Gunnar Carlsson

Topological Data Analysis with Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 16. Dezember 2021
• Englisch
• ISBN-13: 9781108983945
• Artikelnr.: 66181299

Autorenporträt

Gunnar Carlsson is Professor Emeritus at Stanford University. He received his doctoral degree from Stanford in 1976, and has taught at the University of Chicago, University of California, San Diego, Princeton University, and since 1991 at Stanford University. His work within mathematics has been concentrated in algebraic topology, and he has spent the last 20 years on the development of topological data analysis. He is also passionate about the transfer of scientific findings to real-world applications, leading him to the founding of the topological data analysis-based company Ayasdi in 2008.

Inhaltsangabe

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.