## 4 Experiment Evaluation
### Experimental Analysis
#### 4.3.2 Drift Detection Performance Analysis  
This section will provide a detailed analysis of the drift detection performance of various drift detection algorithms, including VFDDMs, focusing on detection delay, true positives, and false positives. Table 5 presents the performance of VFDDMs and other comparison algorithms on the sudden drift datasets. From this table, it can be observed that regardless of the base classifier or the type of sudden drift dataset, VFDDMs successfully detected all configured drift positions with a true positive rate of 100%. Additionally, the false positive rate and detection delay remained at low levels. MWDDM, HDDM_W, BDDM, and VFDDMs exhibited shorter detection delays for concept drift in Sine and Mixed data streams, followed by MDDM, WMDDM, and FHDDM. It can be observed that drift detectors with shorter detection delays are generally based on instance weighting strategies. Among these, MWDDM applies the highest level of weighting, resulting in the lowest drift detection delay in abrupt drift data streams. However, excessive weighting can also lead to an increase in false positive rates, as shown in the table where MWDDM exhibits a high false positive rate. This indicates that an excessive focus on achieving faster detection speeds inevitably compromises the false positive rate, a point also demonstrated by HDDM_W. Among the drift detectors with faster detection speeds, VFDDMs show relatively better performance in terms of false positive rates. For example, in the Mixed dataset, VFDDMs and BDDM demonstrated significantly lower false positive rates than MWDDM and HDDM_W. BDDM, based on the Bhattacharyya distance, issues a drift alert when the Bhattacharyya distance between the current and historical optimal moment's instance distributions exceeds a threshold. BDDM also employs an instance weighting strategy to further enhance detection speed. VFDDMs outperformed BDDMs in terms of accuracy, highlighting their superiority. In the comparison among algorithms based on the same statistical test, VFDDM_H exhibits a larger detection delay compared to MWDDM. This is because MWDDM employs relatively large weighting parameters during the warning phase. In this study, the weighting weight during the warning phase is set to 5, which results in significant differences in the weights between new and old instances. Consequently, when the data stream encounters drift risks, the speed of drift detection increases. However, this comes at the cost of higher false positive rates, especially evident in the Mixed dataset where the false positive rate is 9 times that of VFDDM_H. This indicates that VFDDM_H demonstrates a dual advantage of low false positive rates and low latency in detecting sudden drifts. VFDDM_M and MDDM exhibit nearly identical performance in both true positive and false positive rates. However, VFDDM_M surpasses MDDM in detection delay. This is because MDDM employs fixed weighting parameters, whereas VFDDM_M adjusts its weighting strategy based on variance. In relatively stable data streams during non-drift states, VFDDM_M adopts a more lenient weighting strategy, thus enhancing drift detection speed. In terms of accuracy comparison, VFDDM_M also outperforms MDDM in average rankings on the sudden drift datasets. In summary, it can be concluded that VFDDM_M outperforms MDDM in detecting sudden drifts. The same rationale applies to WMDDM. VFDDM_M exhibits lower latency across all four sudden drift conditions. It only has slightly higher false positive rates than WMDDM on the HT-Mixed dataset. Additionally, VFDDM_K exhibits the highest detection delay among VFDDMs. This is because the Kolmogorov test cannot weight data instances, thus failing to reflect differences in importance among them. As a result, its performance in terms of detection delay is not as good as VFDDM_H and VFDDM_M. However, its advantage lies in relatively lower false positive rates, and the delay rate is significantly improved compared to FHDDM, which also lacks weighting.