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A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules...