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A Semi-Quantitative Drug Affinity Responsive Target Stability DARTS assay for studying Rapamycin/mTOR interaction
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GhostUMAP2: Measuring and Analyzing $(r,d)$-Stability of UMAP.

Myeongwon Jung, Takanori Fujiwara, Jaemin Jo

    IEEE Transactions on Visualization and Computer Graphics
    |December 4, 2025
    PubMed
    Summary

    Uniform Manifold Approximation and Projection (UMAP) results can be unstable due to its random processes. We introduce (r,d)-stability to quantify and analyze projection stability, improving UMAP

    Area of Science:

    • Data Science
    • Machine Learning
    • Dimensionality Reduction

    Background:

    • Uniform Manifold Approximation and Projection (UMAP) is a popular dimensionality reduction technique.
    • The stochastic nature of UMAP's optimization can lead to unstable projection results.
    • The impact of this stochasticity on UMAP's reliability is not well understood.

    Purpose of the Study:

    • To introduce a novel framework, (r,d)-stability, for analyzing the stability of UMAP projections.
    • To quantify the impact of stochastic elements, such as initial positions and negative sampling, on UMAP results.
    • To provide tools and guidelines for assessing and improving UMAP projection stability.

    Main Methods:

    • Introduction of 'ghosts' (duplicate data points) to represent potential positional variations due to stochasticity.

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  • Definition of (r,d)-stability based on the confinement of ghost projections within a specified radius.
  • Development of an adaptive dropping scheme for efficient computation of ghost projections.
  • Main Results:

    • The proposed (r,d)-stability framework effectively analyzes the impact of stochasticity in UMAP.
    • An adaptive dropping scheme reduces runtime by up to 60% while preserving ~90% of unstable points.
    • A visualization tool facilitates interactive exploration of data point projection stability.

    Conclusions:

    • The (r,d)-stability framework provides a robust method for evaluating UMAP projection reliability.
    • The adaptive dropping scheme offers significant computational efficiency gains.
    • The developed tools and guidelines aid researchers in achieving more stable and interpretable UMAP results.