stylistic:style_transfer
Derivation

Thus we have derived the AdaBoost algorithm: At each iteration, choose the classifier k m {\displaystyle k_{m}}, which minimizes the total weighted error ∑ y i ≠ k m (x i) w i (m) {\textstyle \sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}}, use this to calculate the error rate ϵ m = ∑ y i ≠ k m (x i) w i (m) ∑ i = 1 N w i (m) {\displaystyle \epsilon _{m}={\frac {\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}}{\sum _{i=1}^{N}w_{i}^{(m)}}}}, use this to calculate the weight α m = 1 2 ln (1 − ϵ m ϵ m) {\displaystyle \alpha _{m}={\frac {1}{2}}\ln \left({\frac {1-\epsilon _{m}}{\epsilon _{m}}}\right)}, and finally use this to improve the boosted classifier C m − 1 {\displaystyle C_{m-1}} to C m = C (m − 1) + α m k m {\displaystyle C_{m}=C_{(m-1)}+\alpha _{m}k_{m}}.