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  3. Topological Data Analysis with Applications
  • Cited by 53
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    • Publisher:
      Cambridge University Press
      Publication date:
      25 November 2021
      16 December 2021
      ISBN:
      9781108975704
      9781108838658
      DOI:
      https://doi.org/10.1017/9781108975704
      Dimensions:
      (244 x 170 mm)
      Weight & Pages:
      0.58kg, 230 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Knowledge Management, Databases and Data Mining, Computer Science, Geometry and Topology
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    Subjects:
    Mathematics, Knowledge Management, Databases and Data Mining, Computer Science, Geometry and Topology
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    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

    ‘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 Source: The Mathematical Intelligencer

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