# A Novel Ensemble Belief Rule-Based Model for Online Payment Fraud Detection
## 2 Related Works
### Methods for Solving Class Imbalance  
Imbalanced classification has long been a challenge that researchers strive to address, as it is a phenomenon widely observed in real-world scenarios. Fraud detection, in particular, is a classic example of an imbalanced binary classification task, often characterized by a significantly high imbalance ratio. In current research, methods for addressing imbalanced classification can generally be divided into two categories: data-level approaches and algorithm-level approaches. Data-level methods can be categorized into two kinds: oversampling [31; 32] and under sampling. Oversampling involves increasing instances of the minority class, while undersampling involves decreasing instances of the majority class to achieve the desired class distribution. [PERSON], in studying the oversampling problem for multiclass imbalanced datasets, focused on analyzing class features and demonstrated a significant improvement in oversampling methods for specific types of sample preprocessing [33]. According to the ratio between the minority and majority classes, when resampling both classes, experimental results have shown that the performance of the sampling algorithm is closely related to this ratio [34]. [PERSON] et al. developed a density-based undersampling method combined with cost-sensitive classification methods for integration, with experimental results showing its superiority over most ensemble classification algorithms [35]. [PERSON] et al. simultaneously used oversampling and undersampling techniques, comparing their performance and finding that oversampling outperformed undersampling [6]. [PERSON] et al. proposed a clustering-based synthetic data generation method combined with evolutionary algorithms for ensemble creation, and experimental conclusions demonstrated its superiority over current majority ensemble algorithms [36]. [PERSON] et al. evaluated two famous sampling methods, namely random undersampling and SMOTE (Synthetic Minority Oversampling Technique), and concluded that undersampling is more efficient in dealing with imbalanced datasets when combined with random forests [37]. Data-level methods have the advantage of being easy to implement and independent of the classification algorithm. However, they also come with certain drawbacks. For instance, the sampling ratio can significantly affect model performance. Additionally, oversampling may lead to overfitting, while undersampling risks losing important information, potentially resulting in reduced model performance. Algorithm-level methods primarily involve integrating cost-sensitive learning techniques with traditional machine learning algorithms. Cost-sensitive learning mitigates the impact of imbalanced data on models by constructing a cost matrix that assigns different weights to different samples. Typically, majority class samples are assigned lower weights, while minority class samples are given higher weights. In the field of fraud detection, cost-sensitive learning methods are also used. For example, [PERSON] et al. [38] combined cost-sensitive learning methods with random forest and KNN algorithms for application in payment card fraud detection. Compared to data sampling methods, cost-sensitive learning does not carry the risks of overfitting or information loss. However, in practical applications, determining the parameters of the cost matrix can be challenging, which brings certain limitations to its use. In addition to the methods mentioned above, ensemble learning methods have also been used in recent years to address imbalanced classification problems. [PERSON] et al. proposed an ensemble approach that utilizes cost-sensitive classifiers to solve the decomposed sub-problems and then combines the results of the sub-classifiers using a voting method [39]. In some domains, highly imbalanced classification scenarios occur, which require simultaneously addressing multiple issues such as the accuracy of classifiers for highly imbalanced multiclass data, training efficiency and sensitivity to high imbalance.