## 3 The Proposed Co-Training Scheme
\begin{table}
\begin{tabular}{c l} \hline \hline
**Algorithm** & \multicolumn{2}{c}{**Parameters**} \\ \hline k-NN & Number of neighbors: 5 \\  & Distance function: Euclidean distance \\ SVM & Kernel function: RBF \\ DT & Splitting criterion: gini \\  & Min instances per leaf = 2 \\ LR & Norm: L2 \\ NB & Gaussian distribution \\ Self-training & MaxIter = 20 \\ Co-training & MaxIter = 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Configuration of exploited algorithms’ parameters. different labeled ratio scenarios concerning the top five algorithms, based on total Friedman Ranking statistical process along with a smaller statistical comparison concerning only the top five algorithms. For a deeper analysis, the total results can be found in [[http://mL.math.upatras.gr/wp-content/uploads/2019/12/Official_results_co_training_ssoffec_voting.%z](http://mL.math.upatras.gr/wp-content/uploads/2019/12/Official_results_co_training_ssoffec_voting.%z)]([http://mL.math.upatras.gr/wp-content/uploads/2019/12/Official_results_co_training_ssoffec_voting.%z](http://mL.math.upatras.gr/wp-content/uploads/2019/12/Official_results_co_training_ssoffec_voting.%z)). Moreover, a pie chart has been provided in Figure 1, depicting the participation, into per centage style, of the pair of classifiers that were employed into the proposed strategy as base learner during all the experiments. For evaluating the predictive performance of the proposed algorithm, three representative and widely used evaluation measures were adopted for measuring the obtained performance over the test set: classification accuracy, F\({}_{1}\)-score, and Area Under the ROC Curve (AUC). Accuracy corresponds to the percentage of correctly classified instances, while F\({}_{1}\)-score is an appropriate metric for imbalanced datasets and is defined as the harmonic mean of recall (r) and precision (p). In the case of a binary classification problem, they are defined as:

\[Accuracy=(tp+tn)/n \tag{6}\]

\[F_{1}score=2\times tp/(2\times tp+fp+fn). \tag{7}\]

where \(tp\), \(tn\), \(fp\), \(fn\), and \(n\) correspond to the number of true positive, true negative, false positive, false negative, and total number of instances, respectively. Finally, the latter one is related to the quality of the examined classifier ranking of any randomly chosen instance and is computed by aggregating the corresponding performance across all possible classification thresholds. The most favorable manner to visualize this metric is through plots of \(TPR\) vs. \(FPR\) or Sensitivity vs. (1-Specificity) relationship at different classification thresholds, where \(TPR\) stands for True Positive Rate, while \(FPR\) stands for False Positive Rate. Their analytical formulas are provided here:

\[TPR=tp/(tp+fn), \tag{8}\]

\[FPR=fp/(fp+tn). \tag{9}\]

The experimental results using 10% labeled ratio are summarized in Tables 3-5, where the best value per dataset is bold highlighted. Overall, it appears that the co-training Vote performs better than the corresponding self-training variants. Moreover, among the co-training variants employed, the proposed algorithm takes precedence over the rest on most of the datasets. In addition, we applied a familiar statistical tool to confirm the observed results. Hence, the Friedman Aligned Ranks [56] non-parametric test (significance level \(\alpha\) = 0.05) was used to compare all the employed SSL methods (Table 6). According to the calculated results, the algorithms are sorted from the best performer (lowest ranking) to the worst one (higher ranking). Therefore, it is statistically confirmed the supremacy of the \(Co(Vote_{self}^{SEC})\) algorithm, while the null hypothesis \(H_{0}\) (i.e., the means of the results of two or more algorithms are the same) is rejected. Furthermore, the Nemenyi post-hoc test [57] (\(\alpha\) = 0.05) was applied to detect the specific differences between the algorithms, which is a commonly used non-parametric test for pairwise multiple comparisons.