Algorithm 1.

Algorithm for TMF model

Input:	temporal adjacency matrices ${\{A(t)\}}_{t=1}^T$ the order d of V(t) and latent dimension k.
Output:	results of factor matrices U and ${\{{\mathit{W}}^{(i)}\}}_{i=1}^d$ and the predict adjacency matrix A(T + 1).
1.	Set k and d.
2.	Randomly initialize U and ${\{{\mathit{W}}^{(i)}\}}_{i=1}^d$.
3.	while not stopping criterion do
4.	Compute “decayed error term” ξ(t) for each time stamp t.
5.	Compute partial derivatives $\frac{\partial J\left(\mathit{U},\mathit{W}\right)}{\partial \mathit{U}}$ and $\frac{\partial J\left(\mathit{U},\mathit{W}\right)}{\partial {\mathit{W}}^{(i)}}$ using ξ(t) by Eq.(15) and Eq.(16).
6.	Determine the step size λ by line search.
7.	Update $\mathit{U}=\mathit{U}-\lambda \frac{\partial J\left(\mathit{U},\mathit{W}\right)}{\partial \mathit{U}}$
8.	for i = 1,…,d do
9.	Update ${\mathit{W}}^{(i)}={\mathit{W}}^{(i)}-\lambda \frac{\partial J\left(\mathit{U},\mathit{W}\right)}{\partial {\mathit{W}}^{(i)}}$
10.	end
11.	end
12.	Compute predict adjacency matrix $A\left(T+1\right)=\mathit{UV}{\left(T+1\right)}^T=\mathit{U}{({\displaystyle {\sum }_{i=0}^d{\mathit{W}}^{(i)}}{(T+1)}^i)}^T$