Conformational B-Cell Epitopes Prediction from Sequences Using Cost-Sensitive Ensemble Classifiers and Spatial Clustering

Procedure 1

Procedure Cost-Sensitive Boosting scheme.

BEGIN

  Data preparation:  𝐷={(𝑙₁,𝑥₁,𝑐₁),(𝑙₂,𝑥₂,𝑐₂),…,(𝑙_𝑛,𝑥_𝑛,𝑐_𝑛)},  where  𝑥_𝑖∈𝑋,𝑦_𝑖∈𝑌={−1,+1}

  𝐶_𝑖⊂(0,+∞),𝑖=1,…,𝑛

  Initialization:

  (a) Initialize the classifier  𝐻=∅

  (b) Initialize the weights distribution  𝑊¹=(𝑤¹₁,…,𝑤¹_𝑛),𝑤¹_𝑡∈[0,1],∑^𝑀_𝑡=1𝑤¹_𝑡=1. (Usually 𝑤¹_𝑡=1/𝑛)

  Iteration:

  (1) Train the base learner  ℎ_𝑡: using weight distribution  𝑊^𝑡

  (2) Choose the weight updating parameter:

  𝛼_𝑡=12log1+∑_{𝑖,𝑦𝑖=ℎ𝑡(𝑥𝑖)}𝐶_𝑖⋅𝑊^𝑡(𝑖)−∑_{𝑖,𝑦𝑖≠ℎ𝑡(𝑥𝑖)}𝐶_𝑖⋅𝑊^𝑡(𝑖)1−∑_{𝑖,𝑦𝑖=ℎ𝑡(𝑥𝑖)}𝐶_𝑖⋅𝑊^𝑡(𝑖)+∑_{𝑖,𝑦𝑖≠ℎ𝑡(𝑥𝑖)}𝐶_𝑖⋅𝑊^𝑡(𝑖)

  (3) Updating and normalize the sample weights:

  𝑊^𝑡+1𝑊(𝑖)=^𝑡(𝑖)exp(−𝛼_𝑡𝐶_𝑖ℎ_𝑡(𝑥_𝑖)𝑙_𝑖)𝑍_𝑡,  where  𝑍_𝑡=∑_𝑖𝑊_𝑡(𝑖)exp(−𝛼_𝑡𝑙_𝑖ℎ_𝑡(𝑥_𝑖))

  End Iteration

  Output the final classifier:

  𝐻(𝑥)=sign(∑^𝑇_𝑡=1𝛼_𝑡tanh((ℎ_𝑡(𝑥)−𝜇)/𝜎))  where  𝜇  and  𝜎  are the mean and the standard deviation of scores produced

  by the sub-classifiers

  RETURN  𝐻(𝑥).

END