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Research questionWhen can a random projection preserve JL distance bounds yet lose geometric variation needed for rankings and inference?In high-dimensional data, distances can concentrate around a common baseline while the smaller variations that distinguish points carry the useful information. A projection may therefore meet a Johnson–Lindenstrauss guarantee while losing information needed for comparisons and inference.
Information Retrieval
Machine Learning
Research Paper
Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Exact Limits of Random Projections for Preserving Geometry: Distance Recovery, Nearest-Neighbor Rankings, and Covariance Shape in Gaussian ModelsThe analysis concerns rank-m Gaussian linear sketches of isotropic Gaussian data. It establishes limits for recovering features of squared distances, Kendall rank correlation, nearest-neighbor agreement, and scale-free covariance shape, including regimes where the sketch dimension is much smaller than the ambient dimension.research paper · Sep 2, 2026
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