Functional and shape data analysis - Srivastava, Anuj; Klassen, E. (Springer, New York, 2016)
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. Covering a broad range of ideas from different disciplines, it is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. 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.
Motivation for function and shape analysis -- Previous techniques in shape analysis -- Background : relevant tools from geometry -- Functional data and elastic registration -- Shapes of planar curves -- Shapes of planar closed curves -- Statistical modeling on nonlinear manifolds -- Statistical modeling of functional data -- Statistical modeling of planar shapes -- Shapes of curves in higher dimensions -- Related topics in shape analysis of curves -- Background material -- The dynamic programming algorithm.
Includes bibliographical references (pages 439-443) and index.
Keywords: Functional analysis; Analisi funzionale; Functional analysis