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New bounds for circulant Johnson-Lindenstrauss embeddings
This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as
an important class of structured random JL embeddings, are formed by
randomizing the column signs of a circulant matrix generated by a random
vector. With the help of recent decoupling techniques and matrix-valued
Bernstein inequalities, we obtain a new bound
for Gaussian circulant JL embeddings.
Moreover, by using the Laplace transform technique (also called Bernstein's
trick), we extend the result to subgaussian case. The bounds in this paper
offer a small improvement over the current best bounds for Gaussian circulant
JL embeddings for certain parameter regimes and are derived using more direct
methods.Comment: 11 pages; accepted by Communications in Mathematical Science
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