# Weakly Supervised U-Net with Limited Upsampling for Sound Event Detection
## 4 Experiments
### Performance Evaluation Metrics  
The output of binary classifiers is _true_ or _false_, where _true_ means that the corresponding event is active and _false_ means being inactive. The predicted output is compared to the ground truth, and it is indicated as true positive (TP), true negative (TN), false positive \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Name** & **Input Shape** & **Output Shape** & **Output Size** \\ \hline \multirow{6}{*}{encoder} & \(Conv(16)\) & \((312,64,1)\) & \((312,64,16)\) & \multirow{6}{*}{79,872} \\  & \(AvgPool(2,2)\) & \((312,64,16)\) & \((156,32,16)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv(16)\) & \((156,32,16)\) & \((156,32,32)\) & \\ \cline{1-1} \cline{2-5}  & \(AvgPool(2,2)\) & \((156,32,32)\) & \((78,16,32)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv(64)\) & \((78,16,64)\) & \((78,16,64)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv(128)\) & \((39,8,64)\) & \((39,8,128)\) & \\ \cline{1-1} \cline{2-5}  & \(Dropout2D(0.2)\) & \((39,8,128)\) & \((78,8,64)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv21(32)\) & \((78,8,128)\) & \((156,8,32)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv21(16)\) & \((156,8,64)\) & \((312,8,16)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv1(1,C)\) & \((312,8,32)\) & \((312,8,C)\) & 2,496\(\times\)C \\ \hline \multicolumn{5}{l}{total output size} & \multicolumn{3}{c}{299,520 + 2,496\(\times\)C} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The proposed LUU-Net (U-Net with limited upsampling) design for sound event detection. The encoder blocks are identical to U-Net, but the decoder used _DeConv21_, which upsamples along the time axis, but not along the frequency axis. Therefore, the vertical size does not change in the decoder, all 8. In the _Concat_ layers, \(AvgPool(1,s)\) is applied, where \(s\in\{2,4,8\}\) to match the vertical lengths of the encoder and decoder outputs. \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Name** & **Input Shape** & **Output Shape** & **Output Size** \\ \hline \multirow{6}{*}{encoder} & \(Conv(3,16)\) & \((312,64,1)\) & \((312,64,16)\) & \multirow{6}{*}{79,872} \\  & \(AvgPool(2,2)\) & \((312,64,16)\) & \((156,32,16)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv(3,16)\) & \((156,32,16)\) & \((156,32,32)\) & \\ \cline{1-1} \cline{2-5}  & \(AvgPool(2,2)\) & \((156,32,32)\) & \((78,16,32)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv(3,64)\) & \((78,16,32)\) & \((78,16,64)\) & \\ \cline{1-1} \cline{2-5}  & \(AvgPool(2,2)\) & \((78,16,64)\) & \((39,8,64)\) & 19,968 \\ \cline{1-1} \cline{2-5}  & \(Conv(3,128)\) & \((39,8,64)\) & \((39,8,128)\) & \\ \cline{1-1} \cline{2-5}  & \(Dropout(0.2)\) & \((39,8,128)\) & \((39,8,128)\) & \\ \cline{1-1} \cline{2-5}  & \(Dropout(0.2)\) & \((39,8,128)\) & \((39,8,128)\) & \\ \hline \multirow{6}{*}{decoder} & \(DeConv22(3,64)\) & \((39,8,128)\) & \((78,16,64)\) & \multirow{6}{*}{79,872} \\  & \(Concat\) & \((78,16,64\times 2)\) & \((78,16,64)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv22(3,32)\) & \((78,16,128)\) & \((156,32,32)\) & \\ \cline{1-1} \cline{2-5}  & \(Concat\) & \((156,32,32\times 2)\) & \((78,16,64)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv22(3,32)\) & \((78,16,128)\) & \((156,32,32)\) & \\ \cline{1-1} \cline{2-5}  & \(Concat\) & \((156,32,32\times 2)\) & \((156,32,32)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv22(3,16)\) & \((156,32,64)\) & \((312,64,16)\) & \\ \cline{1-1} \cline{2-5}  & \(Conv22(3,64)\) & \((312,64,32)\) & \((312,64,32)\) & 19,968\(\times\)C \\ \hline \multicolumn{5}{l}{total output size} & \multicolumn{3}{c}{738,816 + 19,968\(\times\)C} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: U-Net design for sound event detection. It is divided into the encoder and decoder. The encoder consists of 3 convolutional blocks with \(2\times 2\) average pooling, followed by a convolutional layer with dropout. The decoder is composed of 3 deconvolutional blocks with skip connections to the encoder feature maps, and the final \(1\times 1\) convolutional layer is for event classification.