLink (Online service)

シリーズ名:

Springer Series in Statistics ;

ISBN:

9781493940202 [1493940201]    

注記:

1. Motivation for Function and Shape Analysis -- 2. Previous Techniques in Shape Analysis -- 3. Background: Relevant Tools from Geometry -- 4. Functional Data and Elastic Registration -- 5. Shapes of Planar Curves -- 6. Shapes of Planar Closed Curves -- 7. Statistical Modeling on Nonlinear Manifolds -- 8. Statistical Modeling of Functional Data -- 9. Statistical Modeling of Planar Shapes -- 10. Shapes of Curves in Higher Dimensions -- 11. Related Topics in Shape Analysis of Curves -- A. Background Material -- B. The Dynamic Programming Algorithm -- References -- Index.
This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future

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