Algorithm 3:

Estimating $B,U$, and $V$

Input:	$R$
1.	Initialize ${\Theta }_0$, $U_0$ , and $B_0$.
2.	For $j=1$ to $n\_\mathit{\text{iteration}}$:
3.	Estimate $W_j$ as its columns are the first $K$ leading eigenvectors of $R-{\Theta }_j$ and $V_j$ as a diagonal matrix which its diagonal elements are the first K leading eigenvalues of $R-{\Theta }_j$.
4.	for $i=1\mathit{\text{to}}K$:
	Compute the nonzero elements of $B_{j_{:i}}^{*}$ as $B_{j_{ki}}^{*}=U_{j_{:i}}*R_{j_{k:}}^{*}$.
	End for
5.	Compute $S=B_j^T{W}_j$.
6.	Compute singular value decomposition of $S=D\Sigma F^T$.
7.	Update $U_j$ as $U_j=D{F}^T$.
8.	Update ${\Theta }_j$ as $\mathit{\text{diag}}\left({\Theta }_j\right)=\mathit{\text{diag}}\left(R-B_j{U}_j{V}_j{\left(B_j{U}_j\right)}^T\right)$.
9.	End for.
Output:	Optimal $B,U,V$.