Functional and Shape Data Analysis
Functional and Shape Data Analysis

Author: Anuj Srivastava

Publisher: Springer

Published: 2016-10-03

Total Pages: 454

ISBN-13: 1493940201

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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.

The Shape of Data in Digital Humanities
The Shape of Data in Digital Humanities

Author: Julia Flanders

Publisher: Routledge

Published: 2018-11-02

Total Pages: 373

ISBN-13: 1317016149

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Data and its technologies now play a large and growing role in humanities research and teaching. This book addresses the needs of humanities scholars who seek deeper expertise in the area of data modeling and representation. The authors, all experts in digital humanities, offer a clear explanation of key technical principles, a grounded discussion of case studies, and an exploration of important theoretical concerns. The book opens with an orientation, giving the reader a history of data modeling in the humanities and a grounding in the technical concepts necessary to understand and engage with the second part of the book. The second part of the book is a wide-ranging exploration of topics central for a deeper understanding of data modeling in digital humanities. Chapters cover data modeling standards and the role they play in shaping digital humanities practice, traditional forms of modeling in the humanities and how they have been transformed by digital approaches, ontologies which seek to anchor meaning in digital humanities resources, and how data models inhabit the other analytical tools used in digital humanities research. It concludes with a glossary chapter that explains specific terms and concepts for data modeling in the digital humanities context. This book is a unique and invaluable resource for teaching and practising data modeling in a digital humanities context.

The Statistical Theory of Shape
The Statistical Theory of Shape

Author: Christopher G. Small

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 237

ISBN-13: 1461240328

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In general terms, the shape of an object, data set, or image can be de fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.

Statistics For Dummies
Statistics For Dummies

Author: Deborah J. Rumsey

Publisher: John Wiley & Sons

Published: 2016-06-07

Total Pages: 423

ISBN-13: 1119293529

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The fun and easy way to get down to business with statistics Stymied by statistics? No fear? this friendly guide offers clear, practical explanations of statistical ideas, techniques, formulas, and calculations, with lots of examples that show you how these concepts apply to your everyday life. Statistics For Dummies shows you how to interpret and critique graphs and charts, determine the odds with probability, guesstimate with confidence using confidence intervals, set up and carry out a hypothesis test, compute statistical formulas, and more. Tracks to a typical first semester statistics course Updated examples resonate with today's students Explanations mirror teaching methods and classroom protocol Packed with practical advice and real-world problems, Statistics For Dummies gives you everything you need to analyze and interpret data for improved classroom or on-the-job performance.

Statistical Shape Analysis
Statistical Shape Analysis

Author: Ian L. Dryden

Publisher: John Wiley & Sons

Published: 2016-06-28

Total Pages: 496

ISBN-13: 1119072506

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A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded `Statistical Shape Analysis’ by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. Statistical Shape Analysis: with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis .

Introductory Business Statistics (paperback, B&w)
Introductory Business Statistics (paperback, B&w)

Author: Alexander Holmes

Publisher:

Published: 2023-06-30

Total Pages: 0

ISBN-13: 9781998109487

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Printed in b&w. Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.

The Shape of Data
The Shape of Data

Author: Colleen M. Farrelly

Publisher: No Starch Press

Published: 2023-09-12

Total Pages: 265

ISBN-13: 1718503091

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This advanced machine learning book highlights many algorithms from a geometric perspective and introduces tools in network science, metric geometry, and topological data analysis through practical application. Whether you’re a mathematician, seasoned data scientist, or marketing professional, you’ll find The Shape of Data to be the perfect introduction to the critical interplay between the geometry of data structures and machine learning. This book’s extensive collection of case studies (drawn from medicine, education, sociology, linguistics, and more) and gentle explanations of the math behind dozens of algorithms provide a comprehensive yet accessible look at how geometry shapes the algorithms that drive data analysis. In addition to gaining a deeper understanding of how to implement geometry-based algorithms with code, you’ll explore: Supervised and unsupervised learning algorithms and their application to network data analysis The way distance metrics and dimensionality reduction impact machine learning How to visualize, embed, and analyze survey and text data with topology-based algorithms New approaches to computational solutions, including distributed computing and quantum algorithms

The Shape of Data
The Shape of Data

Author: Colleen M. Farrelly

Publisher: No Starch Press

Published: 2023-09-12

Total Pages: 265

ISBN-13: 1718503083

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This advanced machine learning book highlights many algorithms from a geometric perspective and introduces tools in network science, metric geometry, and topological data analysis through practical application. Whether you’re a mathematician, seasoned data scientist, or marketing professional, you’ll find The Shape of Data to be the perfect introduction to the critical interplay between the geometry of data structures and machine learning. This book’s extensive collection of case studies (drawn from medicine, education, sociology, linguistics, and more) and gentle explanations of the math behind dozens of algorithms provide a comprehensive yet accessible look at how geometry shapes the algorithms that drive data analysis. In addition to gaining a deeper understanding of how to implement geometry-based algorithms with code, you’ll explore: Supervised and unsupervised learning algorithms and their application to network data analysis The way distance metrics and dimensionality reduction impact machine learning How to visualize, embed, and analyze survey and text data with topology-based algorithms New approaches to computational solutions, including distributed computing and quantum algorithms