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An Introduction to Johnson-Lindenstrauss Transforms

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arxiv 2103.00564 v1 pith:2JT2TZKS submitted 2021-02-28 cs.DS cs.LG

classification cs.DScs.LG
keywords theydatamanytransformscharacteristicsdeeplydevelopmentdifferential
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Computationally-efficient Graph Modeling with Refined Graph Random Features

    cs.LG 2025-10 conditional novelty 6.0 of 10

    Stitching several short random walks into a product of unbiased feature matrices approximates graph node kernels with less variance and better long-range coverage than single long walks.

  2. FedRP: A Communication-Efficient Approach for Differentially Private Federated Learning Using Random Projection

    cs.LG 2025-09 reject novelty 5.0 of 10

    FedRP claims to preserve FedAvg-level accuracy while sending only a few numbers per client per round and providing an (epsilon, delta)-DP guarantee.

  3. The Blessing and Curse of Dimensionality in Safety Alignment

    cs.AI 2025-07 conditional novelty 5.0 of 10

    Compressing LLM internals via FJLT projection or a bottleneck layer disrupts linear safety directions and blocks activation-steering jailbreaks, at some utility cost and with no defense against non-linear attacks.

  4. A remark on dimensionality reduction in discrete subgroups

    math.MG 2025-01 reject novelty 5.0 of 10

    A discrete-lattice version of the Johnson-Lindenstrauss lemma is attempted, but a scaling error in the lower distortion bound leaves the central claim unproved.

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