Hi Sebastian, Yes Mahout ALS and Oryx runs fine on the same matrix because Sean calls QR decomposition.
But the ALS objective should give us strictly positive definite matrix..I am thinking more on it.. There are some random factor assignment step but that also initializes factors with normal(0,1)...which I think is not a big deal... About QR decomposition, jblas has Solve.solve and Solve.solvePositive...solve should also run fine but it does a LU factorization and better way will be to do a QR decomposition. Seems breeze has QR decomposition and we can make use of that...But QR by default is also not correct since if the matrix is positive definite BLAS psov (Solve.solvePositive) is much faster due to cholesky computation.. I believe we need a singular value check and based on that we should call solvePositive/solve or qr from breeze.. There is also a specialized version of TSQR (tall and skinny QR decomposition) from Chris which might be good to evaluate as well: https://github.com/ccsevers/scalding-linalg I am going to debug it further and try to understand why I am getting non positive definite matrix and publish the findings... Any suggestions on how to proceed further on this ? Should I ask for a PR and we can discuss more on it ? Thanks. Deb On Thu, Mar 6, 2014 at 6:47 AM, Sebastian Schelter <s...@apache.org> wrote: > I'm not sure about the mathematical details, but I found in some > experiments with Mahout that the matrix there was also not positive > definite. Therefore, we chose QR decomposition to solve the linear system. > > > --sebastian > > > On 03/06/2014 03:44 PM, Debasish Das wrote: > >> Hi, >> >> I am running ALS on a sparse problem (10M x 1M) and I am getting the >> following error: >> >> org.jblas.exceptions.LapackArgumentException: LAPACK DPOSV: Leading minor >> of order i of A is not positive definite. >> at org.jblas.SimpleBlas.posv(SimpleBlas.java:373) >> at org.jblas.Solve.solvePositive(Solve.java:68) >> >> This error from blas shows up if the hessian matrix is not positive >> definite... >> >> I checked that rating matrix is all > 0 but of course like netflix they >> are >> not bounded within 1 and 5.... >> >> Is there some sort of specific initialization of factor matrices done >> which >> can make the hessian matrix non positive definite ? >> >> I am printing out the eigen vectors and fullXtX matrix to understand it >> more but any help will be appreciated. >> >> Thanks. >> Deb >> >> >
