Geometric and topological inference /
Boissonnat, J.-D.(Jean-Daniel),1953-author.
Chazal, Frédéric,1971-author.
Yvinec, Mariette,1953-author.
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.
Includes bibliographical references (pages 224-230) and index.
Part I. Topological Preliminaries : 1. Topological Spaces -- 2. Simplicial Complexes -- Part II. Display 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 -- 19. Distance to Probability Measures -- 11. Homology Inference.
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.
Shapes
Geometric analysis.
Pattern perception.
Topology.
Geometric analysis.
Pattern perception.
Topology.