[Banach] Abstract of a paper by Kasper Green Larsen and Jelani Nelson

This is an announcement for the paper "The Johnson-Lindenstrauss lemma is optimal for linear dimensionality reduction" by Kasper Green Larsen and Jelani Nelson.

Abstract: For any $n>1$ and $0<\varepsilon<1/2$, we show the existence of an $n^{O(1)}$-point subset $X$ of $\mathbb{R}^n$ such that any linear map from $(X,\ell_2)$ to $\ell_2^m$ with distortion at most $1+\varepsilon$ must have $m = \Omega(\min{n, \varepsilon^{-2}\log n})$. Our lower bound matches the upper bounds provided by the identity matrix and the Johnson-Lindenstrauss lemma, improving the previous lower bound of Alon by a $\log(1/\varepsilon)$ factor.

Archive classification: cs.IT cs.CG cs.DS math.FA math.IT

Submitted from: minilek@seas.harvard.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1411.2404

or

http://arXiv.org/abs/1411.2404