Algorithm 2 BLMKM Algorithm

Input: dataset $D$, number of clusters $k$

Output: optimal BN $N_G^{*}$ and score $s^{*}$

1. $C=\{C_1,C_2,\dots ,C_k\}\leftarrow \mathit{MKM}(D,k)$

2. $Theskeletonofthenetwork(MB)\leftarrow \mathit{MMPC}(D)$

3. $Allpossiblediagrams{\delta }^{*}\leftarrow \mathit{Combine}(C,Theskeletonofthenetwork)$

4. for $i=1,2,\dots 2^m$ do

5. $N_{G_i}^{*}and{s}_i{}^{*}\leftarrow \mathit{Pruned}\mathit{Dynamic}\mathit{Programming}(D,{\delta }_i^{*})$

6. end for

7. Optimal BN $N_G^{*}\leftarrow \arg \max (s_i{}^{*},N_{G_i}^{*})\mathrm{and}{s}^{*}\leftarrow \max (s_i{}^{*},N_{G_i}^{*})$