## 2 Related Works
### Concept Drift Detection Methods  
Concept drift is an important factor affecting the performance of classification models. Literature [13] divides concept drift detectors into three categories: (1) Error rate-based methods: These methods monitor the online error rate of the base classifier. If the error rate is significant changes will trigger a drift warning. DDM [3] and EDDM [4] are representatives of this group; (2) Distribution monitoring methods: This type of algorithm mainly monitors changes in data distribution. Significant differences in data distribution will be labeled as concept drift, and most unsupervised methods fall into this category; (3) Multiple hypothesis testing: This type of method uses multiple hypothesis tests to detect concept drift in different ways. Error rate is a commonly used metric in concept drift detection research. This type of drift detector uses the classifier accuracy results as the basis for judging the occurrence of drift, and uses experience or statistical theory to judge significant changes in accuracy to issue drift alarm. This idea is also the focus of this study. DDM [3] is a classic drift detection method based on error rate. This algorithm is based on binomial distribution and defines two thresholds: warning and drift. The online error rate \(p\) and standard deviation \(s\) are detection metrics, by adjusting confidence intervals to detect concept drift. EDDM [4] uses the distance between error rates as a metric to enhance the detection ability of gradual drift. The Reactive Drift Detection Method (RDDM) [14] uses an explicit mechanism to discard older instances based on DDM, thus improving the performance loss of DDM. After experimental verification, RDDM has a faster detection speed and higher overall accuracy than DDM. Similar to the idea of error rate monitoring, CusumDM [15] is based on the principle of Cumulative Sum (Cusum), the algorithm monitors the changes in cumulative sum, and uses the significant change in cumulative sum as the basis for judging the occurrence of drift. Drift detection methods based on error rates are often combined with sliding window mechanisms. ADWIN [5] is a classic window mechanism detector. This algorithm combines adjoining windows with sub-window mechanisms. When there is a significant difference between the sub-window means in the new window, discard old windows when differences are noted. FHDDM [6] is based on a single window mechanism and judges concept drift by comparing the difference between the window observation mean and the expected mean. The significant difference between the two means illustrates the occurrence of concept drift. This algorithm determines the significant difference based on Hoeffding inequality. MWDDM_H [7] is also based on Hoeffding's inequality and extends the window into a superimposed window to improve the speed of gradual drift detection. At the same time, the author proposes a multi-level weighted strategy, which adopts a weak weighted strategy  
Figure 2: The process of data distribution changes in four types of concept drift. in the stable phase and a strong weighted strategy in the warning phase, thereby further improving the speed of drift detection. MWDDM_H ranks among the top in terms of drift detection speed among current drift detectors, but it comes at the cost of a higher false positive rate. The primary goal of drift detection research is to help classification models maintain high accuracy. Both slower detection speeds and higher false positive rates can adversely affect the performance of classification models. Therefore, balancing detection speed and false positive rate is crucial for drift detectors. Achieving a good balance is essential to ensure the optimal performance of classification models, and addressing this issue is one of the key focuses of our research. Error rate-based drift detection methods are often based on various statistical tests, such as FHDDM and MWDDM_H based on the Hoeffding test.