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### The Fast Johnson–Lindenstrauss Transform and Approximate

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

### Approximate Nearest Neighbors and the Fast - CS Technion

(p = 1, 2), called the Fast-Johnson-Lindenstrauss-. Transform. The FJLT is faster than standard random pro- jections and just as easy to implement. It is based upon the preconditioning of a sparse projection matrix with a randomized Fourier transform. Sparse random projections are unsuitable for low-distortion embeddings.