# An Adaptive Active Learning Method for Multiclass Imbalanced Data Streams with Concept Drift
## 3 The Proposed AdaAL-MID Algorithm  
### Motivation  
Because of the continuous developments in the field of data stream mining, many algorithms have been proposed in recent years for learning from data streams. However, the issues of multiclass imbalance and concept drift within data streams have not been widely studied, especially when these two phenomena occur simultaneously. Additionally, most algorithms addressing such issues assume that labels for all instances in the data stream are immediately available (i.e., supervised learning algorithms), overlooking the problem of labels potentially not arriving in a timely manner. To address the additional challenge of limited labels, researchers have turned their attention to active learning [28; 29; 30] and learning from data streams under limited label budgets. Existing active learning solutions involve selecting a finite number of instances for labeling within a fixed budget, which can be considered as uniform allocation of the budget across the data stream. However, in scenarios with concept drift, classifiers need to swiftly adjust during drift periods to adapt to new concepts. However, under a fixed budget, it is not possible to ensure that instances of new concepts are learned in a timely manner. Therefore, this paper proposes a dynamic label budget adjustment strategy for scenarios with concept drift, aiming to learn from data streams containing concept drift, thereby reducing the impact of concept drift on classifiers and accelerating recovery. The key to active learning is to find the most important instances for labeling and to explore the instance space as much as possible. In the case of a limited label budget, developing a well-designed label request strategy is pivotal for enhancing the performance of active learning. Most active learning methods use a mixed strategy, where the core of the mixed strategy is the uncertainty strategy. The uncertainty strategy aims to select instances that are most uncertain or most representative in predictions, typically those near the decision boundary. Existing methods mostly determine whether to request labels by comparing the uncertainty measures of instance predictions with a threshold. However, most of them consider only one measure, namely, the difference between the probability of the most predicted class and the second most predicted class, which is not comprehensive for identifying representative instances. Additionally, they use original thresholds in comparisons, thus failing to emphasize the importance of new instances at concept drift points. Therefore, this paper proposes a hybrid label request strategy, including an uncertainty strategy based on a dual-margin dynamic threshold matrix and a random strategy. The uncertainty strategy combines two predictive uncertainty measures, complementing each other to better identify instances with high information content in the data stream. Thisincreases the uncertainty threshold under a dynamic labeling budget, favoring a higher selection probability for instances during concept drift and for minority class instances. Learning from multiclass imbalanced data streams is also a major challenge, as minority classes are difficult to classify correctly because of their insufficient representation. The most common approach to address such issues is to combine resampling with online ensembles, but previous methods did not consider label budgets during oversampling. Theoretically, with lower budgets, fewer instance labels are accessible in the data stream; hence, the oversampling factor should be higher. Additionally, existing methods consider only class proportions when performing oversampling, meaning higher levels of oversampling are applied only to minority class instances. They overlook the classifier's own classification performance, even though the classifier may have poor performance on majority class instances.