Dimensionality Reduction with Subgaussian Matrices: A Unified Theory

We present a theory for euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and johnson–lindenstrauss-type results obtained earlier for specific datasets. in particular, we recover and, in several cases, improve results for sets of sparse and structured sparse vectors, low-rank matrices and tensors, and smooth manifolds. in addition, we establish a new johnson–lindenstrauss embedding for datasets taking the form of an infinite union of subspaces of a hilbert space.