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Dimensionality reduction with subgaussian matrices: a unified theory (1402.3973v1)
Published 17 Feb 2014 in cs.IT, cs.DS, math.IT, and stat.ML
Abstract: 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 data sets. 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 data sets taking the form of an infinite union of subspaces of a Hilbert space.
