Algorithm 5. Calculating low rank matrix using LRMF method.

input: $X=[x_1,x_2,\dots ,x_n]$

$initilization:x_i\circ {\tau }_i^1=x_i,randominitilization{V}^1,{\mathrm{\Sigma }}^1,{\mathrm{\Pi }}^1$

repeat:

step 1: estimate U, V

use Algorithm 1 to estimate $U^{k+1},V^{k+1},{\mathrm{\Sigma }}^{k+1},{\mathrm{\Pi }}^{k+1}$ based on $U^k,V^k,{\mathrm{\Sigma }}^k,{\mathrm{\Pi }}^k,x_i\circ {\tau }_i^k$

step 2: estimate $\tau$

use Algorithm 3 to estimate $x_i\circ {\tau }_i^{k+1}$ $basedon{U}^{k+1},V^{k+1}$

until meet the stop criteria

$return{R}^{\ast }=U^{k+1}{V^{k+1}}^T$