Mathematical Principles of Topological and Geometric Data Analysis
Mathematical Principles of Topological and Geometric Data Analysis
English | 2023 | ISBN: 3031334396 | 281 Pages | PDF EPUB (True) | 23 MB
English | 2023 | ISBN: 3031334396 | 281 Pages | PDF EPUB (True) | 23 MB
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.