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Sparse Dimensionality Reduction Revisited
Mikael Møller Høgsgaard, Lion Kamma, Kasper Green Larsen +2
The sparse Johnson-Lindenstrauss transform is one of the central techniques in dimensionality reduction. It supports embedding a set of points in into $m=O(\vare…
Barriers for Faster Dimensionality Reduction
Ora Nova Fandina, Mikael Møller Høgsgaard, Kasper Green Larsen
The Johnson-Lindenstrauss transform allows one to embed a dataset of points in into while preserving the pairwise distance between any pair of po…
The Fast Johnson-Lindenstrauss Transform is Even Faster
Ora Nova Fandina, Mikael Møller Høgsgaard, Kasper Green Larsen
The seminal Fast Johnson-Lindenstrauss (Fast JL) transform by Ailon and Chazelle (SICOMP'09) embeds a set of points in -dimensional Euclidean space into optimal $k=O(\vareps…