Algorithm 1. Pseudo code description of COSC-Boosting algorithm.

COSC-Boosting

Input:  label sample set: $L={\left\{\left(x_t^L,y_t^L\right)\right\}}_{t=1}^M,$

unlabeled data set: $U={\left\{\left(x_t^U,-\right)\right\}}_{t=1}^N$,

maximum number of iteration: T

number of randomly chosen samples in the unlabeled set for classifier updating: M’

Output: the eventual classifier f

procedure :

$L_1\leftarrow L$;  % Prepare a labeled sample set L1 for TPSRC;

$L_2\leftarrow L$;  % Prepare a labeled sample set L1 for TPSRC;

Create a buffer pool $U^{\prime }\leftarrow {\left\{\left(x_i^{U^{\prime }},-\right)\right\}}_{i=1}^{M^{\prime }}$ to save the M’ samples randomly chosen from U;

Training TPSRC hTPSRC(x) based on L1 .

For each $x_i^{U^{\prime }}\in U^{\prime }$ $x_i^{U\prime }\in U\prime$

$y_{x_i^{U\prime }}^{TPSRC}=h_{TPSRC}\left(x_i^{U^{\prime }}\right)$;

$y_{x_i^{U\prime }}^{MARSC}=h_{MARSC}\left(x_i^{U^{\prime }}\right)$;

If $Label\left(y_{x_i^{U^{\prime }}}^{TPSRC}\right)=Label\left(y_{x_i^{U^{\prime }}}^{MARSC}\right)$ % gain the same label from TPSRC and MARSC

$MSE\left(h_{TPSRC};{\mathrm{x}}_i^{U^{\prime }}\right)={\displaystyle \sum _{x_i\in L_1}}\left\{{\left[y_i-h_{TPSRC}\left(x_i\right)\right]}^2-{[y_i-h_{TPSRC}^{*}\left(x_i\right)]}^2\right\};$

$MSE\left(h_{MARSC};x_i^{U^{\prime }}\right)={\displaystyle \sum _{x_i\in L_2}}\left\{{\left[y_i-h_{MARSC}\left(x_i\right)\right]}^2-{[y_i-h_{MARSC}^{*}\left(x_i\right)]}^2\right\};$

If both $MSE\left(h_{TPSRC};x_i^{U^{\prime }}\right)\ge 0$ and $MSE\left(h_{MARSC};x_i^{U^{\prime }}\right)\ge 0$

$h_{TPSRC}\leftarrow h_{TPSRC}^{*}$;   %Update $h_{TPSRC}$;

$h_{MARSC}\leftarrow h_{MARSC}^{*}$;   %Update $h_{MARSC}$;

End If

End If

End For

${\mathsf{\pi }}_{TPSRC}\leftarrow \varphi$;

If exist $MSE\left(h_{TPSRC};x_i^{U^{\prime }}\right)\ge 0$ % find the labeling of most confidence

${\tilde{x}}_{TPRSC}^{U^{\prime }}\leftarrow agr\text{max}\left\{MSE\left(h_{TPSRC};x_i^{U^{\prime }}\right)\right\};y_{TPRSC}^{U^{\prime }}\leftarrow h_{TPRSC}\left({\tilde{x}}_{TPRSC}^{U^{\prime }}\right);$

${\mathsf{\pi }}_{TPSRC}\leftarrow \left\{\left({\tilde{x}}_{TPRSC}^{U^{\prime }},y_{TPRSC}^{U^{\prime }}\right)\right\}$;

End If

${\mathsf{\pi }}_{MARSC}\leftarrow \varphi$;

If exist $MSE\left(h_{MARSC};x_i^{U^{\prime }}\right)\ge 0$ % find the labeling of most confidence

${\tilde{x}}_{MARSC}^{U^{\prime }}\leftarrow agr\text{max}\left\{MSE\left(h_{MARSC};x_i^{U^{\prime }}\right)\right\};y_{TPRSC}^{U^{\prime }}\leftarrow h_{MARSC}\left({\tilde{x}}_{MARSC}^{U^{\prime }}\right);$

${\mathsf{\pi }}_{MARSC}\leftarrow \left\{\left({\tilde{x}}_{MARSC}^{U^{\prime }},y_{TPRSC}^{U^{\prime }}\right)\right\}$;

$L_1\leftarrow L_1{{\displaystyle \cup }}^{\text{}}{\mathsf{\pi }}_{TPRSC};L_2\leftarrow L_2{{\displaystyle \cup }}^{\text{}}{\mathsf{\pi }}_{TPRSC};$

If neither L1 and L2 changes then directly exit the repeating;

Else

Training hTPRSC(x) based on L1 and hMARSC(x) based on L2 separately;

Reset U’ and Randomly select M’ samples from U with replacement to U’;

End If

End Repeat

Output: the ultimate classifier $f\left(x\right)=\frac{1}{2}\left(h_{TPRSC}\left(x\right)+h_{MARSC}\left(x\right)\right);$;