enDNA-Prot: Identification of DNA-Binding Proteins by Applying Ensemble Learning

Algorithm 1

The pseudocode of Unbalanced-AdaBoost.

Input:

positive train dataset 𝑆⁺_Train=(𝑥₁,𝑦₁,(𝑥₂,𝑦₂),…,(𝑥_𝑛,𝑦_𝑛)};

negative train dataset 𝑆⁻_Train=(𝑥₁,𝑦₁,(𝑥₂,𝑦₂),…,(𝑥_𝑙,𝑦_𝑙)}; (𝑙+𝑛=𝑚)

Base learning algorithm 𝐿={𝑙𝑎₁,𝑙𝑎₂,…,𝑙𝑎₂₀};

Number of learning rounds 𝑇=20.

Output:

        𝐻(𝑥)=sign𝑓(𝑥)=sign∑^𝑇_𝑡=1𝛼_𝑡ℎ_𝑡(𝑥)

Process:

(1)    𝑊₁(𝑖)=1𝑙(𝑖=1,2,…,𝑙) //Initialize the weight distribution on 𝑆⁻_Train

(2)   For  𝑡=1,2,…,𝑇:

(3)    𝑆⁻_sample=sampling(𝑆⁻_Train,𝑊_𝑡); //sampling negative samples from the negative train dataset 𝑆⁻_Train with weight

   distribution 𝑊_𝑡

(4)  𝑆_𝑡=𝑆⁺_Train+𝑆⁻_sample; //combine the positive train dataset 𝑆⁺_Train and sampled dataset 𝑆⁻_sample into a dataset

(5)  ℎ_𝑡=𝑙𝑎_𝑡(𝑆_𝑡); //train the base learner ℎ_𝑡 on the dataset 𝑆_𝑡

(6)  𝜀_𝑡=Pr_{(𝑥𝑖,𝑦𝑖)∈𝑆}⁻_Train[ℎ_𝑡(𝑥_𝑖≠𝑦_𝑖)]; //test ℎ_𝑡 on the negative dataset 𝑆⁻_Train and calculate its predicted error

(7)  𝛼_𝑖=log₁₀1−𝜀_𝑡𝜀_𝑡; //calculate the voting weight of the base learner ℎ_𝑡

(8)  𝑊_𝑡+1𝑊(𝑖)=^𝑡(𝑖)𝑍_𝑡×log_sizesize+1−𝜀_𝑡𝜀_𝑡ifℎ_𝑡(𝑥_𝑖)≠𝑦_𝑖1ifℎ_𝑡𝑥_𝑖=𝑦_𝑖 //calculate the weight distribution for the next learning round,

   where size denotes the number of samples in 𝑆⁻_Train and 𝑍_𝑡 used to ensure that 𝑊_𝑡+1 is a distribution.

(10) End