Buch, Englisch, Band 57, 246 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 405 g
Buch, Englisch, Band 57, 246 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 405 g
Reihe: Cambridge Texts in Applied Mathematics
ISBN: 978-1-108-41089-2
Verlag: Cambridge University Press
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.
Autoren/Hrsg.
Weitere Infos & Material
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.