# Dimensionality reduction with subgaussian matrices: a unified theory

arXiv: https://arxiv.org/abs/1402.3973 · HTML: https://mlsanity.com/paper/1402.3973/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2014.

## Built on by (most cited first, 7 of 7)

- [An Introduction to Johnson-Lindenstrauss Transforms](https://mlsanity.com/paper/2103.00564/) (2021)
- [Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications](https://mlsanity.com/paper/2311.05116/) (2023)
- [A unified framework for learning with nonlinear model classes from arbitrary linear samples](https://mlsanity.com/paper/2311.14886/) (2023)
- [On Fast Johnson-Lindenstrauss Embeddings of Compact Submanifolds of ℝN with Boundary](https://mlsanity.com/paper/2110.04193/) (2021)
- [How many measurements are enough? Bayesian recovery in inverse problems with general distributions](https://mlsanity.com/paper/2505.10630/) (2025)
- [Linear Convergence of Reshuffling Kaczmarz Methods With Sparse Constraints](https://mlsanity.com/paper/2304.10123/) (2023)
- [Uniform Recovery Guarantees for Quantized Corrupted Sensing Using Structured or Generative Priors](https://mlsanity.com/paper/2401.08402/) (2024)

## Abstract (arXiv)

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.