Algorithm.

for solving the DSL optimization in (7)

Input: ${\left\{{\mathbf{x}}_i^{\left(1\right)}\right\}}_{i=1,\dots ,N_1}$ and ${\left\{{\mathbf{x}}_j^{\left(2\right)}\right\}}_{j=1,\dots ,N_2}$; stopping criteria, ${\mathrm{ϵ}}_{\mathrm{A}\mathrm{O}}$, ${\mathrm{ϵ}}_{EM}$; tuning parameters.
Output: solutions for ${\mathbf{\Theta }}^{\left(1\right)},{\mathbf{\Theta }}^{\left(2\right)},\mathit{ }\mathit{C}$.
1.	Compute covariance matrices ${\left\{{\mathbf{S}}_i^{\left(1\right)}\right\}}_{i=1,\dots ,N_1}$ and ${\left\{{\mathbf{S}}_j^{\left(2\right)}\right\}}_{j=1,\dots ,N_2}$
2.	Initialize: ${{ }^0\mathbf{\Theta }}^{\left(1\right)};{{ }^0\mathbf{\Theta }}^{\left(2\right)};m\leftarrow 0\mathrm{ };$
3.	Repeat
4.	Compute ${ }^m\mathit{C}$ by solving the quadratic programming in (11);
5.	Compute ${{ }^{m+1}\mathbf{\Theta }}^{\left(1\right)}$ using the proposed EM algorithm:
5.1	Input ${\left\{{\mathit{S}}_i^{\left(1\right)}\right\}}_{i=1,\dots ,N_1}$, ${ }^m\mathit{C},\mathit{ }{{ }^m\mathbf{\Theta }}^{\left(1\right)}$ and ${{ }^m\mathbf{\Theta }}^{\left(2\right)}$
5.2	Initialize ${ }^{\left(0\right)}\mathbf{\Theta }={{ }^m\mathbf{\Theta }}^{\left(1\right)};t\leftarrow 0$;
5.3	Repeat
5.4	E step: derive $Q\left(\mathbf{\Theta }\right|{ }^{\left(\mathrm{t}\right)}\mathbf{\Theta })$ using Proposition 2;
5.5	M step: compute ${ }^{\left(t+1\right)}\mathbf{\Theta }$ using BCD;
5.6	$t\leftarrow t+1$
5.7	Until $\left|\left|{ }^{\left(t\right)}\mathbf{\Theta }-{ }^{\left(t+1\right)}\mathbf{\Theta }\right|\right|\le {\mathrm{ϵ}}_{EM}$
5.8	${{ }^{m+1}\mathbf{\Theta }}^{\left(1\right)}\leftarrow { }^{\left(t+1\right)}\mathbf{\Theta }$;
6.	Compute ${{ }^{(m+1)}\mathbf{\Theta }}^{\left(2\right)}$ by following similar steps under 5;
7.	$m\leftarrow m+1$;
8.	until ${\sum }_{v=1}^2\left|\left|{{ }^{m+1}\mathbf{\Theta }}^{\left(v\right)}-{{ }^m\mathbf{\Theta }}^{\left(v\right)}\right|\right|\le {\mathrm{ϵ}}_{\mathrm{A}\mathrm{O}}$