# Benchmarking Change Detector Algorithms from Different Concept Drift Perspectives
## 5 Experimental Results
### Detection Performance  
The initial results presented in this study relate to the detection of abrupt drifts. Figure 2 displays F1 score results for varying quantities of drifts, ranging from 1 to 5. It is evident that the algorithms achieved a maximum performance with an equivalent F1  
Figure 1: Stream of data over time, acceptance interval, no drift area over time and delay of detection represented.  
score for a quantity of 1 of abrupt drifts, as shown in Figure 2. However, when the number of drifts was increased to 2, the HDDMW, HDDMA, and DDM algorithms consistently displayed reduced F1 scores, whereas the EDDM algorithm yielded a markedly inferior score. Notably, the algorithms exhibited a decreasing F1 score as the number of drifts increased. Nevertheless, the HDDMW algorithm maintained the most suitable average F1 score, while the EDDM algorithm yielded the least favorable average score.  
For incremental drifts, unlike abrupt drifts, only the EDDM algorithm yielded a good result, with an F1 score close to the maximum possible. With a significant discrepancy, HDDMW had the second-best performance, while HDDMA and DDM obtained much lower and almost negligible scores. In Figure 3, it is possible to compare the algorithms' performances regarding incremental drifts.  
As we only used one incremental drift per stream, unlike abrupt drifts, the figure presents the F1 score result for only one unit of drift.  
The detection performance for gradual drifts is presented in Figure 4. When the amount of drifts is 1 or 2, all algorithms yielded an identical performance, as evidenced by their respective F1 scores close to 1. However, when the number of drifts is increased to 3 or 4, the HDDMW, DDM and EDDM algorithms maintained their performance levels, while the HDDMA algorithm exhibited a decrease in its average F1 score. For five drifts, all four algorithms achieved equitable performance levels, exhibiting F1 scores of approximately 0.8. The overall results show that HDDMW, DDM, and EDDM algorithms showed equivalent performances, while the HDDMA algorithm demonstrated an inferior performance.  
We evaluate the drift detection performance in terms of F1 score based on a statistical analysis grounded on the non-parametric [PERSON] statistical test [PERSON] (1984) to determine any significant differences among EDDM, DDM, HDDMW, and HDDMA with 300 streams. Following the [PERSON] test, we performed a Nemenyi post hoc test [PERSON] (1984) with a significance level of 0.05. The null hypothesis posits that the drift detectors' performances are comparable based on the average F1 score per stream. If the null hypothesis is rejected, the Nemenyi post hoc test can be used. This test establishes that the performance of two detectors is significantly distinct if the average ranks differ by at least a critical difference (CD) value. Figure 5 shows the CD diagram for the F1 score. Particularly, we assume that there are no significant differences between HDDMA and DDM. All other differences are  
Figure 2: F1 score of detection methods when dealing with abrupt drifts.