## 3 SAL: Proposed Self-Augmentation Labeling Approach
### Hybrid Voting-Based Ensemble Approach
In the former, the classifier's decision that does not consent with the majority of the participating ones will be excluded from the final decision, while in the latter, the classifier will participate in the final decision even with a low prediction probability score. The accuracy performance of both techniques is almost entirely dependent on the amount of labeled data. Therefore, the percentage of available labeled data is critical because it affects both hard and soft voting techniques' performance. The more labeled data that are available, the more accurate the results. To tackle the above problem, we aim to optimize the accuracy performance of the labeling processes even with a tiny labeled dataset. This is performed by hybridising hard voting with soft voting to build a robust model that is able to control threshold tuning for a strong labeling process. In addition, the proposed approach imposes additional restricted rules for the labeling process, especially in the first steps, where we have a negligible percentage of labeled data. In the proposed hybrid voting ensemble technique, a soft voting technique is applied to compute prediction probability scores for each unlabeled observation using a number of classifiers. Therefore, if the prediction probability score from all classifiers exceeds the given threshold, then the predicted label is assigned to the unlabeled observation. Due to the small size of the labeled data set, we intend to start with strict constraints to ensure that the unlabeled observations are labeled as accurately as possible. The strict constraints are preserved or relaxed based on the amount of labeled data in each iteration of the labeling process. The final decision in the proposed hybrid ensemble voting approach is presented in the following definition. By holding the assumptions in Definition 1, the final predicted class \(\overline{\gamma}\) for each unlabeled observation is \(w_{j}\), if, and only if, the following conditions hold:  
\[\sum_{i=1}^{C}d_{c_{i}w_{j}}=C \tag{3}\]  
\[\max_{j=1}^{W}P(w_{j})>\alpha\qquad\forall c_{i}\in C \tag{4}\]  
where \(P(w_{j})\) is the prediction probability score for \(w_{j}\) class and \(\alpha\) is the predefined labeling threshold. As illustrated in Figure 4, three classifiers are used to predict the correct label of a given observation, and the first classifier predicts that the observation belongs to the class A by 95%, while the second classifier predicts that the observation belongs to class A by 96%. With remarkable difference, the third classifier predicts that this observation belongs to the class A by 60%. In this illustration, the final decision for both hard and soft voting techniques is that the given unlabeled observation belongs to class A. This is because the hard voting approach is based on majority, and as we can see, all classifiers agree that this type belongs to A. Likewise, the second soft voting technique will classify this type as class A because the average probability score of this observation belonging to class A is quite high. However, the proposed approach does not treat this observation in this manner;  
Figure 3: Soft ensemble voting algorithm. rather, there are constraints that influence the final outcome, which can be controlled by the parameters that will explained in the next section.