# An Adaptive Active Learning Method for Multiclass Imbalanced Data Streams with Concept Drift
## 1 Introduction  
With the continuous development of the information industry, a large number of data streams have emerged in real-world applications, containing valuable information yet to be mined, such as network intrusion detection [1], fault detection [2], and air-quality prediction [3]. Extracting valuable information from the data streams generated by these applications is an interesting yet challenging and arduous task. Among them, data stream classification has become a prominent research direction in the field of machine learning. A common challenge in data stream classification is concept drift [4], which refers to the inconsistency in data distribution over time, severely affecting the stability of data stream classification. Another challenging issue is multiclass imbalance, where the class distribution in a data stream is skewed [5]. Meanwhile, the class proportions in a data stream may change over time. This change may combine with concept drift, making learning from data streams even more challenging. Figure 1 shows two types of data stream changes. Figure 1 represents the original data stream, Figure 1 indicates that the class distribution in the data stream remains unchanged after concept drift, and Figure 1 shows that the class proportions are reversed after combining concept drift with changes in class distribution. The combined challenge of concept drift and multiclass imbalance in data stream classification presents new requirements for machine learning algorithms. In this scenario, algorithms must not only handle the imbalanced state of data stream distribution but also promptly identify the occurrence of concept drift, particularly within minority classes. Sofar, some studies have addressed the issue of classifying imbalanced data streams with concept drift, but most have focused on binary imbalanced classification. Handling the concept drift problem in multiclass imbalance is more challenging because the definitions of majority and minority classes are not fixed in different scenarios, and the roles of different classes may change after concept drift. For example, in Figure 1a, the second largest class is the minority class relative to the largest class, but it is the majority class relative to the smallest class. After concept drift, the previous minority class becomes the majority class, as shown in Figure 1c. Ensemble-based methods have gained extensive attention from researchers in recent years [6]. By combining multiple weak classifiers into a stronger ensemble classifier, they often achieve better performance than single classifiers. The classic leveraging bagging (LB) [7] algorithm uses adaptive window (ADWIN) [8] to detect concept drift in data streams and update the ensemble accordingly. Although LB does not have an explicit mechanism for handling imbalance, its fixed-rate bagging sampling has shown adaptability in handling imbalanced data streams in existing studies. Multiclass oversampling online bagging (MOOB) [9] combines oversampling techniques with online ensembles, determining the sampling rates based on class weights to directly handle multiclass imbalanced data streams. However, it does not effectively address concept drift. The robust online self-adjusting ensemble (ROSE) [10] also adopts the idea of online bagging based on class weights and combines the use of background ensembles to address the combined issue of concept drift and changing class imbalance ratios. In the oversampling strategies of the above algorithms, the sampling rate is determined only by fixed values or class proportions, ignoring the classifier's own performance and, thus, cannot effectively focus on difficult-to-classify instances in the data stream. Additionally, the majority of existing algorithms presuppose unrestricted access to the labels of all instances within the data stream throughout the learning process (i.e., in a supervised environment), but this is unlikely in real-world applications due to the high cost of obtaining all instance labels.