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Date: Wed, 4 Sep 2013 15:29:56 -0400
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Subject: Re: ALS and SVD feature vectors
From: Koobas <koobas@gmail.com>
To: user@mahout.apache.org
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On Wed, Sep 4, 2013 at 3:06 PM, Sean Owen <srowen@gmail.com> wrote:

> The feature vectors? rows of X and Y? no, they definitely should not be
> normalized. It will change the approximation you so carefully built quite a
> lot.
>
> As you say U and V are orthornormal in the SVD. But you still multiply all
> of them together with Sigma when making recs. (Or you embed Sigma in U and
> V.)  So yes the singular values are used; they give proper weights to
> features.
>
> You can think of X and Y as being like that, with Sigma mixed in in some
> arbitrary way. Normalizing it would not be valid.
>
> Excellent!
Straight to the point.
That's the answer I was looking for.
Also, thanks to Ted. He pretty much said the same thing.

>
> On Wed, Sep 4, 2013 at 6:07 PM, Koobas <koobas@gmail.com> wrote:
>
> > In ALS the coincidence matrix is approximated by XY',
> > where X is user-feature, Y is item-feature.
> > Now, here is the question:
> > are/should the feature vectors be normalized before computing
> > recommendations?
> >
> > Now, what happens in the case of SVD?
> > The vectors are normal by definition.
> > Are singular values used at all, or just left and right singular vectors?
> >
>

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