# A Density-Based Random Forest for Imbalanced Data Classification
## 2 Related Work
### Algorithm-Level Methods for Imbalanced Data  
Three approaches for imbalanced datasets at the algorithmic level are predominantly used: cost-sensitive learning [17], ensemble learning [18], and single-class classification [19]. Cost-sensitive learning methods apply various misclassification costs to classification decision-making. The goal is to minimize the overall misclassification cost rather than reduce the error rate. When the amount of data between categories is severely imbalanced, the classifier tends to predict all testing data as belonging to a majority category. To solve this problem, a classification method based on distinction is no longer applicable; therefore, a method based on learning recognition and single-class learning is proposed herein. The single-class learning method is designed to learn only the samples of the target class of interest, that is to train only the samples of majority classes and to fully learn their features. The goal is to identify the majority class sample from the test sample instead of distinguishing whether a sample belongs to the minority or majority class. A new sample is distinguished by comparing the similarities between the sample and the target class. In ensemble learning, multiple basic learners are combined to obtain better generalization performance than a single classifier [18]. Three approaches have been explored for ensemble-learning-based imbalanced data processing: data resampling combined with ensemble learning, cost-sensitive learning combined with ensemble learning, and increasing the diversity of classifiers in ensemble learning. SMOTEBoost [20] is a combination of SMOTE and AdaBoost [21]. First, the SMOTE algorithm is used to generate new minority samples in each iteration. Then, the minority samples receive more attention in the next iteration. Because each base classifier is constructed using different training sets, this method improves the decision domain after the vote integration. [PERSON] et al. [22] developed a method that combines oversampling and undersampling and is effective for highly imbalanced data. First, it balances the sample set with undersampling and then optimizes the basic properties of the dataset, such as the data distribution and diversity, by oversampling. The AdaCost algorithm [23] improves the recall rate and accuracy of the boosting algorithm [24] by introducing the misclassification cost of each training sample during the weight update of the boosting algorithm. In AdaCost, the weight update rule is as follows: (1) if the weak classifier misclassifies the samples with higher misclassification cost, its weight is increased; (2) if it classifies correctly, its weight is decreased. [PERSON] et al. [25] proposed the random forest variants balanced random forest (BRF) and weighted random forest (WRF). BRF performs the random replication of the minority class when constructing the training subset. WRF integrates the idea of cost-sensitive learning with random forest classifiers, that is increasing the weight of minority classes. Meanwhile, during voting, the weight multiplied by the number of votes is used as the final result. The weight is updated using the out-of-bag error data. These methods improve the data prediction of the algorithm. The imbalance problem involves other factors in addition to class bias, such as class overlap, decision boundaries, and sample distribution. [PERSON] and [PERSON] [26] proposed an algorithm that decomposes the complex imbalance problem into simpler sub-problems by a fuzzy clustering method and then assigns weights to each sub-classifier for voting classification. Biased random forest (BRAF) [27] reduces the prediction error rate of minority classes by increasing the diversity of ensemble learning. First, undersampling is used to construct the critical areas on the original dataset. Then, the critical areas are used to train the subtree. Finally, the trained subtree is merged with the standard random forest.