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

Algorithm 1

EasyEnsemble algorithm.

(i)   Input: A minority training set 𝒫 and a majority training set 𝒩, |𝒫|≪|𝒩|. T: the number of

  subsets undersampling from 𝒩, 𝑠_𝑖: the number of iterations in Adaboost learning.

(ii)  Training Phase:

(iii) For  𝑖=1  to  𝑇  do

  (1) Randomly sample a subset 𝒩_𝑖 from 𝒩, 𝒩_𝑖=|𝒫|.

  (2) Learn an ensemble classifier 𝐻_𝑖 using 𝒫 and 𝒩_𝑖. 𝐻_𝑖 is an Adaboost ensemble with 𝑠_𝑖

   number of weak classifiers ℎ_𝑖,𝑗, corresponding weights 𝛼_𝑖,𝑗 and threshold 𝜃_𝑖:

        𝐻_𝑖(𝑥)=sign∑^𝑠𝑖_𝑗=1𝛼_𝑖,𝑗ℎ_𝑖,𝑗(𝑥)−𝜃_𝑖.

(iv) Endfor

(v)   Output: The final ensemble:

        𝐻(𝑥)=sign∑^𝑇∑^𝑠_𝑖=1^𝑖_𝑗=1𝛼_𝑖,𝑗ℎ_𝑖,𝑗(𝑥)−∑^𝑇_𝑖=1𝜃_𝑖.

Here, sign(𝑥)=1 means that 𝑥 is predicted as the positive class. Conversely, it means that

𝑥 belongs to the negative class.