Topological Data Analysis
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Computational Topology for Data Analysis
Author: Tamal Krishna Dey
language: en
Publisher: Cambridge University Press
Release Date: 2022-03-10
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Topological Data Analysis with Applications
Author: Gunnar Carlsson
language: en
Publisher: Cambridge University Press
Release Date: 2021-12-16
This timely text introduces topological data analysis from scratch, with detailed case studies.
Topological Data Analysis for Genomics and Evolution
Author: Raul Rabadan
language: en
Publisher: Cambridge University Press
Release Date: 2019-12-19
Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.