# An Adaptive Active Learning Method for Multiclass Imbalanced Data Streams with Concept Drift
## 1 Introduction
Therefore, classifying data streams under a limited label budget has become a new problem and challenge. To address this issue, researchers have begun exploring active-learning-based methods [11]. Active learning can effectively address the limited label problem by requesting the most informative instance labels for model learning. The online active learning ensemble framework (OALEnsemble) [12] is based on a hybrid labeling strategy and constructs an ensemble classifier framework consisting of a stable classifier and multiple dynamically updated classifiers, effectively handling gradual and sudden drifts in data streams, but it does not address the imbalance problem. The recently proposed comprehensive active learning method for multiclass imbalanced data streams with concept drift (CALMID) [13] can handle both mixed concept drift and multiclass imbalance in data streams, selecting the most representative instances through a hybrid labeling query strategy based on an asymmetric marginal threshold matrix, providing more opportunities for minority classes. However, existing active learning methods only operate under a fixed label budget and do not effectively allocate the label budget, and higher label budgets and looser selection thresholds should be used at concept drifts. Figure 1: Multiclass imbalanced data streams with concept drift. (The gray shapes and lines represent instances and decision boundaries at time \(t\), while the red ones indicate the state at time \(t+1\) after concept drift. Different shapes represent instances of different classes). Learning from multiclass imbalanced data streams with concept drift is particularly challenging when operating under a limited label budget. To overcome the limitations of existing methods, this paper introduces an adaptive active learning algorithm tailored for multiclass imbalanced data streams experiencing concept drift. The primary contributions are as follows:  
1. A dynamic label budget strategy was designed for concept drift scenarios, using ADWIN to detect drifts and adaptively adjust the budget, allowing for the learning of more new instances at concept drifts and accelerating postdrift model recovery. 2. An uncertainty strategy leveraging a dual-margin dynamic threshold matrix was proposed, which, when combined with a random strategy, offers increased learning opportunities for minority class instances and crucial instances. 3. An adaptive sampling strategy for multiclass imbalanced data streams was proposed, and classifiers were updated online based on weighted ensemble ideas. This strategy tends to perform higher levels of oversampling for minority classes and difficult-to-classify instances. 4. Based on the above strategies, we propose an adaptive active learning algorithm. Various experiments were conducted to validate the algorithm's effectiveness and feasibility, including parameter sensitivity experiments, algorithm comparison experiments, nonparametric statistical analysis, and ablation studies. These experiments comprehensively compared existing supervised and active learning algorithms, providing detailed analysis.