## 3 Analysis Plan
### Smote  
Many methods have been proposed to address the problem of class imbalance. In the literature, those methods are typically categorized into four groups: algorithm-level, data-level, cost-sensitive, and ensemble approaches [8; 9]. The algorithm-level approaches modify existing classification algorithms to be biased toward the minor classes to improve the performance of the model in predicting the minor classes [23; 24]. These approaches require knowledge of the specific classifiers, and why the classifiers fail to modify the algorithms. The data-level approaches rebalance the imbalanced classes by over-sampling the minor classes or under-sampling the major classes to alleviate the effect of imbalanced classes [19]. Because these approaches are implemented in the preprocessing step, they are independent of specific classifiers and also can be more easily implemented. The cost-sensitive approaches combine both the data- and algorithm-level approaches by adding high misclassification costs for the minor classes (data level approaches), and also modifying the classification algorithms to accept the costs ([25], algorithm level approaches). Recently, the ensemble approaches are attracting more and more attention as a solution to the class imbalance problem. Hybridizing the bagging and boosting paradigms in ensemble methods with the algorithm-level, data-level, and cost-sensitive approaches for the imbalanced dataset turned out to be very promising. Readers who are interested in a more compressive review on this topic are referred to the works of [PERSON] et al. [9] and [PERSON] et al. [8].  
In this study, we used SMOTE [19] from the data-level approaches to address the problem of class imbalance. In the data-level approaches, the under-sampling randomly eliminates some major classes to make the major classes less effective on the learning process. However, the under-sampling could remove major classes which are more representative and informative than others, and therefore the decision boundary could be biased. The over-sampling randomly replicates the minor classes to make the minor classes more effective on the learning process. However, the over-sampling creates repeated copies of the same minor class instances many times, and therefore the classifiers could overfit to these minor class instances. After reviewing previous studies on over- and under-sampling, [PERSON] et al. [19] summarized that the under-sampling showed better performance than the over-sampling, and the combination of the over- and under-sampling did not outperform the under-sampling. They proposed SMOTE as a new over-sampling technique in which the minor class instances are over-sampled by creating synthetic instances rather than creating the same minor instances multiple times with replacement, and showed that the combination of SMOTE and under-sampling performed better than the plain under-sampling. In SMOTE, the minor class instances are over-sampled by creating synthetic instances along the line segments joining the \(k\) nearest neighbor instances with minor classes. The idea behind the SMOTE is to over-sample similar instances rather than to over-sample the same instances multiple times so that the classifiers are not overfitted to the minor class instances.