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 2 Attribute selection and splitting.

Input: evidential training set $T_{p l} = (x, p l_{y})$ , possible splitting attribute $A = \{A^{1}, \dots, A^{D}\}$

Output: selected attribute $A^{*}$ , instance sets in child nodes $T_{i}$ , $(i = 1, \dots, K)$

1:
compute the normal distribution parameters $(μ_{k}^{d}, σ_{k}^{d})$ for each $A^{d}$ and $C_{k}$ by $E^{2} M$ algorithm;
2:
for each attribute $A^{d}$ do
3:
for each instance $I^{n}$ do
4:
generate BBA $m_{n}^{d}$ from normal distributions $N_{k}^{d} (μ_{k}^{d}, {σ_{k}^{d}}^{2}), k = 1, \dots, K$ ;
5:
$E_{n}^{d} = E (m_{n}^{d})$ ; {Calculate Deng entropy for all generated BBAs}
6:
end for
7:
$E (A^{d}) = A v e r a g e (E_{n}^{d})$ ; {Calculate average Deng entropy for each attribute}
8:
end for
9:
split on attribute $A^{*} = \underset{A^{d}}{\arg min} (E (A^{d}))$ ; {The attribute with minimum average entropy is selected}