Functional And Shape Data Analysis

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Functional and Shape Data Analysis

Anuj Srivastava,Eric P. Klassen
Functional and Shape Data Analysis Book PDF

Author : Anuj Srivastava,Eric P. Klassen
Publisher : Springer
Page : 447 pages
File Size : 50,9 Mb
Release : 2016-10-03
Category : Mathematics
ISBN : 9781493940202

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Functional and Shape Data Analysis by Anuj Srivastava,Eric P. Klassen Pdf

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.

Functional Data Analysis with R and MATLAB

James Ramsay,Giles Hooker,Spencer Graves
Functional Data Analysis with R and MATLAB Book PDF

Author : James Ramsay,Giles Hooker,Spencer Graves
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 46,8 Mb
Release : 2009-06-29
Category : Computers
ISBN : 9780387981857

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Functional Data Analysis with R and MATLAB by James Ramsay,Giles Hooker,Spencer Graves Pdf

The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems

Analysis of Variance for Functional Data

Jin-Ting Zhang
Analysis of Variance for Functional Data Book PDF

Author : Jin-Ting Zhang
Publisher : CRC Press
Page : 412 pages
File Size : 49,7 Mb
Release : 2013-06-18
Category : Mathematics
ISBN : 9781439862742

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Analysis of Variance for Functional Data by Jin-Ting Zhang Pdf

Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional linear models with functional responses, ill-conditioned functional linear models, diagnostics of functional observations, heteroscedastic ANOVA for functional data, and testing equality of covariance functions. Although the methodologies presented are designed for curve data, they can be extended to surface data. Useful for statistical researchers and practitioners analyzing functional data, this self-contained book gives both a theoretical and applied treatment of functional data analysis supported by easy-to-use MATLAB® code. The author provides a number of simple methods for functional hypothesis testing. He discusses pointwise, L2-norm-based, F-type, and bootstrap tests. Assuming only basic knowledge of statistics, calculus, and matrix algebra, the book explains the key ideas at a relatively low technical level using real data examples. Each chapter also includes bibliographical notes and exercises. Real functional data sets from the text and MATLAB codes for analyzing the data examples are available for download from the author’s website.

Functional Data Analysis

James Ramsay,B. W. Silverman
Functional Data Analysis Book PDF

Author : James Ramsay,B. W. Silverman
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 48,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475771077

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Functional Data Analysis by James Ramsay,B. W. Silverman Pdf

Included here are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, applied data analysts, and to experienced researchers; and as such is of value both within statistics and across a broad spectrum of other fields. Much of the material appears here for the first time.

Introduction to Functional Data Analysis

Piotr Kokoszka,Matthew Reimherr
Introduction to Functional Data Analysis Book PDF

Author : Piotr Kokoszka,Matthew Reimherr
Publisher : CRC Press
Page : 311 pages
File Size : 41,8 Mb
Release : 2017-09-27
Category : Mathematics
ISBN : 9781498746694

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Introduction to Functional Data Analysis by Piotr Kokoszka,Matthew Reimherr Pdf

Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

S+Functional Data Analysis

Douglas B. Clarkson,Chris Fraley,Charles Gu,James Ramsay
S Functional Data Analysis Book PDF

Author : Douglas B. Clarkson,Chris Fraley,Charles Gu,James Ramsay
Publisher : Springer Science & Business Media
Page : 195 pages
File Size : 51,8 Mb
Release : 2006-06-02
Category : Computers
ISBN : 9780387283937

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S+Functional Data Analysis by Douglas B. Clarkson,Chris Fraley,Charles Gu,James Ramsay Pdf

This book can be considered a companion to two other highly acclaimed books involving James Ramsay and Bernard Silverman: Functional Data Analysis, Second Edition (2005) and Applied Functional Data Analysis (2002). This user's manual also provides the documentation for the S+FDA library for S­Plus.

Recent Advances in Functional Data Analysis and Related Topics

Frédéric Ferraty
Recent Advances in Functional Data Analysis and Related Topics Book PDF

Author : Frédéric Ferraty
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 43,6 Mb
Release : 2011-06-15
Category : Mathematics
ISBN : 9783790827361

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Recent Advances in Functional Data Analysis and Related Topics by Frédéric Ferraty Pdf

New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.

Elastic Shape Analysis of Three-Dimensional Objects

Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava
Elastic Shape Analysis of Three Dimensional Objects Book PDF

Author : Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava
Publisher : Morgan & Claypool Publishers
Page : 187 pages
File Size : 51,6 Mb
Release : 2017-09-15
Category : Computers
ISBN : 9781681730288

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Elastic Shape Analysis of Three-Dimensional Objects by Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava Pdf

Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in R, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.

Applied Functional Data Analysis

J.O. Ramsay,B.W. Silverman
Applied Functional Data Analysis Book PDF

Author : J.O. Ramsay,B.W. Silverman
Publisher : Springer
Page : 191 pages
File Size : 40,8 Mb
Release : 2007-11-23
Category : Mathematics
ISBN : 9780387224657

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Applied Functional Data Analysis by J.O. Ramsay,B.W. Silverman Pdf

This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.

