Belief Entropy Tree and Random Forest: Learning from Data with Continuous Attributes and Evidential Labels

. 2022 Apr 26;24(5):605. doi: 10.3390/e24050605

Algorithm 3 Induction of belief entropy trees (BE-tree).

Input: evidential training set $T_{p l}$ , classifier type $T Y P E$

Output: belief entropy tree $T r e e$

1:
construct a root node containing all instances $T_{p} l$ ;
2:
if stopping criterion is met then
3:
if $T Y P E = O B E$ then
4:
output precise prediction generated from original plausibility label for the whole node;
5:
else if $T Y P E = L B E$ then
6:
combine BBAs generates during each splitting $\hat{m} = m_{1}^{*} \oplus \cdot \cdot \cdot \oplus m_{Q}^{*}$ for each instance;
7:
combine BBAs of all instances in previous node generated in step 6 that ${\hat{m}}_{l e a f} = {\hat{m}}_{1} \oplus \cdot \cdot \cdot \oplus {\hat{m}}_{P}$ ;
8:
output ${\hat{m}}_{l e a f}$ as a mass prediction for the whole leaf node;
9:
output $\hat{C} = P i g n i s t i c ({\hat{m}}_{l e a f})$ as a precise prediction for the whole leaf node;
10:
end if
11:
return $T r e e$ =root node;
12:
else
13:
apply Algorithm 2 to select splitting attribute $A^{*}$ ;
14:
induce each subset ${T_{p l}}_{c h i l d}$ based on $A^{*}$ ;
15:
for all ${T_{p l}}_{c h i l d}$ do
16:
$T r e e_{c h i l d} = B E$ - $t r e e ({T_{p l}}_{c h i l d})$ ; {Recursively build the tree on the new child node}
17:
attach $T r e e_{c h i l d}$ to the corresponding $T r e e$ ;
18:
end for
19:
end if