Topological Data Analysis with Applications

This timely text introduces topological data analysis from scratch, with detailed case studies.

Gunnar Carlsson (Author), Mikael Vejdemo-Johansson (Author)

9781108838658, Cambridge University Press

Hardback, published 16 December 2021

230 pages
25.1 x 17.5 x 1.6 cm, 0.58 kg

The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.

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.

Subject Areas: Machine learning [UYQM], Mathematical theory of computation [UYA], Topology [PBP]