Computational Topology for Data Analysis

Erscheinungsjahr 2022
ISBN: 978-1-009-09816-8
Verlag: Cambridge University Press

Buch, Englisch, 452 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 803 g

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.

Autoren/Hrsg.

Dey, Tamal Krishna

Wang, Yusu

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Mustererkennung, Biometrik
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Automatische Datenerfassung, Datenanalyse
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

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.

Über Autor(innen)

Wang, Yusu
Yusu Wang is Professor in the Haliciouglu Data Science Institute at University of California, San Diego. Prior to joining UCSD, she was Professor of Computer Science and Engineering at the Ohio State University and post-doctoral fellow at Stanford University. Yusu primarily works in topological and geometric data analysis, developing effective and theoretically justified algorithms for data analysis using geometric and topological ideas, as well as in applying them to practical domains. She received the DOE Early Career Principal Investigator Award in 2006 and NSF Career Award in 2008.

Dey, Tamal Krishna
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.