Tighter bounds for random projections of manifolds

Abstract

The Jolinson-Lindenstrauss random projection lemma gives a simple way to reduce the dimensionality of a set of points while approximately preserving their pairwise distances. The most direct application of the lemma applies to a finite set of points, but recent work has extended the technique to affine subspaces, curves, and general smooth manifolds. Here the case of random projection of smooth manifolds is considered, and a previous analysis is sharpened, reducing the dependence on such properties as the manifold's maximum curvature. Copyright 2008 ACM.