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

'This text serves as a welcome invitation to delve further into the subject. [It] is aimed at kindling interest. That is, it is well written but does not aim to be comprehensive. There is, however, an extensive bibliography, which will be particularly useful for locating the work showcased in that third section on application. This will serve readers well. The case studies presented are varied enough that absorbing every detail would be challenging. However, it is this varied nature of the examples that convincingly makes the case that these ideas are applicable and highlights the appeal of the subject.' Michele Intermont, The Mathematical Intelligencer

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]