OSNAP: Faster Numerical Linear Algebra Algorithms via Sparser Subspace Embeddings

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over matrices Π ∈ Rm×n such that for any linear subspace W ⊆ Rn with dim(W) = d, PΠ~D(∀x ∈ W ||Πx||2 ∈ (1 ± ε)||x||2) > 2/3. We show that a certain class of distributions, Oblivious Sparse Norm-Approximating Projections (OSNAPs), provides OSE's with m = O...More