Jean-Daniel Boissonnat

Geometric and Topological Inference (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 27. September 2018
• Englisch
• ISBN-13: 9781108321334
• Artikelnr.: 54178799

Autorenporträt

Jean-Daniel Boissonnat is a Research Director at the Institut national de recherche en informatique et en automatique, France. His research interests are in computational geometry and topology. He has published several books and more than 180 research papers, and is on the editorial board of the Journal of the ACM and of Discrete and Computational Geometry. He received the IBM award in Computer Science in 1987, the EADS award in Information Sciences in 2006 and was awarded an advanced grant from the European Research Council in 2014. He has taught at several universities in Paris and at the Collège de France.

Inhaltsangabe

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.