# Weakly Supervised U-Net with Limited Upsampling for Sound Event Detection
## 4 Experiments
### Random Onset Synthetic Policy  
Table 11 shows the audio tagging and sound event detection results of the dataset synthesized by the random onset policy in Table 1. The maximum event length was set to be 2.0 s, and the mean and standard deviation of the event length were 1.7 and 0.51 s, which were the same as the original synthetic policy. In the original policy, the event onset and offset times were configured so that there should not be any overlap. However, the random onset policy does not have such requirements, so there were significantly many overlaps among the events. In Table 11, U-Net with GWRP showed 48.1 tagging and 35.6 detection F1 scores, which were much lower than the 62.9 and 49.2 for the original policy. By using the proposed LUU-Net, the F1 scores were 49.8 and 37.1, which were 1.7 and 1.5 higher than those of U-Net. U-Net showed good recall scores in both the tagging and detection tasks, but other measures were lower than LUU-Net. The number of steps increased from 8.67 to 27.26, so LUU-Net was 3.14-times faster than U-Net. GWRP showed a good F1 score, which was similar to MEX, but the iteration speed was about 30% slower because of sorting. The last 3 rows use the proposed GTAP with \(\alpha\in\{0.2,0,-0.4\}\). The tagging F1 scores were 50.5, 50.0, and 52.1, respectively. The best and the second-best F1 scores were obtained with \(\alpha=-0.4\) and 0.2, respectively, which were the same as the original policy. However, the F1 score difference was much less: original policy 4.3 and random onset 1.6. The detection F1 scores were 40.8, 40.0, and 34.0, respectively. The sum of the F1 scores of the tagging and detection tasks was 91.3 with \(\alpha=0.2\) and 86.1 with \(\alpha=-0.4\). Therefore, the value that showed a higher sum of F1 scores and well-balanced performances in the tagging and detection tasks was \(\alpha=0.2\). Figure 10 shows the sound event detection examples for the mixtures generated by the random onset synthetic policy. Various models and various global pooling methods were applied. In the CNN detection example in (c), there were many false detections scattered in the segmentation map. As shown in (d,e), U-Net and LUU-Net provided relatively clean detection results, but there were still many false detections. In (f,g), using AlphaMEX and MEX, it can be seen that the false detections mostly disappeared. In (h), using the proposed GTAP with \(\alpha=0.2\), it provided very clean detection results. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Pooling** & \multicolumn{3}{c}{**AT Task**} & \multicolumn{3}{c}{**SED Task**} & \multirow{2}{*}{**\#Step/s**} \\  & **Method** & **mPrc** & **mRcl** & & & & & & \\ \hline \multirow{5}{*}{CNN} & GWRP & 36.9 & 60.9 & 42.6 & 31.0 & 37.0 & 30.8 & 3.66 \\ \cline{2-9}  & \(\text{GTAP}_{\alpha=0.2}\) & 30.6 & 66.1 & 40.4 & 61.7 & 13.5 & 20.7 & \\ \cline{2-9}  & \(\text{GTAP}_{\alpha=0}\) & 28.4 & 68.4 & 38.7 & 54.9 & 17.0 & 24.2 & 4.54 \\ \cline{2-9}  & \(\text{GTAP}_{\alpha=-0.4}\) & 39.1 & 33.9 & 32.0 & 19.8 & 30.1 & 20.2 & \\ \hline \multirow{5}{*}{U-Net} & GWRP & 39.4 & 66.7 & 48.1 & 29.2 & 49.2 & 35.6 & 8.67 \\ \cline{2-9}  & \(\text{GTAP}_{\alpha=0.2}\) & 38.0 & 65.7 & 46.8 & 48.1 & 36.1 & 39.6 & \\ \cline{2-9}  & \(\text{GTAP}_{\alpha=0}\) & 35.5 & 66.6 & 45.1 & 43.4 & 38.5 & 39.6 & 12.97 \\ \cline{2-9}  & \(\text{GTAP}_{\alpha=-0.4}\) & 53.7 & 50.8 & 50.7 & 26.7 & 45.8 & 32.5 & \\ \hline \multirow{5}{*}{LUU-Net} & AlphaMEX & 43.9 & 60.7 & 49.4 & 51.2 & 19.5 & 26.7 & 21.13 \\ \cline{2-9}  & MEX & 40.8 & 64.2 & 48.6 & 35.6 & 41.9 & 37.2 & 32.33 \\ \cline{1-1} \cline{2-9}  & GWRP & 42.9 & 64.5 & 49.8 & 34.3 & 43.7 & 37.1 & 27.26 \\ \cline{1-1} \cline{2-9}  & \(\text{GTAP}_{\alpha=0.2}\) & 43.4 & 64.2 & 50.5 & 46.9 & 37.7 & 40.8 & \\ \cline{1-1} \cline{2-9}  & \(\text{GTAP}_{\alpha=0}\) & 42.3 & 65.0 & 50.0 & 42.3 & 39.7 & 40.0 & 33.64 \\ \cline{1-1} \cline{2-9}  & \(\text{GTAP}_{\alpha=-0.4}\) & 51.3 & 55.7 & 52.1 & 28.4 & 45.6 & 34.0 & \\ \hline \hline \end{tabular}
\end{table}