  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.
