Algorithm 2 ANNMC Algorithm

Input:$\tilde{\mu },{\alpha }_{-1}=0.5,{\mathbf{Y}}_{-1}={\mathbf{Y}}_0,L_{-1}=L_0,{\gamma }_0\ge \tilde{\mu },{\lambda }_0=1,\vartheta ,{\epsilon }_{\tilde{i}}>0$; Output:${\mathbf{Y}}_{t_{max}}$, $rank\left({\mathbf{Y}}_{t_{max}}\right)$;   1:for$t=1,2,\dots ,t_{max}$do   2:   solve subproblem (8) by Algorithm 1;   3:end for   4:if the (k,j)-th component of ${\mathbf{Y}}_{t_{max}}$ satisfies       $\left(p_{a_{i-1}}{a}_{i-1}+p_{a_i}{a}_i\right)/\phantom{\left(p_{a_{i-1}}{a}_{i-1}+p_{a_i}{a}_i\right)\left(p_{a_{i-1}}+p_{a_i}\right)}\left(p_{a_{i-1}}+p_{a_i}\right)\le {\left({\mathbf{Y}}_{t_{max}}\right)}_{j,k}<\left(p_{a_i}{a}_i+p_{a_{i+1}}{a}_{i+1}\right)/\phantom{\left(p_{a_i}{a}_i+p_{a_{i+1}}{a}_{i+1}\right)\left(p_{a_i}+p_{a_{i+1}}\right)}\left(p_{a_i}+p_{a_{i+1}}\right)$,    $\mathrm{where}{p}_{a_i}=N_{\mathsf{\Omega }}\left(a_i\right)/\phantom{N_{\mathsf{\Omega }}\left(a_i\right)N_{\mathsf{\Omega }}}{N}_{\mathsf{\Omega }}$ and $i=2,\dots ,I$;   5:   then   6:      ${\left({\mathbf{Y}}_{t_{max}}\right)}_{j,k}=a_i$;   7:else   8:      ${\left({\mathbf{Y}}_{t_{max}}\right)}_{j,k}=0$;   9:end if 10:return${\mathbf{Y}}_{t_{max}}$, $rank\left({\mathbf{Y}}_{t_{max}}\right)$;