## 4 Discussion  
Before discussing the results obtained for individual methods, it is necessary to explain how to interpret the various metrics and their combinations. The low macro-averaged scores across all methods shown in Table 2 can have different causes. To understand these, we will build upon the discussion of the importance of jointly analyzing different metrics, given in Section 2.3.3, and focus on the various reasons for false-positive or false-negative results in the following. For instance, a low F1 score may be due to an insufficient anomaly score, which prevents the detection of the true anomaly, or it may be due to a poor choice of threshold, leading to an increase in false positives. Figure 10 illustrates this using different results for the autoencoder model. A high F1 score and a UCR score of one at the same time indicate the successful detection of the true anomaly without any--or with very few--false-positive results, depending on the value of the F1 score, as shown in Figure 10a,d. On the other hand, a low F1 score and a UCR score of 0, as shown in Figure 10b,f, indicate that the anomaly was not detected due to an insufficient anomaly score. In this case, a high AUC ROC value may indicate that the anomaly could have been detected with a low anomaly score, but the threshold was set too high, resulting in the subsequence not being classified as anomalous. Figure 10b,f also demonstrate that AUC ROC is generally not a suitable measure to assess the quality of  
Figure 9: Comparing AUC ROC, F1- and UCR score of the baseline RRCF using the raw time series as input (RRCF@points) to RRCF applied on sliding window statistics (RRCF@sequences). (**a**) Macro-averaged performance metrics for each method. The error bars indicate the standard deviation caused by random effects over six repetitions of the experiment. (**b**) 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 timeseries containing that type is shown in parenthesis. results in highly unbalanced problems in a meaningful way. In both cases, the anomaly score is not suitable for detecting the true anomaly. A high F1 score but a UCR score of 0, as shown in Figure 10c, indicates that the true anomaly was detected, but a false-positive result has a higher anomaly score. A UCR score of one but a low F1 score signifies the correct detection of the true anomaly with the highest anomaly score, but false-positive or false-negative results lead to a low F1 score. Figures 11 and 12 illustrate the different reasons for this situation, which can be caused by a poor threshold value, as shown in Figure 11b; or the detected anomaly's subsequence length being much longer, as in Figure 11a, or shorter than the ground truth label, as in Figure 12b. This leads to increased false-positive or false-negative results, respectively. A fourth case with this result occurs from the detection of a short anomaly within the 100 time steps tolerance, which is considered in the definition of the UCR score in Equation (3). This is shown in Figure 12a. Figure 10: Interpretation of results shown on examples of the autoencoder model. The top figure represents the time series with the true anomaly marked in red, while the bottom figure shows the anomaly score, with the pink horizontal line being the determined threshold and the predicted anomalies highlighted in green. (**a**) High AUC ROC, F1- and UCR scores indicate correct detections without or with very few false positives. (**b**) High AUC ROC but low F1- and UCR score indicate an insufficient anomaly score and/or an insufficient threshold. (**c**) A high F1- but a low UCR score indicates the detection of the true anomaly but a false positive has a higher anomaly score. (**d**) Low AUC ROC but high F1- and UCR score indicate a correct detection of the labeled anomaly without or with few false positives but the detected subsequence is shorter than the true anomaly.