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Table 9 The GraRep overall algorithm

From: NEMPD: a network embedding-based method for predicting miRNA-disease associations by preserving behavior and attribute information

GraRep Algorithm
Input
Adjacency matrix S on graph
Maximum transition step K
Log shifted factor β
Dimension of representation vector d
1. Get k-step transition probability matrix Ak
Compute A = D−1S
Calculate A−1, A−2,  A−3, …,  Ak, respectively
2. Get each k-step representations
For k = 1 to K
 2.1 Get positive log probability matrix
 calculate \( {\Gamma}_1^k,{\Gamma}_2^k,{\Gamma}_3^k,\dots, {\Gamma}_N^k \) (\( {\Gamma}_i^k={\sum}_p{A}_{p,j}^k \)) respectively
 calculate \( \left\{{X}_{i,j}^k\right\} \)
  \( {X}_{i,j}^k \) = log (\( \frac{A_{i,j}^k}{\Gamma_j^k} \)) – log(β)
 assign negative entries of Xk to 0
 2.2 Construct the representation vector Wk
 SVD(Xk) = [Uk, ∑k, (Vk)T]
\( {W}^k={U}_d^k\ {\left({\sum}_d^k\right)}^{\frac{1}{2}} \)
End for
3. Concatenate all the k-step representations
W = [W1, W2, W3, …Wk]
Output
Matrix of the graph representation W