New bounds for circulant Johnson-Lindenstrauss embeddings

Hui Zhang; Lizhi Cheng

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arXiv · 1308.6339

New bounds for circulant Johnson-Lindenstrauss embeddings

Hui Zhang·Lizhi Cheng

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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 $k=O(ε^{-2}\log^{(1+δ)} (n))$ 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.

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BibTeX RIS

Hui Zhang, Lizhi Cheng. 2013-08-29. New bounds for circulant Johnson-Lindenstrauss embeddings. https://arxiv.org/abs/1308.6339

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