A Subspace Embedding Method in L2 Norm via Fast Cauchy Transform

Abstract

We propose a subspace embedding method via Fast Cauchy Transform (FCT) in $L_2$ norm. It is motivated by and complements the work of the subspace embedding method in $L_{\mathrm{p}}$ norm, for all $p\in [1,\infty ]$ except $p=2$, by K. L. Clarkson (ACM-SIAM, 2013). Unlike the traditionally used orthogonal basis in Johnson-Lindenstrauss (JL) embedding, we employ the well-conditioned basis in $L_2$ norm to obtain concentration property of FCT in $L_2$ norm.