I think I solved it. Including solution below if anyone is interested!
First we define a variable S_u below which is the cost function from Equation \eqref{eq:implicit-cost-function} but where we have fixed u so that we are calculating the predicted errors for one specific user...
Hi,
I'm trying to derive a result from this paper:
http://www.research.yahoo.net/files/HuKorenVolinsky-ICDM08.pdf
given cost function
\min_{x_* , y_* } \sum_{u, i} c_{ui} (p_{ui} - x^T_u y_i)^2 + \lambda \left( \sum_u ||x_u||^2 + \sum_i ||y_||^2 \right)
Where both xu and yi...