Algorithm 1: Rule elimination based on feature contribution and feature pattern

1: Input: The number of layers $N$, the number of RFs $V$, the number of trees T, random forest $RF$, list of dSets ${\mathrm{List}}_{\mathrm{dSet}}$ 2: Start with an empty list of $\mathrm{dSets}$ 3: ${\mathrm{List}}_{\mathrm{dSet}}=\varnothing$ 4: Learn LMRF 5: For each $l$ layer: 6: For each $v$ RF: 7: For each $t$ tree: 8: - Split a $i$-th rule from a decision tree 9: - Calculate feature contribution of a $i$-th rule $feat.contrib\left(i,*\right)$, Equation (2) 10: - Calculate rule contribution for $i$-th rule ${\mathrm{r}}_i^t, \mathrm{Equation} \left(1\right)$ 11: - Add rule and its ${\mathrm{r}}_i^t$ to $\mathrm{dSet}\left(v,l\right)$ 12: End 13: - Compute feature pattern $fr{e}_v^l\left(x_j=A\right)$ by splitting rules in $\mathrm{dSet}\left(v,l\right), \mathrm{Equation} \left(3\right)$ 14: - Re-compute a new rule contribution ${{\mathrm{r}}^{*}}_i$, Equation (4) 15: - Sort rules in $\mathrm{dSet}\left(v,l\right)$ according to ${{\mathrm{r}}^{*}}_i$ 16: - Add $\mathrm{dSet}\left(v,l\right)$ to ${\mathrm{List}}_{\mathrm{dSet}}$ of $l$-th layer 17:              ${\mathrm{List}}_{\mathrm{dSet}}\left[l\right]={\mathrm{List}}_{\mathrm{dSet}}\left[l\right]+\mathrm{dSet}\left(v\right)$ 18: End 19: End 20: Output: The ${\mathrm{List}}_{\mathrm{dSet}}\left[l\right]$ consists of $l$ layers