## 3 The Proposed Co-Training Scheme
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **\# Instances** & **\# Features** & **Dataset** & **\# Instances** & **\# Features** \\ \hline bands & 365 & 19 & monk-2 & 432 & 6 \\ breast & 277 & 48 & pima & 768 & 8 \\ bupa & 345 & 6 & saheart & 468 & 9 \\ chess & 3196 & 38 & sick & 3772 & 33 \\ colic.orig & 368 & 471 & tic-tac-toe & 958 & 27 \\ diabetes & 768 & 8 & vote & 435 & 16 \\ heart-stat\(\underline{\text{t}}\)og & 270 & 13 & wdbc & 569 & 30 \\ kr-vs-kp & 3196 & 40 & wisconsin & 683 & 9 \\ mammographic & 830 & 5 & & & \\ \hline \hline \end{tabular} \#: the cardinality of the corresponding quantity.

\end{table} 
Table 1: Description of datasets used from the UCI repository. individual variants without voting. Thus, 16 different supervised classifiers were exhibited as base learners, all imported by the scikit-learn Python library [51] and in particular:

The SVMs using Radial Basis Function as kernel inside its implementation, representing one universal learner that tries to separate instances using hyper-planes and 'Kernel-trick' [52],

* The k-Nearest Neighbor (kNN) instance-based learner [53] with k equal to 5, a very effective method for classification problems, using the Euclidean metric as a similarity measure to determine the distance between two instances,
* A simple Decision Tree (DT) algorithm, a variant of tree induction algorithms with large depth that split the feature space using 'gini' criterion [44],
* The NB probabilistic classifier, a simple and quite efficient classification algorithm based on the assumption that features are independent of each other given the class label [54],
* The Logistic Regression (LR), a well-known discriminative algorithm that assumes the log likelihood ratio of class distributions is linear in the provided examples. Its main function supports the binomial case of the target variable, exporting posterior probabilities in a direct way. In our implementation, L2-norm during penalization stage was chosen [55]. For simplicity, we made use of the following notation in the experiments, while the parameters' configuration for all applied classification methods is presented in Table 2:

* [noitemsep,topsep=0 pt]
* C \(\equiv\) {SVM, kNN, DT, NB, LR}, the list of participant classification algorithms,
* \(Self(learner)\), where \(learner\in\) C,
* \(Self(Vote(learner_{i},learner_{j}))\), where \(learner_{i}\), \(learner_{j}\in\) C with \(i\
eq j\),
* \(Self(Vote(all))\), where all participants of C are exploited under the Voting scheme,
* \(Co(learner)\), where this kind of approach corresponds to the case that learner1 \(\equiv\) learner2 \(\equiv\) learner, with \(learner\in\) C,
* \(Co(Vote(learner_{i},learner_{j}))\), where \(learner_{i}\), \(learner_{j}\in\) C with \(i\
eq j\), and the ensemble Voting learner is the same for both views, similar with the previous scenario,
* \(Co(Vote(all))\), where all participants of C are exploited under the Voting scheme for each view, and finally,
* \(Co(Vote_{soft}^{SEC})\), which coincides with the proposed semi-supervised algorithm. As mentioned before, there are 10 different pairs of algorithms that can be formatted with a pool of five candidate classifiers. In addition, the case of applying each one individually takes also place, as well as the case that all participants of pool C are exploited under the same Voting stage. Thus, 16 self-training variants and 16 co-training variants are examined against the proposed co-training algorithm, which selects through a static selection strategy the soft-Voting ensemble base learner into its operation per different task. As it concerns the parameter f, it has been set equal to 10, leading to a 10-fold-cross-validation procedure per examined dataset. The next tables depict only one out of three