johnson-lindenstrauss

First probabilistic framework for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty; A non-trivial martingale extension of Johnson-Lindenstrauss (JL) to sequentially adaptive data processes.

TL;DR: We simplify and unify various constructions of the Johnson-Lindenstrauss (JL) lemma, including spherical and sub-Gaussian models, and provide the first rigorous proof for spherical construction’s effectiveness. Our work extends the Hanson-Wright inequality and solidifies the JL lemma’s theoretical foundation, enhancing its practical applications in computational algorithms.