Introduction to Riemannian geometry and geometric statistics from basic theory to implementation with geomstats
Containing many practical Python examples, this monograph is a valuable resource both for mathematicians and applied scientists to learn the theory of Riemann geometry and its use in practice implemented with the Geomstats package where most of the difficulties are hidden under high-level functions.
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| Weitere Verfasser: | , |
| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Boston, Delft
now
2023
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| Schriftenreihe: | Foundations and trends in machine learning
volume 16, issue 3 (2023) |
| Schlagworte: | |
| Online Zugang: | Inhaltsverzeichnis |
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Tag hinzufügen | Zusammenfassung: | Containing many practical Python examples, this monograph is a valuable resource both for mathematicians and applied scientists to learn the theory of Riemann geometry and its use in practice implemented with the Geomstats package where most of the difficulties are hidden under high-level functions. Intro -- Introduction -- Differentiable manifolds -- Differentiable manifolds and tangent spaces -- Implementation in geomstats -- Riemannian manifolds -- Riemannian metrics -- Affine connections and the Levi-Civita connection -- Distance and Geodesics -- Curvature -- Lie groups -- Lie groups, Lie algebras and Lie subgroups -- The exponential map -- Invariant metrics on Lie groups -- Group action and homogeneous spaces -- Metrics defined by invariance properties -- Submersions and quotient metrics -- Homogeneous spaces -- Symmetric spaces -- Statistics and machine learning with Geomstats -- Probability distributions and sampling -- Distance-based algorithms -- The Fréchet mean -- Generalizations of PCA -- Geodesic Regression -- Conclusion -- Acknowledgment -- List of Examples -- List of Figures -- Appendices -- Lexicon -- SE(n) with an anisotropic metric -- Geodesics -- Curvature -- One parameter subgroups -- References. |
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| Beschreibung: | Literaturverzeichnis: Seite 165-174 |
| Beschreibung: | 174 Seiten Diagramme |
| ISBN: | 9781638281542 978-1-63828-154-2 |