## 2 Related Work  
### Multi-Class Imbalance Data Classification Method  
With the intensive study of researchers, several types of solutions for handling multi-class imbalanced data have been proposed. Currently, multi-class imbalanced data classification methods are mainly classified into data balancing methods and algorithm-level classification methods. Data balancing methods mainly balance data distribution by adding minority class samples (oversampling) or removing majority class samples (under-sampling) [10]. Currently, data resampling methods can be divided into oversampling, under-sampling, and hybrid sampling. In oversampling methods, Synthetic Minority Over-sampling Technique (SMOTE) [11] is the most representative method, which artificially synthesizes new samples based on minority class samples and adds them to the dataset. However, SMOTE can generate incorrect samples, leading to overfitting problems. In under-sampling methods, the combination of clustering methods and under-sampling can reduce the information loss caused by under-sampling. [PERSON] et al. [12] proposed a clustering-based under-sampling (CUS) method. By clustering majority class instances and under-sampling instances with the most information, multiple balanced datasets are formed. This method achieves high accuracy in classifying both majority and minority class instances. In hybrid sampling methods, Random Balance [13] is a preprocessing strategy for binary imbalanced data, using random class ratios for random under-sampling and SMOTE oversampling. Based on this, [PERSON] et al. [14] proposed the MultiRandBal method, extending it to multi-class imbalanced datasets. Unlike previous methods, this method uses randomly generated priors for sampling instead of class ratios. [PERSON] et al. [15] combined dynamic ensemble selection with MultiRandBal in their HAR-MI method, maintaining the diversity of data and classifiers, and achieving higher performance with a small number of classifiers. In this paper, we intend to borrow the idea of random balance strategy to determine the number of samples per class based on the class proportion of each data chunk. In addition, using spectral clustering to post-cluster the class instances of each chunk, which can better preserve the original data distribution and avoid the problem of information loss due to under-sampling [16]. Algorithm-level classification methods primarily involve ensemble learning techniques. Ensemble learning is an effective approach for addressing multi-class imbalance problems, as it generally outperforms single classifier methods. Hybrid ensembles, which combine ensemble learning methods (such as Bagging or Boosting) with data resampling techniques, create a balanced training set for the base learner [17]. This combination improves the performance of the ensemble classifier when classifying multi-class imbalanced data. [PERSON] et al. [2] proposed two ensemble methods based on resampling, namely Multi-class Oversampling Online Bagging (MOOB) and Multi-class Under-sampling Online Bagging (MUOB). These algorithms adaptively adjust the weights of each class of samples in the data stream using Poisson distribution to determine the sampling rate. They can directly process multi-class data online and consider the algorithm's performance in both stationary and variable data streams. [PERSON] et al. [18] introduced Improved SMOTE Online Ensemble (ISOE) and Improved Online Ensemble (IOE) methods based on SMOTE, which dynamically balance the training set. ISOE processes data instances through a sliding window and sets a recall-based rate parameter as a sampling threshold to sample data with SMOTE and train the ensemble after sampling. In IOE, only the rate parameter is retained, and minority classes are oversampled using recall-based class weights. [PERSON] et al. [19] proposed a method based on a weighted ensemble for classification and handling class imbalance problems, called Weighted Ensemble with one-class Classification and Oversampling and Instance selection (WECOI).