I want to implement Constrained PMF(mentioned in section 4 of paper), I have difficulty in calculating $\frac{\partial{E}}{\partial{W_k}}$ $$ E = \frac{1}{2} \sum_{i = 1}^{N} \sum_{j = 1}^{M} I_{i,j} (R_{i,j} - g([Y_i + \frac{\sum_{k=1}^{M}I_{i,k}W_k}{\sum_{k = 1}^{M} I_{i,k}}]^TV_j)) ^ 2 + \frac{\lambda}{2}(\sum_{i = 1}^{N}||Y_i||^2 + \sum_{j = 1}^{M}||V_j||^2 + \sum_{k = 1}^{M}\lvert \lvert W_k\rvert\rvert^2 ) $$
I have come up with these terms for $Y_i$ and $V_j$
$$ \frac{\partial{E}}{\partial{Y_i}} = \sum_{j = 1}^{M} I_{i,j} g'([Y_i + \frac{\sum_{k=1}^{M}I_{i,k}W_k)}{\sum_{k = 1}^{M} I_{i,k}}]^TV_j) (R_{i,j} - g([Y_i + \frac{\sum_{k=1}^{M}I_{i,k}W_k)}{\sum_{k = 1}^{M} I_{i,k}}]^TV_j)) V_j + \lambda Y_i $$
$$ \frac{\partial{E}}{\partial{V_j}} = \sum_{i=1}^{B}I_{i,j}g'([Y_i + \frac{\sum_{k=1}^{M}I_{i,k}W_k)}{\sum_{k = 1}^{M} I_{i,k}}]^TV_j) (R_{i,j} - g([Y_i + \frac{\sum_{k=1}^{M}I_{i,k}W_k)}{\sum_{k = 1}^{M} I_{i,k}}]^TV_j)) (Y_i + \frac{\sum_{k=1}^{M}I_{i,k}W_k}{\sum_{k = 1}^{M} I_{i,k}}) + \lambda V_j $$
How should I calculate $\frac{\partial{E}}{\partial{W_k}}$?