Name
Abstract | ||
|---|---|---|
We study geometric and topological properties of the image of a smooth submanifold of $$\\mathbb {R}^{n}$$Rn under a bi-Lipschitz map to $$\\mathbb {R}^{m}$$Rm. In particular, we characterize how the dimension, diameter, volume, and reach of the embedded manifold relate to the original. Our main result establishes a lower bound on the reach of the embedded manifold in the case where $$m \\le n$$m≤n and the bi-Lipschitz map is linear. We discuss implications of this work in signal processing and machine learning, where bi-Lipschitz maps on low-dimensional manifolds have been constructed using randomized linear operators. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00454-016-9847-6 | Discrete & Computational Geometry |
Keywords | DocType | Volume |
Manifolds,Reach,Bi-Lipschitz maps,Compressive sensing,Random projections,28A75,53A07,57R40,68P30,94A12 | Journal | abs/1512.06906 |
Issue | ISSN | Citations |
3 | 0179-5376 | 0 |
PageRank | References | Authors |
0.34 | 11 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Armin Eftekhari | 1 | 129 | 12.42 |
| Michael B. Wakin | 2 | 4299 | 271.57 |