[R] Random projection

[rosie fleming]

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!
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[Jeff Newmiller]

Your multiplication description sounds more like matrix multiplication than scalar multiplication. R supports matrix multiplication with the %*% operator.

I didn't follow the rest of your description... are you doing a homework assignment? There is a no homework policy on this list...

Post by rosie fleming
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)
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!
______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Jan Galkowski]

Ms Fleming,

This blog post (of mine) may be of interest and hopefully of help:

https://667-per-cm.net/2018/11/20/the-johnson-lindenstrauss-lemma-and-the-paradoxical-power-of-random-linear-operators-part-1/
Cheers!

--
Jan Galkowski (o°)
Westwood, MA

(pronouns: *he, him, his*)

*Keep your energy local*. --John Farrell, *ILSR[1]*



Links:

1. http://ilsr.org

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