## 3 Results
### Performance Analysis by Anomaly Type  
The second area of interest in this study is the differences between the analyzed methods to detect certain types of anomalies. Therefore, we aggregated our results based on the 16 anomaly classes described in Section 2.2.2. The results are shown in Figure 6.  
The anomaly that was detected by all methods except RRCF is the \"steep increase\" anomaly shown in Figure 7a. This anomaly can be found in two time series of the UCR Anomaly Archive which represent the same data but were distorted in one case, which is shown in Figure 7a. According to the UCR score, MDI and MERLIN detect this anomaly in every repetition of the experiment with the highest UCR score. As both methods are deterministic, it is expected that the results do not differ between multiple runs. AE finds this anomaly in 11/12 cases. GANF and TranAD detect the \"steep_increase\" anomaly only in the undistorted version of the time series. RRCF and TranAD detect the \"smoothed increase\" anomaly shown in Figure 7b where a normally steep increase was smoothed by increasing the number of different values in one cycle. For RRCF, this is also the only type this method can find. While RRCF has a UCR score below 0.05 for 14/16 anomaly types, it  
Figure 5: Distribution of results for the AUC ROC, F1 Score and UCR score aggregated by model class. The dashed lines encode the quartiles of the distributions. The area under the peaks around 1 is larger for the Classical ML methods for F1- and UCR score. detects the \"smoothed increase\" anomaly with a UCR score of 1.0 and an F1 score of 0.86. TranAD finds this anomaly in 5/6 cases. For the remaining anomaly types, the results are more diverse. GANF, MERLIN and TranAD find the majority of the 23 \"outlier\" anomalies, with GANF and TranAD performing better than MERLIN on this type. The 23 \"noise\" anomalies, however, are detected by AE, GANF and MDI, with MDI finding every single one with the highest anomaly score. From a method point-of-view, MDI achieves UCR scores above or equal to 0.5 for the classes \"time warping\", \"steep increase\", \"sampling rate\", \"noise\", \"missing peak\", \"local peak\" and \"local drop\". For the \"noise\"-type anomalies, the F1 score is above 0.5 as well. The results for AE tend to look similar to those of MDI, but the scores for AE are mostly a few points lower; therefore, AE has a UCR score above 0.5 only for \"noise\" and \"steep increase\", with the latter having an F1 Score of 0.92. MERLIN shows a UCR score above or equal to 0.5 for \"steep increase\", \"outlier\", \"missing drop\", \"local peak\", \"frequency change\" and \"amplitude change\" anomalies, making \"steep increase\" and \"missing peak\" the only classes in which both methods have a UCR score above or equal 0.5. In terms of F1 Score, MERLIN scores above 0.5 for the classes \"noise\" and \"steep increase\". GANF is the best-performing method regarding the anomaly types \"time warping\" and \"outlier\"  
Figure 6: The heatmaps show the macro-averaged AUC ROC, F1 and UCR scores for the 16 annotated anomaly types over six repetitions of the experiment. Next to the anomaly type, the number of times series containing that type is shown in parenthesis. The standard deviations resulting from random effects can be found in Appendix A.3. Figure 7: Time Series containing “steep increase” (**a**) and “smoothed increase” (**b**) anomalies. (**a**) Overview (top) and detail (bottom) plot of the distorted time series containing the “steep increase” anomaly. The ground truth anomaly is highlighted in green. (**b**) Overview (top) and detail (bottom) plot of the time series containing the “smoothed increase” anomaly. The ground truth anomaly is highlighted in green, while the sections where the smoothing is visible are highlighted in red. with UCR scores of 0.75 and 0.78 and F1 scores of 0.78 and 0.45, respectively. Additionally, GANF detects at least half of the anomalies with the type \"steep increase\" and \"noise\".