An Introduction to Johnson-Lindenstrauss Transforms

TL;DR

This paper introduces Johnson-Lindenstrauss Transforms, explaining their purpose in data dimensionality reduction, their historical development, and their applications across various fields like machine learning and privacy.

Contribution

It provides a comprehensive overview of Johnson-Lindenstrauss Transforms, including their definition, historical context, and references for further exploration.

Findings

Effective in reducing data dimensions while preserving structure

Widely applicable in machine learning and privacy

Established theoretical foundations since the 1980s

Abstract

Johnson--Lindenstrauss Transforms are powerful tools for reducing the dimensionality of data while preserving key characteristics of that data, and they have found use in many fields from machine learning to differential privacy and more. This note explains what they are; it gives an overview of their use and their development since they were introduced in the 1980s; and it provides many references should the reader wish to explore these topics more deeply.