Hi Greg,
currently, I still can not get the answer about this questions.
In fact, if someone can get the ##\frac{\partial f}{\partial W_i}##, wher ##W_i## is the ##i##th row of W, it is also OK.
Here is the original paper: "Collaborative matrix factorization with multiple similarities for...
C \in \mathbb{R}^{m \times n}, X \in \mathbb{R}^{m \times n}, W \in \mathbb{R}^{m \times k}, H \in \mathbb{R}^{n \times k}, S \in \mathbb{R}^{m \times m}, P \in \mathbb{R}^{n \times n}
##{S}## and ##{P}## are similarity matrices (symmetric).
##\lambda##, ##\alpha## and ##\beta## are...