[PDF] Computational Topology For Data Analysis eBook

Author : Tamal Krishna Dey
Publisher : Cambridge University Press
Page : 456 pages
File Size : 40,12 MB
Release : 2022-03-10
Category : Mathematics
ISBN : 1009103199

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Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.

Author : Rodrigo Rojas Moraleda
Publisher : CRC Press
Page : 116 pages
File Size : 36,6 MB
Release : 2019-07-12
Category : Medical
ISBN : 0429810997

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This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic. Features: Presents a practical guide to algebraic topology as well as persistence homology Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data

Author : Tamal Krishna Dey
Publisher : Cambridge University Press
Page : 455 pages
File Size : 41,91 MB
Release : 2022-03-10
Category : Computers
ISBN : 1009098160

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This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Author : Gunnar Carlsson
Publisher : Cambridge University Press
Page : 233 pages
File Size : 46,61 MB
Release : 2021-12-16
Category : Computers
ISBN : 1108838650

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This timely text introduces topological data analysis from scratch, with detailed case studies.

Author : Herbert Edelsbrunner
Publisher : American Mathematical Society
Page : 241 pages
File Size : 46,70 MB
Release : 2022-01-31
Category : Mathematics
ISBN : 1470467690

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Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

Author : Raúl Rabadán
Publisher : Cambridge University Press
Page : 521 pages
File Size : 25,5 MB
Release : 2019-10-31
Category : Science
ISBN : 1108753396

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Biology has entered the age of Big Data. The technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce questions to a comparison of algebraic invariants, such as numbers, which are typically easier to solve. Topological data analysis is a rapidly-developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology alongside mathematicians interested in applied topology.

Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
Page : 229 pages
File Size : 49,91 MB
Release : 2017-05-17
Category : Mathematics
ISBN : 1470434431

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Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Author : Julien Tierny
Publisher : Springer
Page : 158 pages
File Size : 41,50 MB
Release : 2018-01-16
Category : Mathematics
ISBN : 3319715070

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Combining theoretical and practical aspects of topology, this book provides a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a painstaking but intuitive manner, with numerous high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in detail, and their application is carefully demonstrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis for lecturers, students and researchers.

Author : Jean-Daniel Boissonnat
Publisher : Cambridge University Press
Page : 247 pages
File Size : 21,69 MB
Release : 2018-09-27
Category : Computers
ISBN : 1108419399

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A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Author : Robert W. Ghrist
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 29,55 MB
Release : 2014
Category : Mathematics
ISBN : 9781502880857

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This book gives an introduction to the mathematics and applications comprising the new field of applied topology. The elements of this subject are surveyed in the context of applications drawn from the biological, economic, engineering, physical, and statistical sciences.