Abstract

Let Φ∈Rm×n be a sparse Johnson–Lindenstrauss transform (Kane and Nelson in J ACM 61(1):4, 2014) with s non-zeroes per column. For a subset T of the unit sphere, ε∈(0,1/2) given, we study settings for m, s required to ensure EΦsupx∈T∣∣∥Φx∥22−1∣∣<ε, i.e. so that Φ preserves the norm of every x∈T
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