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.
Computational Topology for Biomedical Image and Data Analysis
Computational Topology for Biomedical Image and 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 Biomedical Image and Data Analysis write by Rodrigo Rojas Moraleda. This book was released on 2019-07-12. Computational Topology for Biomedical Image and Data Analysis available in PDF, EPUB and Kindle. 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
Research in Computational Topology
Research in Computational Topology - 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 Research in Computational Topology write by Erin Wolf Chambers. This book was released on 2018-07-30. Research in Computational Topology available in PDF, EPUB and Kindle. Based on the first Workshop for Women in Computational Topology that took place in 2016, this volume assembles new research and applications in computational topology. Featured articles range over the breadth of the discipline, including topics such as surface reconstruction, topological data analysis, persistent homology, algorithms, and surface-embedded graphs. Applications in graphics, medical imaging, and GIS are discussed throughout the book. Four of the papers in this volume are the product of working groups that were established and developed during the workshop. Additional papers were also solicited from the broader Women in Computational Topology network. The volume is accessible to a broad range of researchers, both within the field of computational topology and in related disciplines such as statistics, computational biology, and machine learning.
A Short Course in Computational Geometry and Topology
A Short Course in Computational Geometry and Topology - 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 A Short Course in Computational Geometry and Topology write by Herbert Edelsbrunner. This book was released on 2014-04-28. A Short Course in Computational Geometry and Topology available in PDF, EPUB and Kindle. This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
Computational Topology
Computational Topology - 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 write by Herbert Edelsbrunner. This book was released on 2022-01-31. Computational Topology available in PDF, EPUB and Kindle. 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.
