[scikit-learn] Does NMF optimise over observed values

[Andy]

On 08/28/2016 12:29 PM, Raphael C wrote:
> To give a little context from the web, see e.g. 
> http://www.quuxlabs.com/blog/2010/09/matrix-factorization-a-simple-tutorial-and-implementation-in-python/ where 
> it explains:
>
> "
> A question might have come to your mind by now: if we find two 
> matrices \mathbf{P} and \mathbf{Q} such that \mathbf{P} \times 
> \mathbf{Q} approximates \mathbf{R}, isn’t that our predictions of all 
> the unseen ratings will all be zeros? In fact, we are not really 
> trying to come up with \mathbf{P} and \mathbf{Q} such that we can 
> reproduce \mathbf{R} exactly. Instead, we will only try to minimise 
> the errors of the observed user-item pairs.
> "
Yes, the sklearn interface is not meant for matrix completion but 
matrix-factorization.
There was a PR for some matrix completion for missing value imputation 
at some point.

In general, scikit-learn doesn't really implement anything for 
recommendation algorithms as that requires a different interface.
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