Q:

Matrix Factorization In Matlab using Stochastic Gradient Descent

I have to factorize Matrix R[mn] to two low-rank Matrices (U[Km] and V[K*n]), I do this for predicting missing values of R by U and V.
 
The problem is, for factorizing R I can't use Matlab factorization methods, so I have to work on objective function which minimizes the sum-of-squared-errors for enhancing factorization accuracy:

details are shown below:  
 

My Question in this post is how to minimize function F in Matlab Using Stochastic Gradient Descent method to decompose R into U and V matrices.
Thanks for any help!

A:

Finally I figured out with help of this page :)
I explain the approach in some steps:

Create U[k*m] and V[k*n] and fill them arbitrarily
Compute derivatives for objective function on Ui and Vj
Do gradient descent as follows:
while (your criteria satisfies(optimizing error function F))
{
   Ui=Ui+a(U'i);
   Vj=Vj+a(V'j);
   Evaluate F using new values of Ui and Vj;
}
With the minimum F , take U and V, compute transpose(U)*V and the
result is estimated R (a is step size or learning rate)

