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Topological and Statistical Methods for Complex Data

Topological and Statistical Methods for Complex Data
Author: Janine Bennett
Publisher: Springer
Total Pages: 297
Release: 2014-11-19
Genre: Mathematics
ISBN: 3662449005
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This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.

Computational Topology for Data Analysis

Computational Topology for Data Analysis
Author: Tamal Krishna Dey
Publisher: Cambridge University Press
Total Pages: 456
Release: 2022-03-10
Genre: 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.

Topological Methods in Data Analysis and Visualization

Topological Methods in Data Analysis and Visualization
Author: Valerio Pascucci
Publisher: Springer Science & Business Media
Total Pages: 265
Release: 2010-11-23
Genre: Mathematics
ISBN: 3642150144
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Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . The editors have brought together the most prominent and best recognized researchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Snowbird, Utah, US. The 2009 "TopoInVis" workshop follows the two successful workshops in 2005 (Slovakia) and 2007 (Germany).

Geometric and Topological Inference

Geometric and Topological Inference
Author: Jean-Daniel Boissonnat
Publisher: Cambridge University Press
Total Pages: 247
Release: 2018-09-27
Genre: 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.

Topological Methods in Data Analysis and Visualization V

Topological Methods in Data Analysis and Visualization V
Author: Hamish Carr
Publisher: Springer Nature
Total Pages: 264
Release: 2020-12-10
Genre: Mathematics
ISBN: 3030430367
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This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world’s leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.

Topological Methods in Data Analysis and Visualization III

Topological Methods in Data Analysis and Visualization III
Author: Peer-Timo Bremer
Publisher: Springer Science & Business
Total Pages: 276
Release: 2014-04-22
Genre: Mathematics
ISBN: 3319040995
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This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world’s leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.

Functional and High-Dimensional Statistics and Related Fields

Functional and High-Dimensional Statistics and Related Fields
Author: Germán Aneiros
Publisher: Springer Nature
Total Pages: 254
Release: 2020-06-19
Genre: Mathematics
ISBN: 3030477568
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This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Topological Data Analysis for Genomics and Evolution

Topological Data Analysis for Genomics and Evolution
Author: Raul Rabadan
Publisher: Cambridge University Press
Total Pages: 521
Release: 2019-12-19
Genre: Science
ISBN: 1107159547
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An introduction to geometric and topological methods to analyze large scale biological data; includes statistics and genomic applications.

Computational Homology

Computational Homology
Author: Tomasz Kaczynski
Publisher: Springer Science & Business Media
Total Pages: 488
Release: 2006-04-18
Genre: Mathematics
ISBN: 0387215972
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Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

The Structure and Stability of Persistence Modules

The Structure and Stability of Persistence Modules
Author: Frédéric Chazal
Publisher: Springer
Total Pages: 123
Release: 2016-10-08
Genre: Mathematics
ISBN: 3319425455
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This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.