Charting a manifold
| Citation: |
Brand, M., "Charting a Manifold", Neural Information Processing Systems (NIPS), December 2002 (NIPS 15, Paper AA61) |
| MERL Report: | TR2003-13 |
We construct a nonlinear mapping from a high-dimensional sample space to a low-dimensional vector space, effectively recovering a Cartesian coordinate system for the manifold from which the data is sampled. The mapping preserves local geometric relations in the manifold and is pseudo-invertible. We show how to estimate the intrinsic dimensionality of the manifold from samples, decompose the sample data into locally linear low-dimensional patches, merge these patches into a single low-dimensional coordinate system, and compute forward and reverse mappings between the sample and coordinate spaces. The objective functions are convex and their solutions are given in closed form.
