A Novel Selective Ensemble Algorithm for Imbalanced Data Classification Based on Exploratory Undersampling

Algorithm 3

DREP ensemble pruning method.

(i) Input: 𝐻={ℎ_𝑖(𝑥)}^𝑛_𝑖=1: ensemble to be pruned,:

   𝑆=𝑥_𝑖,𝑦_𝑖^𝑚_𝑖=1 validation data set, 𝜌∈(0,1): the tradeoff parameter.

(ii) Output: pruned ensemble 𝐻^∗.

  (1)  initialize 𝐻^∗←Ø.

  (2)  ℎ(𝑥)← the classifier in 𝐻 with the lowest error on 𝑆.

  (3)  𝐻^∗←{ℎ(𝑥)} and 𝐻←𝐻⧵{ℎ(𝑥)}.

  (4)  repeat

  (5)   for each ℎ^′(𝑥)∈𝐻 do

  (6)   compute 𝑑_ℎ′← diff(ℎ^′,𝐻^∗)

  (7)   endfor

  (8)   sort classifiers ℎ^′(𝑥)∈𝐻 in the ascending order of 𝑑_ℎ′.

  (9)   Γ← the first 𝜌⋅|𝐻| classifiers in the sorted list.

  (10) ℎ(𝑥)← the classifier in Γ which most reduces the error of 𝐻^∗ on 𝑆.

  (11)  𝐻^∗←{ℎ(𝑥)} and 𝐻←𝐻⧵{ℎ(𝑥)}

  (12) until the error of 𝐻^∗ on 𝑆 can not be reduced.