Computational Topology for Data Analysis

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. Yusu Wang is Professor in the Halıcıouğlu 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.

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.