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.
Rezensionen / Stimmen
'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, MathSciNet
Sprache
Verlagsort
Zielgruppe
Illustrationen
Worked examples or Exercises
Maße
Höhe: 250 mm
Breite: 175 mm
Dicke: 17 mm
Gewicht
ISBN-13
978-1-108-83865-8 (9781108838658)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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. Mikael Vejdemo-Johansson is Assistant Professor in the Department of Mathematics at CUNY College of Staten Island. He is the chair of the steering committee for the ATMCS conference series and runs the community web resource appliedtopology.org.
Autor*in
Stanford University, California
City University of New York
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.
