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 <[email protected]> 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? > > > >
