Geometric and topological inference
著者
書誌事項
Geometric and topological inference
（Cambridge texts in applied mathematics）
Cambridge University Press, 2018
- : hardback
- : pbk
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注記
Includes bibliographical references (p. 224-230) and index
内容説明・目次
内容説明
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.
目次
- 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.
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