## 2 Related Work
### Concept Drift Data Streams Learning Method  
Concept drift is one of the challenges frequently faced in data stream learning tasks. In concept drift data streams, the data distribution changes over time. [PERSON] et al. [7] described the generation of concept drift, which occurs when the joint probability distribution at two time points \(t\) and \(t+1\) changes, which is noted as \(P_{t}(X,y_{1})\
eq P_{t+1}(X,y_{2})\). Currently, according to the speed of drift change, it can be classified as sudden drift, gradual drift, incremental drift, and recurrent drift, as shown in Figure 1.  
The current concept drift data stream learning methods can be divided into active detection methods and passive adaptive methods [20]. Active detection methods usually use a window mechanism to deal with concept drift. The classic Leveraging Bagging (LB) [21] adapts to the current data stream's changing rate and automatically detects concept drift through the adaptive window (ADWIN) [22], but it does not include a mechanism for handling imbalanced data streams. Adaptive Random Forests (ARF) [23] modified ADWIN by using a lower threshold to detect warnings and drifts, and updating the ensemble by replacing the background tree when real drift occurs. ARF can detect and respond to concept drift more quickly, but at the cost of higher time and space complexity. The Comprehensive online Active Learning method for Multiclass Imbalance Data streams with concept drift (CALMID) [24] is the first algorithm to simultaneously handle mixed drift and varying multi-class imbalanced data streams, using ADWIN as the drift detector. Unlike the LB and ARF, CALMID will create and train a new base classifier with weighted samples from the initialized training sample sequence and add the new classifier to the ensemble when concept drift is detected. At the same time, CALMID assigns weights to samples according to their classification difficulty, improving the classifier's ability to classify difficult and minority class samples. Instead, Boosting-like Online Learning Ensemble (BOLE) [25] uses DDM [26] to detect and handle concept drift, setting additional parameters for DDM to further improve the ensemble's classification performance. In addition, BOLE adopts a higher error limit to accept ensemble classifier votes and experiments show that this strategy helps to improve classification accuracy. In passive adaptive methods, the performance of ensemble members is periodically evaluated, and the best classifiers in the ensemble are retained through dynamic updates during the learning process. Compared to active detection methods, passive adaptive methods can adaptively adjust classifier parameters according to the characteristics and changes of data streams after combining ensemble learning, and have better robustness for complex data streams [27]. The Online Accuracy Updated Ensemble (OAUE) [28] uses a chunk-based ensemble to weigh ensemble members with the final instances in each chunk, enabling rapid tracking of data changes, achieving higher classification accuracy, and adapting to various types of concept drift. The algorithm proposed in this paper is a passive adaptive method, which dynamically updates the ensemble classifier by observing the G-mean of each base classifier in the ensemble on data chunks.  
Figure 1: Concept drift types.