, U P fixed, the update of U p amounts to the following optimization problem: Algorithm 1 Optimization framework Input: iK ) T be the column vectors whose entries are those of the i th row of D p and U p respectively.
the optimization of equation 5can be decomposed into M p optimization problems that can be solved independently, with each corresponding to one row of U p : Equation 6is a standard least squares problems in statistics and the solution is: Algorithm 2 shows the procedure.