## 1 Introduction  
The difficulty of learning from streaming data with concept drift has increased attention in the area of online learning in recent years since this phenomenon happens in many real-time applications like predicting RUL [1, 2, 3] fault detection [4, 5, 6, 7, 8, 9], and risk management [10, 11, 12, 13, 14]. These applications generate continuous non-stationary data streams. The non-stationary nature of the stream causes a change in the statistical properties of data which leads to concept drift and class imbalance problems [15, 16]. The concept drift includes virtual drift, real drift, or hybrid drift [17]. Let us assume, at time \(t\), we have \(xt\) as an input vector for the Machine Learning (ML) model and \(yt\) as the corresponding target output vector. The virtual drift occurs when the distribution of input data \(pt(x)\) changes over time, but the posterior probability of the output \(pt(y\,|\,x)\), which shows the mapping relationship between \(xt\) and \(yt\), does not change with time. In simple words, the data, even after facing changes in input features, still represent the same target output. In real drifts, the posterior probability distributions \(pt(y\,|\,x)\) change over time, but this change is not caused by changes in \(pt(x)\). In contrast, hybrid drift is the combination of both virtual drift and real drift. These major types of drift are further classified into different types based on the frequency of underlying change with respect to time, which are sudden, incremental, gradual, and reoccurring [17; 18]. Figure 1 illustrates all four types of concept drift. The basic definition of each of the drift type is as follows: \begin{tabular}{l l} _Sudden:_ & _The concept of data abruptly changes from one concept to another_ \\ _Incremental:_ & _The concept of data incrementally changes with a constant speed from one concept to another_ \\ _Gradual:_ & _Similar to incremental drift but speed of change of one concept to another is not constant_ \\ _Reoccurring:_ & _The reoccurring drift disappears, and after a certain time period it reappears_ \\ \end{tabular}   
Besides the drift, the change may occur in class distribution, and the number of instances of each class may also vary, leading to a class imbalance problem [19; 20; 15; 21]. In case the stream is multi-class, the changes may occur in multiple classes simultaneously; this becomes more challenging for the drift detection methods to detect the new concept and adapt the existing ML model to the latest concept [22]. When data face a class imbalance problem, it signifies that the data are not equally distributed among classes. Some of the classes may have a very high number of instances called majority classes, and on the contrary, some have very skewed data or a smaller number of instances called minority classes. An ML model which is trained on imbalanced data produces biased results toward the majority class and misclassifies the minority class [23; 24; 25]. Along with that, in non-stationary multi-class streams, the majority class may become the minority class and vice versa [26]. Figure 1: Types of concept drift based on time [17; 18]. In situations where concept drift and class imbalance both appear concurrently, the drift detection method and data balancing approaches are affected as well as the ML classification model. There is a possibility that only the class imbalance ratio alters at some point in time, but the concept remains the same. In such a situation, the distribution-based drift detection method may trigger a 'drift' alarm which is a false alarm. Similarly, the error rate-based drift detection methods monitor the performance of the ML model and may also generate false alarms in case the performance of ML model is decreased due to class imbalance. Therefore, this study experimentally analyzes the existing drift detection methods in presence of multi-class imbalanced data.