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.

中文翻译：

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Johnson-Lindenstrauss变换简介

Johnson-Lindenstrauss变换是功能强大的工具，可在保留数据关键特征的同时降低数据的维数，并且已在从机器学习到差异化隐私等许多领域中使用。本说明解释了它们的含义。自1980年代引入以来，它概述了它们的用途和发展；如果读者希望更深入地探索这些主题，它提供了许多参考。