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From Sean Owen <sro...@gmail.com>
Subject Re: Using SVD-conditioned matrix
Date Mon, 17 Sep 2012 07:30:53 GMT
On Mon, Sep 17, 2012 at 12:11 AM, Ted Dunning <ted.dunning@gmail.com> wrote:

>   A_k = U_k U_k' A_k

> Forgetting S_k is a bit dangerous here.  It is true that
>
>     U_k S_k = A_k V_k
>
> But, of course, right multiplying by V_k' gives us the identity above.
>
> I think that the real confusion is that I am talking about projecting back
> into span A and you are talking about expressing things in terms of the
> latent variables.

Right, this goes all the way to "making recommendations", back to Ak.
I think Lance was asking about how to find the new row in latent
feature space, a row in Uk.

You can't ignore Sk, yes, just trying to get to the essence. Putting
it back in (half-and-half) does get what I posted which indeed is the
project I think that was in question..

Uk * sqrt(Sk) = Ak * Vk * 1/sqrt(Sk)

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