Dimensionality reduction with subgaussian matrices: a unified theory

Sjoerd Dirksen

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arXiv · 1402.3973

Dimensionality reduction with subgaussian matrices: a unified theory

Sjoerd Dirksen

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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.

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Sjoerd Dirksen. 2014-02-17. Dimensionality reduction with subgaussian matrices: a unified theory. https://arxiv.org/abs/1402.3973

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