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  3. Topological Data Analysis with Applications
  • Cited by 48
Publisher:
Cambridge University Press
Online publication date:
November 2021
Print publication year:
2021
Online ISBN:
9781108975704
DOI:
https://doi.org/10.1017/9781108975704
Subjects:
Mathematics, Knowledge Management, Databases and Data Mining, Computer Science, Geometry and Topology
Information

Book description

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.

Reviews

‘It is self-contained, and an understanding of only basic undergraduate-level math is required … One of the book's strengths is its synthetic way of combining abstract theory with the practical sides of the topics discussed. The authors do a great job of making the material accessible to readers with varying levels of math background. The content is introduced step-by-step, beginning with the fundamental topological concepts.’

Jacek Cyranka Source: MathSciNet

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