Dimensionality reduction for \(k\)-distance applied to persistent homology
DOI10.1007/s41468-021-00079-xzbMath1482.55005arXiv2110.05897OpenAlexW3205972864MaRDI QIDQ2063202
Jean-Daniel Boissonnat, Martin Lotz, Kunal Dutta, Shreya Arya
Publication date: 10 January 2022
Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2110.05897
dimensionality reductiontopological data analysispersistent homologyrandom projectionsdistance to measureJohnson-Lindenstrauss lemma\(k\)-distance
Persistent homology and applications, topological data analysis (55N31) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Topological data analysis (62R40)
Uses Software
Cites Work
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- Efficient and robust persistent homology for measures
- A mathematical introduction to compressive sensing
- Dimensionality reduction with subgaussian matrices: a unified theory
- Geometric inference for probability measures
- Random projections of smooth manifolds
- Database-friendly random projections: Johnson-Lindenstrauss with binary coins.
- Applications of random sampling in computational geometry. II
- Topological persistence and simplification
- Witnessed \(k\)-distance
- Terminal embeddings
- New and Improved Johnson–Lindenstrauss Embeddings via the Restricted Isometry Property
- The Structure and Stability of Persistence Modules
- Sparser Johnson-Lindenstrauss Transforms
- Extensions of Lipschitz mappings into a Hilbert space
- On variants of the Johnson–Lindenstrauss lemma
- Tighter bounds for random projections of manifolds
- Towards persistence-based reconstruction in euclidean spaces
- Declutter and resample: Towards parameter free denoising.
- The Persistent Homology of Distance Functions under Random Projection
- High-Dimensional Probability
- An elementary proof of a theorem of Johnson and Lindenstrauss
- Persistent homology for low-complexity models
- The Fast Johnson–Lindenstrauss Transform and Approximate Nearest Neighbors
- Optimal terminal dimensionality reduction in Euclidean space
- Nonlinear dimension reduction via outer Bi-Lipschitz extensions
- Testing the manifold hypothesis
- A new duality result concerning Voronoi diagrams
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