Topological Data Analysis with Applications

by Gunnar E. Carlsson, Mikael Vejdemo-Johansson

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 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.

Genres: Textbooks, Mathematics

230 pages, Hardcover

Published March 24, 2022

Reviews

[Lucille Nguyen · Rating 4 out of 5]

Look, it is what it says on the tin: a summary of topology and its applications for data analysis, with a short section of applications of topology in the sciences. Dense, mathy, but intuitive. And despite some choices in wording that make certain definitions longer than they have to be, there are formal definitions below the reading sections that are much more informative for those with logical or hard mathematical backgrounds. Good as an overview.