A Derandomized Sparse Johnson-Lindenstrauss Transform
arXiv:1006.3585
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].
v3: Improved seed length, alternative proof of JL row optimality, other minor changes; v2: Improved presentation. Added a warmup section, Section 4, which gives a short proof of the JL lemma