Derivation of gradient for non negative matrix factorization I am looking at a paper for non-negative matrix factorization and can't seem to figure out the derivation for the gradient. The function is as follows:
$f(W,H) = \frac{1}{2}||V-WH ||^2_F$ 
Where V is fixed.
The resulting gradients are:
$\nabla_W f(W,H) = (WH-V)H^T $
$\nabla_H f(W,H) = W^T(WH-V) $
I tried looking up rules in various reference manuals but never got anything solid. Even a hint / solid resource would be incredibly helpful.

I find it's often easiest to compute matrix-derivatives in these terms, then translate to whatever the desired means of expressing the derivative is.  That is, I prefer to think of $\nabla_W f$ as a map from $\Bbb R^{m \times n}$ to the set of linear functionals on $\Bbb R^{m \times n}$.
We find that
$$
\DeclareMathOperator{\tr}{tr}
f(W + \delta W, H) = 
\frac 12 \tr[(V - (W + \delta W)H)(V - (W + \delta W)H)^T] =\\
\frac 12 \tr[[(V - WH)- \delta WH][(V - WH) - \delta WH]^T] =\\
f(W,H) + \tr[(WH - V)(\delta W H)^T] + o(\|\delta W\|) =\\
f(W,H) + \tr[[(WH - V)H^T](\delta W)^T] + o(\|\delta W\|)
$$
Thus, I would say that 
$$
[D_W f(W,H)](\delta W) = \tr[[(WH - V)H^T]^T(\delta W)]
$$
Translating this to your matrix calculus in which $\nabla_W$ should be a matrix, we find that
$$
\nabla _W f(W,H) = (WH - V)H^T
$$
as desired.
