A Derandomized Sparse Johnson-Lindenstrauss Transform

TL;DR

This paper presents a derandomized version of the sparse Johnson-Lindenstrauss transform using bounded independence hash functions, improving sparsity bounds and providing an alternative proof.

Contribution

It introduces an efficient derandomization of the sparse Johnson-Lindenstrauss transform with improved sparsity bounds using spectral moment bounds.

Findings

Successfully derandomized the transform with bounded independence

Achieved improved sparsity bounds

Provided an alternative proof technique

Abstract

Recent work of [Dasgupta-Kumar-Sarlos, STOC 2010] gave a sparse Johnson-Lindenstrauss transform and left as a main open question whether their construction could be efficiently derandomized. We answer their question affirmatively by giving an alternative proof of their result requiring only bounded independence hash functions. Furthermore, the sparsity bound obtained in our proof is improved. The main ingredient in our proof is a spectral moment bound for quadratic forms that was recently used in [Diakonikolas-Kane-Nelson, FOCS 2010].