QR decomposition in ALS-WR code

[Dominik Hübner <co...@dhuebner.com>]

I was recently having a look at the ALS-WR factorisation code. Why is there a QR decomposition before computing u_i or m_j instead of multiplying the inverse of A_i with V_i straightaway? (reference to these two classes https://github.com/apache/mahout/blob/trunk/math/src/main/java/org/apache/mahout/math/als/AlternatingLeastSquaresSolver.java and https://github.com/apache/mahout/blob/trunk/math/src/main/java/org/apache/mahout/math/QRDecomposition.java). I'm pretty sure that I am missing something … so any help is appreciated.

Re: QR decomposition in ALS-WR code

[Sebastian Schelter <ss...@apache.org>]

Computing an inverse is more costly than solving a linear system via QR
decompostion.

On 15.03.2013 11:41, Dominik Hübner wrote:
> I was recently having a look at the ALS-WR factorisation code. Why is there a QR decomposition before computing u_i or m_j instead of multiplying the inverse of A_i with V_i straightaway? (reference to these two classes https://github.com/apache/mahout/blob/trunk/math/src/main/java/org/apache/mahout/math/als/AlternatingLeastSquaresSolver.java and https://github.com/apache/mahout/blob/trunk/math/src/main/java/org/apache/mahout/math/QRDecomposition.java). I'm pretty sure that I am missing something … so any help is appreciated.
> 

Re: QR decomposition in ALS-WR code

[Sean Owen <sr...@gmail.com>]

I think you are referring to the same step? QR decomposition is how you
solve for u_i which is what I imagine the same step you have in mind.