Algorithm 1 IVA-S3

Require: datasets $\mathbf{X}$ = $[{\left({\mathbf{X}}^{\left[1\right]}\right)}^{\top }$, …, ${\left({\mathbf{X}}^{\left[K\right]}\right)}^{\top }{]}^{\top }$$\in {\mathbb{R}}^{NK\times T}$  ${\mathcal{W}}_{\mathrm{init}}\leftarrow$ MCCA SUMCORR ($\mathbf{X}$)  ${\mathcal{W}}_{\mathrm{IVA}-\mathrm{G}}\leftarrow$ IVA-G ($\mathbf{X},{\mathcal{W}}_{\mathrm{init}}$)  ${\left({\mathbf{Y}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}}\leftarrow$ ${\left({\mathbf{W}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}}{\mathbf{X}}^{\left[k\right]}$  ${\mathbf{y}}_n\leftarrow {\left({\mathbf{Y}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}}$  for $n=1:N$  do     ${\sigma }_n=\frac{{\lambda }_{n1}-{\lambda }_{n2}}{{\lambda }_{n1}}$     if ${\sigma }_n>\Delta$ then         Shared subspace ←${\mathbf{y}}_n$     else         Non-shared subspace ←${\mathbf{y}}_n$     end if  end for  ${\left({\mathbf{Y}}_{\mathrm{s}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}}\leftarrow$ shared subspace, ${\left({\mathbf{Y}}_{\mathrm{ns}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}}\leftarrow$ non-shared subspace  ${\mathcal{W}}_{\mathrm{s}}\leftarrow$ IVA (${\left({\mathbf{Y}}_{\mathrm{s}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}},\mathcal{I}$), ${\mathcal{W}}_{\mathrm{ns}}\leftarrow$ IVA (${\left({\mathbf{Y}}_{\mathrm{ns}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}},\mathcal{I}$)  ${\left({\mathbf{Y}}_{\mathrm{s}}^{\left[\mathbf{k}\right]}\right)}_{\mathrm{S}3}\leftarrow$${\left({\mathbf{W}}_{\mathrm{s}}^{\left[k\right]}\right)}_{\mathrm{S}3}{\left({\mathbf{Y}}_{\mathrm{s}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}}$, ${\left({\mathbf{Y}}_{\mathrm{ns}}^{\left[\mathbf{k}\right]}\right)}_{\mathrm{S}3}\leftarrow$${\left({\mathbf{W}}_{\mathrm{ns}}^{\left[k\right]}\right)}_{\mathrm{S}3}{\left({\mathbf{Y}}_{\mathrm{ns}}^{\left[k\right]}\right)}_{\mathrm{IVA}-\mathrm{G}}$