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From Koobas <koo...@gmail.com>
Subject Re: alternating least squares
Date Tue, 08 Jan 2013 22:55:34 GMT
I am trying to wrap my head around it.
>From the Mahout documentation it looks like it's a standard (dense) QR with
Householder reflectors.
But the user-item matrix is usually extremely sparse.
So, is the sparsity somehow taken into account,
or are the sparse right-hand-side vectors packed in dense storage and hit
with Householder?
The underlying question being the computational complexity, i.e. number of
floating point operations involved.


On Tue, Jan 8, 2013 at 4:03 PM, Sebastian Schelter <ssc@apache.org> wrote:

> Hi Koobas,
>
> We have two classes that implement the solutions described in the
> ALS-related papers:
>
> For explicit feedback data [1] we have AlternatingLeastSquaresSolver,
> for implicit feedback data [2] we have
> ImplicitFeedback-AlternatingLeastSquaresSolver. Both can be found in the
> org.apache.mahout.math.als package.
>
> Internally the use Mahout's QRDecomposition to solve the linear systems
> associated with ALS.
>
> Best,
> Sebastian
>
> [1]
>
> http://www.hpl.hp.com/personal/Robert_Schreiber/papers/2008%20AAIM%20Netflix/netflix_aaim08(submitted).pdf
> [2] http://research.yahoo.com/pub/2433
>
>
> On 08.01.2013 21:53, Koobas wrote:
> > Perhaps somebody can shed some light on the topic.
> > What algorithm is used to solve the least squares problem
> > when computing low-rank approximation using Alternating Least Squares?
> >
>
>

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