Random projection

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Random projection

RosieFleming
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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Re: Random projection

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...

On December 4, 2018 2:06:43 PM PST, rosie fleming <[hidden email]> wrote:

>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!
>______________________________________________
>[hidden email] mailing list -- To UNSUBSCRIBE and more, see
>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.

--
Sent from my phone. Please excuse my brevity.

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[hidden email] mailing list -- To UNSUBSCRIBE and more, see
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Re: Random projection

Jan Galkowski-2
In reply to this post by RosieFleming
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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______________________________________________
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