Mathematical Principles of Topological and Geometric Data Analysis
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to...
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| Autors principals: | , |
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| Autor corporatiu: | |
| Format: | Electrònic eBook |
| Idioma: | anglès |
| Publicat: |
Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| Edició: | 1st ed. 2023. |
| Col·lecció: | Mathematics of Data,
2 |
| Matèries: | |
| Accés en línia: | https://doi.org/10.1007/978-3-031-33440-5 |
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Taula de continguts:
- Introduction
- Topological foundations, hypercomplexes and homology
- Weighted complexes, cohomology and Laplace operators
- The Laplace operator and the geometry of graphs
- Metric spaces and manifolds
- Linear methods: Kernels, variations, and averaging
- Nonlinear schemes: Clustering, feature extraction and dimension reduction
- Manifold learning, the scheme of Laplacian eigenmaps
- Metrics and curvature.