Topological Data Analysis With Applications
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Topological Data Analysis With Applications
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Author : Gunnar Carlsson
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Topological Data Analysis With Applications written by Gunnar Carlsson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Computers categories.
This timely text introduces topological data analysis from scratch, with detailed case studies.
Computational Topology For Data Analysis
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Author : Tamal Krishna Dey
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-10
Computational Topology For Data Analysis written by Tamal Krishna Dey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Computers categories.
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Topological Methods In Data Analysis And Visualization
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Author : Valerio Pascucci
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23
Topological Methods In Data Analysis And Visualization written by Valerio Pascucci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.
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).
Topological Dynamics And Topological Data Analysis
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Author : Robert L. Devaney
language : en
Publisher: Springer Nature
Release Date : 2021-09-23
Topological Dynamics And Topological Data Analysis written by Robert L. Devaney and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Mathematics categories.
This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.
Topological Data Analysis
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Author : Nils A. Baas
language : en
Publisher: Springer Nature
Release Date : 2020-06-25
Topological Data Analysis written by Nils A. Baas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-25 with Mathematics categories.
This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.
Topological Methods In Data Analysis And Visualization Iv
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Author : Hamish Carr
language : en
Publisher: Springer
Release Date : 2017-06-01
Topological Methods In Data Analysis And Visualization Iv written by Hamish Carr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.
This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.
Topological Methods In Data Analysis And Visualization Iii
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Author : Peer-Timo Bremer
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-22
Topological Methods In Data Analysis And Visualization Iii written by Peer-Timo Bremer and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-22 with Mathematics categories.
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.
Topological Data Analysis For Genomics And Evolution
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Author : Raul Rabadan
language : en
Publisher: Cambridge University Press
Release Date : 2019-12-19
Topological Data Analysis For Genomics And Evolution written by Raul Rabadan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-19 with Science categories.
Biology has entered the age of Big Data. A 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 comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. 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 as well as mathematicians interested in applied topology.
Topological Methods In Data Analysis And Visualization Vi
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Author : Ingrid Hotz
language : en
Publisher: Springer Nature
Release Date : 2021-09-28
Topological Methods In Data Analysis And Visualization Vi written by Ingrid Hotz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-28 with Mathematics categories.
This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.
Algebraic Foundations For Applied Topology And Data Analysis
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Author : Hal Schenck
language : en
Publisher: Springer Nature
Release Date : 2022-11-21
Algebraic Foundations For Applied Topology And Data Analysis written by Hal Schenck and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-21 with Mathematics categories.
This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience. The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a user’s guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field. Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.