Algorithm 5 ONMFTV-SPRING

1:Input$X\in {\mathbb{R}}_{\ge 0}^{M\times N},K\in \mathbb{N},{\sigma }_1,{\sigma }_2,\tau >0,s_r\in \mathbb{N},i=0$ 2:Initialize$U^{[0,1]},W^{[0,1]}\in {\mathbb{R}}_{\ge 0}^{M\times K},V^{[0,1]}\in {\mathbb{R}}_{\ge 0}^{K\times N}$ 3:repeat 4:for$j=1,\cdots ,s_r$do 5:${\displaystyle {\eta }_{U^{[i,j]}}=P_{\mathrm{OWER}}{I}_{T_U}(V^{[i,j]},W^{[i,j]})}$ 6:${\displaystyle U^{[i,j+1]}={\left. [{prox}_{\tau {\eta }_{U^{[i,j]}}\mathcal{J}}\left(U^{[i,j]}-{\eta }_{U^{[i,j]}}{\tilde{\nabla }}_U^{i,j}\mathcal{F}(U^{[i,j]},V^{[i,j]},W^{[i,j]})\right)\right]}_{\ge 0}}$ 7:${\displaystyle {\eta }_{V^{[i,j]}}=P_{\mathrm{OWER}}{I}_{T_V}\left(U^{[i,j+1]}\right)}$ 8:${\displaystyle V^{[i,j+1]}={\left. [V^{[i,j]}-{\eta }_{V^{[i,j]}}{\tilde{\nabla }}_V^{i,j}\mathcal{F}(U^{[i,j+1]},V^{[i.j]},W^{[i,j]})\right]}_{\ge 0}}$ 9:${\displaystyle {\eta }_{W^{[i,j]}}=P_{\mathrm{OWER}}{I}_{T_W}\left(U^{[i,j+1]}\right)}$ 10:${\displaystyle W^{[i,j+1]}={\left. [W^{[i,j]}-{\eta }_{W^{[i,j]}}{\nabla }_W\mathcal{F}(U^{[i,j+1]},V^{[i,j+1]},W^{[i,j]})\right]}_{\ge 0}}$ 11:end for 12:${\displaystyle U^{[i+1,1]}=U^{[i,s_r+1]},V^{[i+1,1]}=V^{[i,s_r+1]},W^{[i+1,1]}=W^{[i,s_r+1]}}$ 13:${\displaystyle i\leftarrow i+1}$ 14:untilStopping criterion satisfied