New bounds for circulant Johnson-Lindenstrauss embeddings

نویسندگان

  • Hui Zhang
  • Lizhi Cheng
چکیده

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(ǫ log(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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عنوان ژورنال:
  • CoRR

دوره abs/1308.6339  شماره 

صفحات  -

تاریخ انتشار 2013