S+Functional Data Analysis

Douglas B. Clarkson,Chris Fraley,Charles Gu,James Ramsay
S Functional Data Analysis Book PDF

Author : Douglas B. Clarkson,Chris Fraley,Charles Gu,James Ramsay
Publisher : Springer
Page : 192 pages
File Size : 48,5 Mb
Release : 2005-07-01
Category : Computers
ISBN : 0387249699

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S+Functional Data Analysis by Douglas B. Clarkson,Chris Fraley,Charles Gu,James Ramsay Pdf

This book can be considered a companion to two other highly acclaimed books involving James Ramsay and Bernard Silverman: Functional Data Analysis, Second Edition (2005) and Applied Functional Data Analysis (2002). This user's manual also provides the documentation for the S+FDA library for S­Plus.

Statistical Shape and Deformation Analysis

Guoyan Zheng,Shuo Li,Gabor Szekely
Statistical Shape and Deformation Analysis Book PDF

Author : Guoyan Zheng,Shuo Li,Gabor Szekely
Publisher : Academic Press
Page : 508 pages
File Size : 52,6 Mb
Release : 2017-03-23
Category : Computers
ISBN : 9780128104941

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Statistical Shape and Deformation Analysis by Guoyan Zheng,Shuo Li,Gabor Szekely Pdf

Statistical Shape and Deformation Analysis: Methods, Implementation and Applications contributes enormously to solving different problems in patient care and physical anthropology, ranging from improved automatic registration and segmentation in medical image computing to the study of genetics, evolution and comparative form in physical anthropology and biology. This book gives a clear description of the concepts, methods, algorithms and techniques developed over the last three decades that is followed by examples of their implementation using open source software. Applications of statistical shape and deformation analysis are given for a wide variety of fields, including biometry, anthropology, medical image analysis and clinical practice. Presents an accessible introduction to the basic concepts, methods, algorithms and techniques in statistical shape and deformation analysis Includes implementation examples using open source software Covers real-life applications of statistical shape and deformation analysis methods

Riemannian Geometric Statistics in Medical Image Analysis

Xavier Pennec,Stefan Sommer,Tom Fletcher
Riemannian Geometric Statistics in Medical Image Analysis Book PDF

Author : Xavier Pennec,Stefan Sommer,Tom Fletcher
Publisher : Academic Press
Page : 634 pages
File Size : 54,9 Mb
Release : 2019-09
Category : Computers
ISBN : 9780128147252

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Riemannian Geometric Statistics in Medical Image Analysis by Xavier Pennec,Stefan Sommer,Tom Fletcher Pdf

Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Content includes: - The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs - Applications of statistics on manifolds and shape spaces in medical image computing - Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. - A complete reference covering both the foundations and state-of-the-art methods - Edited and authored by leading researchers in the field - Contains theory, examples, applications, and algorithms - Gives an overview of current research challenges and future applications

Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications

Chiara Brombin,Luigi Salmaso,Lara Fontanella,Luigi Ippoliti,Caterina Fusilli
Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications Book PDF

Author : Chiara Brombin,Luigi Salmaso,Lara Fontanella,Luigi Ippoliti,Caterina Fusilli
Publisher : Springer
Page : 115 pages
File Size : 50,9 Mb
Release : 2016-02-19
Category : Mathematics
ISBN : 3319263102

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Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications by Chiara Brombin,Luigi Salmaso,Lara Fontanella,Luigi Ippoliti,Caterina Fusilli Pdf

This book considers specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric tests. The models are simple to understand and interpret and provide a useful tool to describe the global dynamics of the landmark configurations. However, because of the non-Euclidean nature of shape spaces, distributions in shape spaces are not straightforward to obtain. The book explores the use of the Gaussian distribution in the configuration space, with similarity transformations integrated out. Specifically, it works with the offset-normal shape distribution as a probability model for statistical inference on a sample of a temporal sequence of landmark configurations. This enables inference for Gaussian processes from configurations onto the shape space. The book is divided in two parts, with the first three chapters covering material on the offset-normal shape distribution, and the remaining chapters covering the theory of NonParametric Combination (NPC) tests. The chapters offer a collection of applications which are bound together by the theme of this book. They refer to the analysis of data from the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions. For these data, it may be desirable to provide a description of the dynamics of the expressions, or testing whether there is a difference between the dynamics of two facial expressions or testing which of the landmarks are more informative in explaining the pattern of an expression.

Statistics and Analysis of Shapes

Hamid Krim,Anthony Yezzi
Statistics and Analysis of Shapes Book PDF

Author : Hamid Krim,Anthony Yezzi
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 44,8 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817644819

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Statistics and Analysis of Shapes by Hamid Krim,Anthony Yezzi Pdf

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms available in a single resource. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

Object Oriented Data Analysis

J. S. Marron,Ian L. Dryden
Object Oriented Data Analysis Book PDF

Author : J. S. Marron,Ian L. Dryden
Publisher : CRC Press
Page : 436 pages
File Size : 51,7 Mb
Release : 2021-11-18
Category : Computers
ISBN : 9781351189668

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Object Oriented Data Analysis by J. S. Marron,Ian L. Dryden Pdf

Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.