Functional and Shape Data Analysis

✍ Scribed by Anuj Srivastava, Eric P. Klassen (auth.)

• Publisher: Springer-Verlag New York
• Year: 2016
• Tongue: English
• Leaves: 454
• Series: Springer Series in Statistics
• Edition: 1
• Category: Library

✦ Synopsis

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 scientific challenges.

Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

✦ Table of Contents

Front Matter....Pages i-xviii
Motivation for Function and Shape Analysis....Pages 1-19
Previous Techniques in Shape Analysis....Pages 21-37
Background: Relevant Tools from Geometry....Pages 39-72
Functional Data and Elastic Registration....Pages 73-123
Shapes of Planar Curves....Pages 125-165
Shapes of Planar Closed Curves....Pages 167-231
Statistical Modeling on Nonlinear Manifolds....Pages 233-267
Statistical Modeling of Functional Data....Pages 269-303
Statistical Modeling of Planar Shapes....Pages 305-347
Shapes of Curves in Higher Dimensions....Pages 349-384
Related Topics in Shape Analysis of Curves....Pages 385-416
Back Matter....Pages 417-447

✦ Subjects

Statistical Theory and Methods;Functional Analysis;Geometry;Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences