Tamal Krishna Dey (Indiana Purdue University), Yusu Wang (San Diego University of California)

Computational Topology for Data Analysis

• Gebundenes Buch

Produktbeschreibung

Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data in applied domains. This comprehensive text covers the current state of the field for students in mathematics and computer science, providing a computational and algorithmic foundation for techniques in TDA.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 454
• Erscheinungstermin: 10. März 2022
• Englisch
• Abmessung: 235mm x 157mm x 29mm
• Gewicht: 786g
• ISBN-13: 9781009098168
• ISBN-10: 1009098160
• Artikelnr.: 62845313

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.