Computational Topology for Data Analysis

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

Computational Topology for Data Analysis

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

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English

Cambridge University Press
10 March 2022

Data analysis: general; Mathematics & Sciences; Geometry; Topology; Data capture & analysis; Mathematical theory of computation

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.

By: Tamal Krishna Dey (Purdue University Indiana), Yusu Wang (University of California, San Diego)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions: Height: 234mm, Width: 155mm, Spine: 30mm
Weight: 780g
ISBN: 9781009098168
ISBN 10: 1009098160
Pages: 452
Publication Date: 10 March 2022
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

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 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.

Reviews for Computational Topology for Data Analysis

'A must-have up-to-date computational account of a vibrant area connecting pure mathematics with applications.' Herbert Edelsbrunner, IST Austria 'This book provides a comprehensive treatment of the algorithmic aspects of topological persistence theory, both in the classical one-parameter setting and in the emerging multi-parameter setting. It is an excellent resource for practitioners within or outside the field, who want to learn about the current state-of-the-art algorithms in topological data analysis.' Steve Oudot, Inria and Ecole polytechnique