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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Functional and Shape Data Analysis (Paperback, Softcover reprint of the original 1st ed. 2016)
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Functional and Shape Data Analysis (Paperback, Softcover reprint of the original 1st ed. 2016)
Series: Springer Series in Statistics
Expected to ship within 10 - 15 working days
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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.
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