Restricted isometric compression of sparse datasets into low-dimensional varieties

Abstract

This article extends the known restricted isometric projection of sparse datasets in Euclidean spaces ${\mathbb{R}}^N$ down into low-dimensional subspaces ${\mathbb{R}}^k,k\ll N,$ to the case of low-dimensional varieties $\mathcal{M}\subset {\mathbb{R}}^N,$ of codimension $N-k=\omega (N)$. Applications to structured/hierarchical datasets are considered.