Functional and Shape Data Analysis

  • Anuj Srivastava
  • Eric P. Klassen

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Anuj Srivastava, Eric P. Klassen
    Pages 1-19
  3. Anuj Srivastava, Eric P. Klassen
    Pages 21-37
  4. Anuj Srivastava, Eric P. Klassen
    Pages 39-72
  5. Anuj Srivastava, Eric P. Klassen
    Pages 73-123
  6. Anuj Srivastava, Eric P. Klassen
    Pages 125-165
  7. Anuj Srivastava, Eric P. Klassen
    Pages 167-231
  8. Anuj Srivastava, Eric P. Klassen
    Pages 233-267
  9. Anuj Srivastava, Eric P. Klassen
    Pages 269-303
  10. Anuj Srivastava, Eric P. Klassen
    Pages 305-347
  11. Anuj Srivastava, Eric P. Klassen
    Pages 349-384
  12. Anuj Srivastava, Eric P. Klassen
    Pages 385-416
  13. Back Matter
    Pages 417-447

About this book

Introduction

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.

  • Presents a complete and detailed exposition on statistical analysis of shapes that includes appendices, background material, and exercises, making this text a self-contained reference
  • Addresses and explores the next generation of shape analysis
  • Focuses on providing a working knowledge of a broad range of relevant material, foregoing in-depth technical details and elaborate mathematical explanations
Anuj Srivastava is a Professor in the Department of Statistics and a Distinguished Research Professor at Florida State University. His areas of interest include statistical analysis on nonlinear manifolds, statistical computer vision, functional data analysis, and statistical shape theory. He has been the associate editor for the Journal of Statistical Planning and Inference, and several IEEE journals. He is a fellow of the International Association of Pattern Recognition(IAPR) and a senior member of the Institute for Electrical and Electronic Engineers (IEEE).

Eric Klassen is a Professor in the Department of Mathematics at Florida State University. His mathematical interests include topology, geometry, and shape analysis. In his spare time, he enjoys playing the piano, riding his bike, and contra dancing.

Keywords

Riemannian methods shape analysis function data analysis curves mathematical representations vector-space-based statistical analyses square-root representations geodesic

Authors and affiliations

  • Anuj Srivastava
    • 1
  • Eric P. Klassen
    • 2
  1. 1.Department of StatisticsFlorida State UniversityTallahasseeUSA
  2. 2.Department of MathematicsFlorida State UniversityTallahasseeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-4020-2
  • Copyright Information Springer-Verlag New York 2016
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-4018-9
  • Online ISBN 978-1-4939-4020-2
  • Series Print ISSN 0172-7397
  • Series Online ISSN 2197-568X
  • About this book