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- W2017274648 abstract "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 $k=O(epsilon^{-2}log^{(1+delta)} (n))$ 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." @default.
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- W2017274648 date "2013-08-28" @default.
- W2017274648 modified "2023-09-27" @default.
- W2017274648 title "New bounds for circulant Johnson-Lindenstrauss embeddings" @default.
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- W2017274648 doi "https://doi.org/10.48550/arxiv.1308.6339" @default.
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