Algorithm 2: Cost-Sensitive AdaBoost

Input: training dataset $S=\left\{\left(x_1,y_1\right),\dots ,\left(x_2,y_2\right),\dots ,\left(x_n,y_n\right)\right\}$, base learner $h$, the number of iterations $T$.

Output: the final strong classifier $H$.

Procedure: 1.for $i=1:1:n$ 2.compute the weight of the sample $x_i$: $D_1\left(i\right)=\frac{1}{n}$ 3.end for 4.for $t=1:1:T$ 5.select a training data subset $X$ from $S$, fit $h$ using $X$ to get a weak classifier $h_t$ 6.let $n+$ and $n-$ indicate the positive and negative classes, respectively. Compute the error rate ${\epsilon }_t$ of the base learner for both the positive class ${\epsilon }_t^p$ and negative class ${\epsilon }_t^n$: ${\epsilon }_t=\left(\frac{{\epsilon }_t^p+{\epsilon }_t^n}{2}\right),$ where    ${\epsilon }_t^p=P\left[h_t\left(x_i\right)\ne y_i\right]={\displaystyle {\displaystyle \sum }_{i=1}^{n+}}{D}_t\left(i\right)\mathsf{{\rm I}}\left[h_t\left(x_i\right)\ne y_i\right] \mathrm{and} {\epsilon }_t^n=P\left[h_t\left(x_i\right)\ne y_i\right]={\displaystyle {\displaystyle \sum }_{i=1}^{n-}}{D}_t\left(i\right)\mathsf{{\rm I}}\left[h_t\left(x_i\right)\ne y_i\right]$ 7.compute the weight of $h_t$: ${\alpha }_t=\frac{1}{2}\ln \left(\frac{1-{\epsilon }_t}{{\epsilon }_t}\right)$ 8.update the weight of all the instances in $S$: for $i=1:1:n$           $D_{t+1}\left(i\right)=\frac{D_t\left(i\right)}{Z_t}\exp \left(-{\alpha }_t{\beta }_i{y}_i{h}_t\left(x_i\right)\right)$ where $Z_t$ is a normalization factor and is calculated as: $Z_t={\displaystyle \sum }_{i=1}^n{D}_t\left(i\right)\exp \left(-{\alpha }_t{\beta }_i{y}_i{h}_t\left(x_i\right)\right)$ and ${\beta }_i$ is calculated as: ${\beta }_i=\left\{\begin{array}{c}\frac{T{P}_t}{F{P}_t+T{P}_t}{c}_{10}, if y_i=1, h_t\left(x_i\right)=-1\\ \frac{T{N}_t}{F{N}_t+T{N}_t}{c}_{01}, if y_i=-1, h_t\left(x_i\right)=1\\ \frac{T{P}_t}{F{P}_t+T{P}_t}{c}_{11}, if y_i=1, h_t\left(x_i\right)=1\\ \frac{T{N}_t}{F{N}_t+T{N}_t}{c}_{00}, if y_i=-1, h_t\left(x_i\right)=-1\end{array}\right.$ where $T{P}_t$, $T{N}_t$, $F{P}_t$, $F{N}_t$ are true positive, true negative, false positive, and false negative values for iteration $t$. Meanwhile, $c_{10}$, $c_{01}$, $c_{11}$, $c_{00}$ are the cost-sensitive factors, where $c_{10}>c_{00}$ and $c_{01}>c_{11}$. 9.end for 10.end for 11.the final classifier is obtained as follows: $H\left(x\right)=sign\left({\displaystyle \sum }_{t=1}^T{\alpha }_t{h}_t\left(x\right)\right)$