A Subspace Embedding Method inL2Norm via Fast Cauchy Transform

Xu Xiang,Li-Zhi Cheng

doi:10.1155/2013/392034

Abstract

We propose a subspace embedding method via Fast Cauchy Transform (FCT) inL2norm. It is motivated by and complements the work of the subspace embedding method inLpnorm, for allp∈[1,∞]exceptp=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 inL2norm to obtain concentration property of FCT inL2norm.

Highlights

A Subspace Embedding Method in L2 Norm via Fast Cauchy TransformThe State Key Laboratory for High Performance Computation, National University of Defense and Technology, Changsha, Hunan 410073, China
Subspace embedding methods have recently proven useful in modern science and engineering
We propose a subspace embedding method via Fast Cauchy Transform (FCT) in L2 norm

Summary

A Subspace Embedding Method in L2 Norm via Fast Cauchy Transform

The State Key Laboratory for High Performance Computation, National University of Defense and Technology, Changsha, Hunan 410073, China. We propose a subspace embedding method via Fast Cauchy Transform (FCT) in L2 norm. It is motivated by and complements the work of the subspace embedding method in Lp norm, for all p ∈ [1, ∞] except p = 2, by K. Unlike the traditionally used orthogonal basis in Johnson-Lindenstrauss (JL) embedding, we employ the well-conditioned basis in L2 norm to obtain concentration property of FCT in L2 norm

Introduction

Preliminaries

Main Technical Results

Conclusion