Algorithm 2.

MxNE with BCD and active set strategy

Require:	M, G, λ> 0, ε> 0, and S.
1:	Initialization: X = 0, $\mathcal{A}=\left\{\right\}$, η = ℱp (X) − ℱd (Y)
2:	for s = 1 to S do
3:	$\mathit{\mu }[s]=\Vert {\mathbf{G}}_s^T{\mathbf{G}}_s{\Vert }^{-1}$
4:	end for
5:	while η ≥ ε do
6:	$\mathcal{A}\ast \subseteq \{s|\Vert {\mathbf{G}}_s^T(\mathbf{M}-\mathbf{G}\mathbf{X}){\Vert }_{\text{Fro}}>\lambda \}$
7:	$\mathcal{A}=\mathcal{A}\cup \mathcal{A}\ast$
8:	Define ${\mathbf{G}}^{\mathcal{A}}$ and ${\mathbf{X}}^{\mathcal{A}}$ by restricting G and X to $\mathcal{A}$
9:	${\widehat{\mathbf{X}}}^{\mathcal{A}}\leftarrow$ Solve Algorithm 1 with μ, ${\mathbf{G}}^{\mathcal{A}}$ and ${\mathbf{X}}_0={\mathbf{X}}^{\mathcal{A}}$
10:	$\mathbf{X}={\widehat{\mathbf{X}}}^{\mathcal{A}}$ for $s\in \mathcal{A}$, else 0
11:	η = ℱp (X) − ℱd (Y)
12:	end while