Geometric and Topological Inference (Cambridge Texts in Applied Mathematics)
Cambridge University Press, 9/27/2018
EAN 9781108419390, ISBN10: 1108419399
Hardcover, 246 pages, 23.6 x 15.7 x 1.8 cm
Language: English
Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.
Part I. Topological Preliminaries
1. Topological spaces
2. Simplicial complexes
Part II. Delaunay Complexes
3. Convex polytopes
4. Delaunay complexes
5. Good triangulations
6. Delaunay filtrations
Part III. Reconstruction of Smooth Submanifolds
7. Triangulation of submanifolds
8. Reconstruction of submanifolds
Part IV. Distance-Based Inference
9. Stability of distance functions
10. Distance to probability measures
11. Homology inference.