# Sound Event Detection Using Derivative Features in Deep Neural Networks
## 5 Conclusions  
Recently, among the approaches for SED, CRNNs have been widely used and have exhibited better performance than other neural networks. In this study, we proposed the use of the first and second delta features of the log-mel filterbank to improve the performance of state-of-the-art CRNNs. We used two types of CRNNs, a basic CRNN and a mean-teacher model based on an attention-based CRNN. We also used various combinations of weakly, strongly labeled, and unlabeled data to train the CRNNs to confirm the effect of the derivative features on SED. Regarding the basic CRNN, a performance improvement was always attained by using the derivative features in the various combinations of the training data. On the DCASE 2018 test set, an 11.6% average relative improvement in the F-score was obtained, and a 5.3% improvement was obtained on the DCASE 2019 test set. Regarding the mean-teacher model, consistent performance improvement was observed as we changed the number of epochs and test set type were changed. When 200 epochs were used for training, a 5% relative improvement in the DCASE 2018 test set and a 7.5% improvement in the DCASE 2019 test set were observed.  
In this study, we used the derivative features of the log-mel filterbank to improve SED. In the experiments using various combinations of training and test data, we observed a consistent performance improvement in state-of-the-art CRNNs, which, however, was not as significant as in speech recognition. Nevertheless, the results appear to be sufficient to indicate the importance of the derivative features in SED.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Max Epoch = 200**} \\ \hline  & \multicolumn{2}{c}{**Single Channel**} & \multicolumn{2}{c}{**Three Channels**} \\ \hline  & **F-Score (\%)** & **ER** & **F-Score (\%)** & **ER** \\ \hline DCASE 2018 test set & 31.12 & 1.32 & 32.68 & 1.27 \\ Relative Improvement & - & - & 5\% & 3.8\% \\ DCASE 2019 test set & 25.45 & 1.51 & 27.36 & 1.46 \\ Relative Improvement & - & - & 7.5\% & 3.3\% \\ Strongly labeled training set & 73.08 & 0.49 & 75.17 & 0.45 \\ Relative Improvement & - & - & 2.9\% & 8.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: SED results of the mean-teacher model using derivative features (max epoch = 200).  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Max Epoch = 100**} \\ \hline  & \multicolumn{2}{c}{**Single Channel**} & \multicolumn{2}{c}{**Three Channels**} \\ \hline  & **F-Score (\%)** & **ER** & **F-Score (\%)** & **ER** \\ \hline DCASE 2018 test set & 30.88 & 1.35 & 31.82 & 1.35 \\ Relative Improvement & - & - & 3\% & 0\% \\ DCASE 2019 test set & 25.95 & 1.52 & 27.09 & 1.53 \\ (DCASE 2019 baseline) & 23.70 & - & - & - \\ Relative Improvement & - & - & 4.4\% & 0\% \\ Strongly labeled training set & 68.53 & 0.58 & 70.28 & 0.54 \\ Relative Improvement & - & - & 2.5\% & 6.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: SED results of the mean-teacher model using derivative features (max epoch =100).  
**Author Contributions:** Conceptualization, Y.-J.C.; methodology, J.-Y.K. and Y.-J.C.; software, J.-Y.K.; validation, J.-Y.K. and Y.-J.C; formal analysis, Y.-J.C.; investigation, Y.-J.C.; data curation, J.-Y.K.; writing--original draft preparation, Y.-J.C.; writing--review and editing, Y.-J.C.; visualization, J.-Y.K.; supervision, Y.-J.C.; project administration, Y.-J.C.; funding acquisition, Y.-J.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by Ministry of Education (No. 2018R1A2B6009328).  
**Conflicts of Interest:** The authors declare no conflicts of interest.