Topological Persistence in Geometry and Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topological Persistence in Geometry and Analysis write by Leonid Polterovich. This book was released on 2020-05-11. Topological Persistence in Geometry and Analysis available in PDF, EPUB and Kindle. 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.
Computational Topology for Data Analysis
Computational Topology for Data Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Topology for Data Analysis write by Tamal Krishna Dey. This book was released on 2022-03-10. Computational Topology for Data Analysis available in PDF, EPUB and Kindle. 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.
Persistence Theory: From Quiver Representations to Data Analysis
Persistence Theory: From Quiver Representations to Data Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Persistence Theory: From Quiver Representations to Data Analysis write by Steve Y. Oudot. This book was released on 2017-05-17. Persistence Theory: From Quiver Representations to Data Analysis available in PDF, EPUB and Kindle. 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.
Geometric and Topological Inference
Geometric and Topological Inference - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric and Topological Inference write by Jean-Daniel Boissonnat. This book was released on 2018-09-27. Geometric and Topological Inference available in PDF, EPUB and Kindle. A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Topological Data Analysis with Applications
Topological Data Analysis with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topological Data Analysis with Applications write by Gunnar Carlsson. This book was released on 2021-12-16. Topological Data Analysis with Applications available in PDF, EPUB and Kindle. This timely text introduces topological data analysis from scratch, with detailed case studies.
