Persistence Theory From Quiver Representations To Data Analysis
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Persistence Theory From Quiver Representations To Data Analysis
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Author : Steve Y. Oudot
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-02
Persistence Theory From Quiver Representations To Data Analysis written by Steve Y. Oudot and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-02 with Mathematics categories.
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.
Persistence Theory From Quiver Representations To Data Analysis
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Author : Steve Y. Oudot
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-17
Persistence Theory From Quiver Representations To Data Analysis written by Steve Y. Oudot and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with Mathematics categories.
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.
The Structure And Stability Of Persistence Modules
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Author : Frédéric Chazal
language : en
Publisher: Springer
Release Date : 2016-10-17
The Structure And Stability Of Persistence Modules written by Frédéric Chazal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-17 with Mathematics categories.
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.
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.
Topological Persistence In Geometry And Analysis
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Author : Leonid Polterovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-11
Topological Persistence In Geometry And Analysis written by Leonid Polterovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-11 with Education categories.
The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.
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.
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 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.
The Structure And Stability Of Persistence Modules
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Author : Frédéric Chazal
language : en
Publisher: Springer
Release Date : 2016-10-08
The Structure And Stability Of Persistence Modules written by Frédéric Chazal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-08 with Mathematics categories.
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.
Topology In Real World Machine Learning And Data Analysis
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Author : Kathryn Hess
language : en
Publisher: Frontiers Media SA
Release Date : 2022-11-07
Topology In Real World Machine Learning And Data Analysis written by Kathryn Hess and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-07 with Science categories.