Computational Topology for Data Analysis
Hardcover/Mathematics 452 pages English Mar 10, 2022
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Cambridge University Press
Computational Topology for Data Analysis
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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.
- Author:
- Tamal Krishna Dey, Yusu Wang
- Publisher:
- Cambridge University Press
- Publication Date:
- Mar 10, 2022
- Number of pages:
- 452 pages
- Language:
- English
- Binding:
- Hardcover/Mathematics
- ISBN-10:
- 1009098160
- ISBN-13:
- 9781009098168