Topological Data Analysis With Applications

List of contents

Part I. Background: 1. Introduction; 2. Data; Part II. Theory: 3. Topology; 4. Shape of data; 5. Structures on spaces of barcodes; Part III. Practice: 6. Case studies; References; Index.

About the author

Gunnar Carlsson is Professor Emeritus at Stanford University. He received his doctoral degree from Stanford in 1976, and has taught at the University of Chicago, University of California, San Diego, Princeton University, and since 1991 at Stanford University. His work within mathematics has been concentrated in algebraic topology, and he has spent the last 20 years on the development of topological data analysis. He is also passionate about the transfer of scientific findings to real-world applications, leading him to the founding of the topological data analysis-based company Ayasdi in 2008.Mikael Vejdemo-Johansson is Assistant Professor in the Department of Mathematics at CUNY College of Staten Island. He is the chair of the steering committee for the ATMCS conference series and runs the community web resource appliedtopology.org.

Summary

This introduction to topological data analysis keeps prerequisites to a minimum while covering all the key techniques, including persistent homology, cohomology, and Mapper. The final section discusses diverse case studies in detail. Mathematicians, data scientists and computer scientists will appreciate this graduate-level resource.

Product details

• Authors: Gunnar Carlsson, Gunnar (Stanford University Carlsson, Mikael Vejdemo-Johansson, Mikael (City University of New York) Vejdemo-Johansson, Vejdemo-Johansson Mikael
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.03.2022
• EAN: 9781108838658
• ISBN: 978-1-108-83865-8
• No. of pages: 230
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; machine learning, MATHEMATICS / Topology, COMPUTERS / Machine Theory, Topology, Mathematical theory of computation, COMPUTERS / Data Science / Machine Learning