Algorithms A2 Learning process of the AdaBoost algorithm
Input:Dataset${\mathit{D}}_{\mathbf{1}}\left(\mathit{i}\right)=\mathbf{1}/\mathit{m}$;$D=\{(x_1,y_1),(x_2,y_2),\dots ,(x_m,y_m)\}$;    Basic-learner$L$;    Iteration$T$;
Process:
1. $D_1\left(i\right)=1/m$;	% Initialize training set weight
2. for $t=1,\cdots ,T$:
3.  $h_t=L\left(D,D_t\right);$	% use D and Dt to train the learner ht
4.  ${\mathrm{e}}_{\mathrm{t}}={\mathrm{Pr}}_{\mathrm{x}~{\mathrm{D}}_{\mathrm{t},\mathrm{y}}}\mathrm{I}\left[{\mathrm{h}}_{\mathrm{t}}\left(\mathrm{x}\right)\ne \mathrm{y}\right]$;	% Calculate the error of learner ht
5.  if $e_t>0.5$ then break
6.  ${\mathsf{\alpha }}_{\mathrm{t}}=\frac{1}{2}\ln (\frac{1-{\mathrm{e}}_{\mathrm{t}}}{{\mathrm{e}}_{\mathrm{t}}})$;	% Calculate the coefficient of learner ht
7.  $D_{t+1}\left(i\right)=\frac{D_t\left(i\right)}{Z_t}\times \{\begin{array}{c}\exp \left(-{\alpha }_t\right),h_t\left(x_i\right)=y_i\\ \exp \left({\alpha }_t\right),h_t\left(x_i\right)\ne y_i\end{array}=\frac{D_t\left(i\right)\exp \left(-{\alpha }_t{y}_i{h}_t\left(x_i\right)\right)}{Z_t}$
8. % Update the weight of training set, where Zt is the normalization factor.
% $Z_t={\sum }_{i=1}^m{D}_i·\exp \left(-\alpha ·y_i·L\left(x_i\right)\right)$
9. end
Output:$H\left(x\right)=sign({\sum }_{t=1}^T{\alpha }_t{h}_t\left(x\right))$