Tamal Krishna Dey

Computational Topology for Data Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 28. Februar 2022
• Englisch
• ISBN-13: 9781009103190
• Artikelnr.: 66177054

Autorenporträt

Tamal Krishna Dey is Professor of Computer Science at Purdue University. Before joining Purdue, he was a faculty in the CSE department of The Ohio State University. He has held academic positions at Indiana University-Purdue University at Indianapolis, Indian Institute of Technology Kharagpur, and Max Planck Institute. His research interests include computational geometry, computational topology and their applications to geometric modeling and data analysis. He has (co)authored two books Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge University Press) and Delaunay Mesh Generation (CRC Press), and (co)authored more than 200 scientific articles. Dey is a fellow of the IEEE, ACM, and Solid Modeling Association.

Inhaltsangabe

1. Basics
2. Complexes and homology groups
3. Topological persistence
4. General persistence
5. Generators and optimality
6. Topological analysis of point clouds
7. Reeb graphs
8. Topological analysis of graphs
9. Cover, nerve and Mapper
10. Discrete Morse theory and applications
11. Multiparameter persistence and decomposition
12. Multiparameter persistence and distances
13. Topological persistence and machine learning.