# Weakly Supervised U-Net with Limited Upsampling for Sound Event Detection
## 5 Discussion
### Further Analysis of LIU-Net Results  
Figures 13 and 14 show that the proposed LUU-Net and GTAP improved both the audio tagging and sound event detection performances over the conventional U-Net and GWRP. However, it is difficult to choose an optimal value for the hyperparameter \(\alpha\), so that it works best with all the experimental conditions. Therefore, we made a detailed analysis of the experimental results of LUU-Net with GTAP to find a relationship of the hyperparameter \(\alpha\) and audio mixing conditions.  
Figure 15 shows the AT and SED results of LUU-Net only. All the performance metrics, precision, recall, and F1 scores are drawn. For the mean precision, AT, \(\alpha=-0.4\) was the best among the three \(\alpha\) values for all mixing conditions. For the mean recall, AT, \(\alpha=0\) was the best and \(\alpha=-0.4\) the worst. Combining the precision and recall, the F1 scores of \(\alpha=-0.4\) were overall the best. In the SED tasks, the opposite observation was made. \(\alpha=-0.4\) is the worst in the precision scores and was the best in recall scores. The combined F1 scores  
Figure 14: Sound event detection (SED) performance comparison with various deep learning models, pooling methods, and training data generation policies by average F1 scores.  
Figure 13: Audio tagging (AT) performance comparison with various deep learning models, pooling methods, and training data generation policies. Average F1 scores drawn; the x-axis is pooling methods; lines are CNN, U-Net, and LUU-Net. The individual charts are the results with the original, longer clipping, random onsets, and mixed synthetic policies.  
were almost the same for all three \(\alpha\) values. If \(\alpha=-0.4\) in Equation (7), more output map values were chosen to compute the class label predictions for the whole clip in the AT tasks. Having more output map components, the class activation information was kept more in the pooling, so higher precision was obtained. For the SED tasks, the performance metrics were computed as segment-based, so more output map components would lead to higher false positive rates. Therefore, lower precision is obtained by Equation (8). The opposite explanation can be applied to the lower recall scores on the AT tasks with \(\alpha=-0.4\) and the higher recall scores on the SED tasks. In Equation (9), reducing false negatives is directly related to higher recall scores. A larger amount of output maps in GTAP with \(\alpha=-0.4\) would lead to less inclusion of inactive outputs, so higher recall scores were observed in the SED tasks computed in a segment-based manner.  
In summary, the proposed LUU-Net with GTAP was better than the conventional U-Net with GWRP in most cases. The proposed GTAP can be configured to provide versatile choices of target applications by varying a single hyperparameter \(\alpha\). A smaller threshold by a negative \(\alpha\) value is suggested when higher audio tagging performance is required, i.e., the identities of the audio sources are more important. When a higher recall rate in tagging or better sound event detection performance is required, choosing \(\alpha=0\) is suggested.