Algorithm 15.

Choice of number of clusters q and feature penalty α in Gecco+/iGecco+ using BIC

Initialize: $\widehat{s}={\sum }_{k=1}^K{p}_k$, ${\widehat{\mathcal{S}}}_k=\left\{1,\cdots ,p_k\right\}$, $\widehat{\alpha }=1$.

1. Fit iGecco+ with a sequence of γ and fixed $\widehat{\alpha }$. Choose the number of clusters $\widehat{q}$ using BIC. $$\widehat{q}=\underset{q}{\mathrm{argmin}}n\cdot \sum _{k=1}^K{\pi }_{k,{\widehat{S}}_k}{\ell }_k({\mathbf{X}}_{{\widehat{S}}_k}^{\left(k\right)},{\widehat{\mathbf{U}}}_{{\widehat{S}}_k}^{\left(k\right)})+q\log \left(\widehat{s}n\right).$$

2. Fit iGecco+ with a sequence of α and fixed number of clusters $\widehat{q}$. Choose number of features s using BIC. Get corresponding $\widehat{\alpha }$, active set ${\widehat{\mathcal{S}}}_k$ and total number of selected features $\widehat{s}={\sum }_{k=1}^K\left|{\widehat{\mathcal{S}}}_k\right|$. $$\widehat{s}=\underset{s}{\mathrm{argmin}}n\cdot \sum _{k=1}^K\sum _{j=1}^{p_k}\frac{{\ell }_k({\mathbf{X}}_{.j}^{\left(k\right)},{\widehat{\mathbf{U}}}_{.j}^{\left(k\right)})}{{\ell }_k({\mathbf{X}}_{.j}^{\left(k\right)},{\widehat{\mathbf{X}}}_{.j}^{\left(k\right)})}+s\widehat{q}\log \left(n\right).$$

3. Repeat Step 1 and 2 until $\widehat{q}$ and $\widehat{\alpha }$ stabilize.