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### 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

### Lecture 8: Fast Random Projections and FJLT 8 Fast Rando

Today, we will discuss a particular form of random projections known as structured random pro- jections or the FJLT that are “fast” in that one can use fast Fourier methods to apply them quickly to arbitrary or worst case input. We will be able to use this to speed up both random projection as well as random sampling

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