Functional and Shape Data Analysis
Springer-Verlag New York Inc.
978-1-4939-4018-9 (ISBN)
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.
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.
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.
Erscheinungsdatum | 14.08.2016 |
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Reihe/Serie | Springer Series in Statistics |
Zusatzinfo | 182 Illustrations, color; 65 Illustrations, black and white; XVIII, 447 p. 247 illus., 182 illus. in color. |
Verlagsort | New York |
Sprache | englisch |
Maße | 178 x 254 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Schlagworte | Curves • function data analysis • geodesic • mathematical representations • Riemannian methods • shape analysis • square-root representations • vector-space-based statistical analyses |
ISBN-10 | 1-4939-4018-X / 149394018X |
ISBN-13 | 978-1-4939-4018-9 / 9781493940189 |
Zustand | Neuware |
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