Mathematical Principles of Topological and Geometric Data Analysis (Mathematics of Data, 2)

This book is a comprehensive guide to using geometric tools in data analysis.

It covers the mathematical prerequisites, including category theory, algebraic topology, and more, before delving into the most important machine learning techniques for dimension reduction.

The author also develops a new notion of curvature for generalized metric spaces, which can be used for topological representation of geometric information.

With its systematic approach and focus on practical applications, this book is perfect for mathematicians seeking an overview of the methods useful for data analysis, as well as researchers in machine learning and data analysis who want to see a mathematical foundation of their methods.