# On random embeddings and their application to optimisation

arXiv: https://arxiv.org/abs/2206.03371 · HTML: https://mlsanity.com/paper/2206.03371/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2022.

## Built on by (most cited first, 2 of 2)

- [Adaptive Hybrid Subspace Levenberg Marquardt Algorithm with Adequacy Monitor for Large Scale Least Squares Problems](https://mlsanity.com/paper/2608.25524/) (2026)
- [Johnson-Lindenstrauss embeddings for noisy vectors -- taking advantage of the noise](https://mlsanity.com/paper/2209.01006/) (2022)

## Abstract (arXiv)

Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of optimisation, one needs to explore high-dimensional spaces representing the problem data or its parameters and thus the computational cost of solving an optimisation problem is connected to the size of the data/variables. This thesis studies the theoretical properties of norm-preserving random embeddings, and their application to several classes of optimisation problems.