[R] Random projection

rosie fleming ro@iefleming @ending from hotm@il@co@uk
Tue Dec 4 23:06:43 CET 2018

```Hello I was wondering if anyone could help. I am using R to perform random projection on Gaussians.
I need to take k Gaussian random vectors U1,...,Uk in R(reals)
Then for any vector v in d dimensions, perform the random projection:
f(v) = v.U1, v.U2, ..., v.Uk which reduces v from d dimensions to k dimensions
So i need v1,...vn so n vectors

and then the basic idea is that the relative orders will be preserved between the vectors v after projection ie the nearet neighbours for each vectors will be the same before projection (v1,v2,...,vn) and after projection f(v1),...f(vk)

I'm struggling to produce this in R. I've managed to make a matrix for U and V
However I now need to use the scalar product to perform the projection, taking each row of v (vi) and multiplying it with every column of the U matrix. I need to perform this for n vectors and have a matrix as the outcome.

This would then allow me to find the distances between each f(vi)!

Any help would be greatly appreciated, thankyou!
```