Great. On Tue, Jan 8, 2013 at 4:25 PM, Koobas <[email protected]> wrote:
> On Tue, Jan 8, 2013 at 7:18 PM, Ted Dunning <[email protected]> wrote: > > > But is it actually QR of Y? > > > > > Ted, > This is my understanding: > In the process of solving the least squares problem, > you end up inverting a small square matrix (Y' * Y)-1. > How it is done is irrelevant. > Since the matrix is square, one could do LU factorization, a.k.a. Gaussian > elimination. > However, since we are talking here about solving an 100x100 problem, > one might as well do it with QR factorization which, unlike LU, is stable > "no matter what". > > > > > On Tue, Jan 8, 2013 at 3:41 PM, Sean Owen <[email protected]> wrote: > > > > > There's definitely a QR decomposition in there for me since solving A > > > = X Y' for X is X = A Y (Y' * Y)^-1 and you need some means to > > > compute the inverse of that (small) matrix. > > > > > > On Tue, Jan 8, 2013 at 5:27 PM, Ted Dunning <[email protected]> > > wrote: > > > > This particular part of the algorithm can be seen as similar to a > least > > > > squares problem that might normally be solved by QR. I don't think > > that > > > > the updates are quite the same, however. > > > > > > > > On Tue, Jan 8, 2013 at 3:10 PM, Sebastian Schelter <[email protected]> > > > wrote: > > > > > > > >> This factorization is iteratively refined. In each iteration, ALS > > first > > > >> fixes the item-feature vectors and solves a least-squares problem > for > > > >> each user and then fixes the user-feature vectors and solves a > > > >> least-squares problem for each item. > > > >> > > > > > >
