Algorithm 1: GLNMDA

Input: Matrices $M\in {\mathbb{R}}^{m\ast m}$,$D\in {\mathbb{R}}^{\mathrm{n}\ast n}$,$R\in {\mathbb{R}}^{m\ast n}$, parameter α and β.

Output: Predicted association matrix F.

1. Obtain the k value for miRNAs and diseases by ClusterONE algorithm.

2. Repeat:

Update $\tilde{U}$and$\hat{U}$by the following rules:

${\tilde{U}}_{ij}\leftarrow {\tilde{U}}_{ij}\times \sqrt{\frac{{(2R^{T}R\tilde{U})}_{ij}}{{(\tilde{U}{\tilde{U}}^T{R}^{T}R\tilde{U}+R^{T}R\tilde{U}{\tilde{U}}^T\tilde{U})}_{ij}}}$

${\hat{U}}_{ij}\leftarrow {\hat{U}}_{ij}\times \sqrt{\frac{{(2R{R}^T\hat{U})}_{ij}}{{(\hat{U}{\hat{U}}^{T}R{R}^T\hat{U}+R{R}^T\hat{U}{\hat{U}}^T\hat{U})}_{ij}}}$

Until convergence

3. Obtain the reconstructed similarity matrix $\tilde{M}$and $\tilde{D}$:

$\tilde{M}={\tilde{M}}_P^{-1/2}(\tilde{U}{\tilde{U}}^T){\tilde{M}}_P^{-1/2}$

$\tilde{D}={\hat{D}}_P^{-1/2}(\hat{U}{\hat{U}}^T){\hat{D}}_P^{-1/2}$4. Integrate similarity information to get SD and SM according to Equation (12) and Equation (13).

5. Predict from miRNA space and disease space:

Repeat:

$F{D}^{t+1}=\alpha \times SD\times F{D}^t+(1-\alpha )\times R$

$F{M}^{t+1}=\alpha \times SM\times F{M}^t+(1-\alpha )\times R^T$

Until convergence

6. Integrate the results

$F=\beta (FD)+(1-\beta )\times (FM{)}^T$

7. Return F