## 4 Experiment Evaluation
### Experimental Analysis
#### 4.3.1 Base Classifiers Performance Analysis
WMDDM, based on the McDiarmid inequality and instance weighting, also has a theoretical time complexity of \(O(n)\) per window slide. However, in practical implementation, WMDDM incurs additional computational overhead for calculating the McDiarmid bound and dynamically generating weight factors during each window slide. Therefore, the theoretical time complexity of WMDDM is higher than that of MWDDM. It is notable that the overall time efficiency of VFDDM_H is higher than the MWDDM algorithm, belonging to the same Hoeffding test category, demonstrating VFDDM_H's good time performance. Furthermore, VFDDM_M exhibits better time consumption performance compared to the WMDDM based on similar tests. WMDDM's weighting method uses the Sigmoid function, controlled by parameters \(\lambda\) and \(\theta\), resulting in higher computational overhead than VFDDM_M. This analysis demonstrates that the proposed VFDDM possesses excellent time consumption characteristics. Finally, we compiled the ranking statistics for all algorithms on accuracy and CPU Times across all synthetic datasets, as shown in Figure 9. In Figure 9, the horizontal axis represents the ranking. Under the same horizontal coordinate, a larger area occupied by an algorithm indicates that the algorithm achieved that ranking more frequently in that metric. From the left graph, it can be observed that VFDDM demonstrates outstanding classification accuracy. Among the top ranks, VFDDMs' classification accuracy occupies a significant proportion, indicating the general applicability of VFDDM across datasets. Additionally, from the right graph, it can be seen that VFDDMs also perform well in terms of time consumption, with a considerable proportion of cases showing high time efficiency rankings. Compared to other methods using the same test, VFDDMs also demonstrate strong competitiveness. This part of the results demonstrates the high efficiency of our variance quick estimation strategy. In summary, we assert that VFDDM possesses outstanding classification accuracy and time efficiency. Table 4 shows the performance of accuracy and average drift alert count for four real datasets using NB and HT classifiers. Numerous studies indicate that concept drift in real datasets is unknown [16], which also limits the evaluation metrics for assessing drift detectors on real datasets. Due to the unknown drift locations, metrics such as delay, true positives, false positives, and false negatives, based on drift positions, cannot be determined. Therefore, this study focuses on discussing two metrics: classification accuracy and drift warning count, and analyzes the performance of drift detectors using these two metrics, while exploring the factors affecting classification accuracy on real datasets. From Table 4, it can be observed that the DDM and HDDM series algorithms perform well in both NB and HT classifiers. The DDM algorithm performs best in NB-Covertype, HT-Covertype, and HT-Spam, but this performance may not solely be attributed to the drift detector. In fact, in a study by [PERSON] et al. (2019), experiments were conducted on real datasets Electricity and Covertype, testing a learning strategy of periodically restarting the classification model, which resulted in better classification accuracy compared to drift detectors. [PERSON] et al. explained this phenomenon as being due to the existence of time dependency between data stream instances, as also mentioned in the literature ([PERSON] et al., 2019).