Dimensionality reduction with subgaussian matrices: a unified theory
Information Theory
2014-02-18 v1 Data Structures and Algorithms
math.IT
Machine Learning
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.
Cite
@article{arxiv.1402.3973,
title = {Dimensionality reduction with subgaussian matrices: a unified theory},
author = {Sjoerd Dirksen},
journal= {arXiv preprint arXiv:1402.3973},
year = {2014}
}