A Soft-Voting Ensemble Based Co-Training Scheme Using Static Selection for Binary Classification Problems  
[PERSON]  
1 Educational Software Development Laboratory (ESDLab), Department of Mathematics, University of Patras, 26504 Patras, Greece; [EMAIL_ADDRESS] (G.  
for classifying any given example to one out of the included class labels into a predetermined set. Depending on the number of class labels, classification problems may be either binary (with two class labels) or multi-class (with more than two class labels). For that purpose, a number of semi-supervised algorithms have been developed and successfully implemented, such as self-training [6], co-training [7], and tri-training [8], as well as approaches that are based on semi-supervised support vector machines and transductive learning or SSL graph-based methods, to name just a few [9]. Co-training is a representative multi-view SSC algorithm originally based on the assumption that each example can be described by two distinct feature sets, usually referred to as views [7]. Then, two classification algorithms are trained separately on each view and the most confident predictions of each one on the unlabeled data are used to augment the training set of the other. Let \(\mathrm{L_{D}}\) denote a small set of labeled examples and \(\mathrm{U_{D}}\) a large set of unlabeled ones. The two separate classifiers \(\mathrm{C_{1}}\), \(\mathrm{C_{2}}\) are retrained on the enlarged set \(\mathrm{L_{D}}\) and the process is repeated for a predefined number of iterations or until a stopping criterion is satisfied, such as the \(\mathrm{U_{D}}\) pool to be empty. However, since such a two-view assumption can hardly be met in real world problems, several variants of the co-training algorithm have been proposed dealing with the absence or existence of a naturally two-view feature split with notable results. In addition to these, ensemble learning or committee-based learning or learning multiple classifier systems has emerged recently and is considered as one of the most adequate solutions for building powerful and accurate classification models [10]. Instead of using one algorithm for building a learning model, ensemble methods are commonly used to construct and combine a set of classifiers, either weak or strong, generally called base learners. The fundamental points for the effectiveness of an ensemble method concern careful selection of both base learners [11] and the combination method for producing the final hypothesis [12]. Averaging (simple or weighted [13]) and voting (majority, unanimity, plurality, or even weighted votes) are popular and commonly used combination methods [14] depending on the problem which needs to be resolved [10]. Moreover, approaches using committees of base learners into the core of their learning process have also been demonstrated recently, presenting encouraging results [15]. The necessity of accurate and robust decisions inside a semi-supervised scheme play a cardinal role, especially in cases where the number of initially labeled instances is quite small and no decision correcting or editing mechanisms have been placed inside the learning kernel. Therefore, strategies trying to build an ensemble optimizing well-defined criteria could be a useful asset of a compact semi-supervised algorithm for selecting the most suitable structure per task. Although this concept has been highly exploited under the supervised mode, only few works have been detected in the related literature that apply similar approaches [16; 17]. Furthermore, there are some works in this field that apply mechanisms suitably combining the decisions of selected base learners, failing, however, to state the reasons of their choice, apart from some generic properties, such as the combination of one generative and one discriminative approach that favors the diversity of the applied co-training algorithm [18]. In this context, a soft-Voting ensemble-based co-training scheme using static selection strategy, regarding binary classification problems, is proposed.