Algorithm 1 ASNMF-SRP

Input: Initial matrix $\mathit{X}=\left({\mathit{x}}_1,{\mathit{x}}_2,\cdots ,{\mathit{x}}_n\right)\in {ℝ}_{+}^{m\times n}$, number of classes $r$, neighborhood parameter $k$, regularization parameters $\alpha$, $\beta$ and $\lambda$, balance parameters $w_1$ and $w_2$ parameter $d$, threshold $\epsilon$, maximum iterations $t$. Output: Basis matrix $\mathit{U}$ and coefficient matrix $\mathit{V}$. 1. Initialization: $t=0$, Randomly generate basis matrix $\mathit{U}\in {ℝ}^{\mathrm{m}\times r}$ and coefficient matrix $\mathit{V}\in {ℝ}^{r\times n}$; 2. Obtain optimal Laplacian matrix $\mathit{L}$ according to Equations (11)–(17); 3. For $t=1,2,3,\cdots ,\mathrm{maxIter}$ 4. ${\mathit{U}}_{ij}^{t+1}\leftarrow {\mathit{U}}_{ij}^t\sqrt{{\displaystyle \frac{{\left(2{\mathit{X}\mathit{V}}^T+\beta {\mathit{X}\mathit{X}}^T{\mathit{G}}_2\mathit{U}+\beta {\mathit{G}}_2{\mathit{X}\mathit{X}}^T\mathit{U}\right)}_{ij}}{{\left({\mathit{U}\mathit{V}\mathit{V}}^T+{\mathit{X}\mathit{X}}^T\mathit{U}+{\beta }^2{\mathit{U}\mathit{U}}^T{\mathit{G}}_2\mathit{U}+{\beta }^2{\mathit{G}}_2{\mathit{U}\mathit{U}}^T\mathit{U}\right)}_{ij}}}}$; 5. ${\mathit{V}}_{ij}^{t+1}\leftarrow {\mathit{V}}_{ij}^t\sqrt{{\displaystyle \frac{{\left(2{\mathit{U}}^T\mathit{X}+\alpha \mathit{V}{\mathit{L}}^{-}+\lambda \mathit{V}\right)}_{ij}}{{\left({\mathit{U}}^T\mathit{U}\mathit{V}+\mathit{V}+\alpha \mathit{V}{\mathit{L}}^{+}+\lambda \mathit{V}{\mathbf{1}}_n\right)}_{ij}}}}$; 6. if ${‖{\mathit{U}}^t-{\mathit{U}}^{t-1}‖}_{\infty }\le \epsilon$ and ${‖{\mathit{V}}^t-{\mathit{V}}^{t-1}‖}_{\infty }\le \epsilon$ Break and return ($\mathit{U}$,$\mathit{V}$); 7. End if 8. End for