Oh, I thought you were stil referring to the toy example in this thread. Yes, k=10 is definitely larger than its rank. This is why I said Y'*Y is certainly not invertible in this case. I was responding to you showing that ALS still worked -- indeed it does but it never inverts / solves a system involving Y'*Y. It's later, in fold-in.
All that said I don't think inverting is the issue here. Using the SVD to invert didn't change things, and neither did actually solving the Ax=b problem instead of inverting A by using Householder reflections. On Sun, Apr 7, 2013 at 1:45 AM, Koobas <koo...@gmail.com> wrote: > Okay, you do have a problem. > Y'*Y is 10x10, but it's rank is 5. > Has to have something to do with the input data. > > > > On Sat, Apr 6, 2013 at 7:47 PM, Sean Owen <sro...@gmail.com> wrote: > >> For example, here's Y: >> >> Y = >> >> -0.278098 -0.256438 0.127559 -0.045869 -0.769172 -0.255599 >> 0.150450 -0.436548 0.209881 -0.526238 >> 0.613175 -0.600739 -0.291662 -1.142282 0.277204 -0.296846 >> -0.175122 0.031656 -0.202138 -0.254480 >> -0.187816 -0.889571 0.052191 -0.304053 0.498097 -0.049822 >> -0.972282 -0.240532 0.155711 -0.627668 >> -0.065179 -0.055424 0.977480 0.104342 0.594501 0.033205 >> -0.896222 -0.345715 -0.371288 -0.489602 >> -0.434807 -0.403650 0.264583 -0.110285 -1.318951 -0.452470 >> 0.274445 -0.755704 0.313150 -0.903234 >> >> and R from the QR decomposition of Y' * Y: >> >> R = >> >> 2.56259 -1.35164 -2.43837 1.27844 -0.17692 -0.30514 1.09366 >> -0.84664 0.58601 1.06875 >> 0.00000 1.03316 2.61600 -0.46070 -1.46785 -0.10841 0.24828 >> -2.32186 -2.00163 -0.71470 >> 0.00000 0.00000 2.11507 1.15523 1.10757 0.36407 -0.31567 >> 2.77361 0.77367 -0.84055 >> 0.00000 0.00000 0.00000 0.54242 -0.01545 0.21761 0.26630 >> 0.13972 0.44089 0.02783 >> 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00000 -0.00000 >> 0.00000 0.00000 -0.00000 >> 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 >> -0.00000 0.00000 0.00000 >> 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 >> 0.00000 0.00000 -0.00000 >> 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 >> 0.00000 0.00000 -0.00000 >> 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 >> 0.00000 0.00000 0.00000 >> 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 >> 0.00000 0.00000 0.00000 >> >> >> Separately I tried avoiding the inverse altogether here and just using >> the QR decomposition to solve a system where necessary. Probably a >> better move anyway. But same result. I think I'm not really >> quantifying the problem properly, but it's not really a matter of >> condition number or machine precision. Condition numbers are >1 in >> these cases but not that large. >> >> >> On Sun, Apr 7, 2013 at 12:19 AM, Koobas <koo...@gmail.com> wrote: >> > I don't see why the inverse of Y'*Y does not exist. >> > What Y do you end up with? >>
