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### Fast Johnson-Lindenstrauss - Learning With Erro

May 19, 2016 The Johnson-Lindenstrauss (JL) Transform says that, informally, we can embed high-dimensional points into a much lower dimension, while still preserving their pairwise distances. In this post we will start with the classical JL transform, then focus on the Fast JL Transform (FJLT) by Ailon and Chazelle

### The Fast Johnson–Lindenstrauss Transform and Approximat

We introduce a new low-distortion embedding of $\ell_2^d$ into $\ell_p^{O(\log n)}$ ($p=1,2$) called the fast Johnson–Lindenstrauss transform (FJLT). The FJLT is faster than standard random projections and just as easy to implement. It is based upon the preconditioning of a sparse projection matrix with a randomized