## 5 Experiments
### Symbol and Note Component Detection
#### 5.3.3 Results of Cross-Part Training  
Table 7 show the result of cross-part training, that is testing on one of the three parts and training on the two remaining ones. In general, as expected, data augmentation improves the results. The ranking of accuracies follow the quality of the data: in summary, the highest values in \(F_{1}^{\text{all}}\), hSAR, and dSAR are achieved on part 1, followed closely by part 3, and finally part 2. The similar accuracies reached on part 1 and 3 in almost all metrics show the greater similarities of these two parts and in general a clearer notation compared to part 2.  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Detection**} & \multicolumn{3}{c}{**Type**} & \multicolumn{3}{c}{**Position in Staff**} & \multicolumn{2}{c}{**Sequence**} \\  & \(\mathbf{F_{1}^{\text{all}}}\) & \(\mathbf{F_{1}^{\text{note}}}\) & \(\mathbf{F_{1}^{\text{clef}}}\) & \(\mathbf{Acc_{\text{type}}^{\text{note}}}\) & \(\mathbf{Acc_{\text{type}}^{\text{def}}}\) & \(\mathbf{Acc_{\text{pos}}^{\text{note}}}\) & \(\mathbf{Acc_{\text{pos}}^{\text{def}}}\) & hSAR & dSAR \\ \hline \(h_{\text{staff}}=40\) & 0.926 & 0.936 & 0.523 & 0.929 & **0.925** & 0.963 & 0.992 & 0.834 & 0.792 \\ \(h_{\text{staff}}=60\) & 0.953 & 0.961 & 0.655 & 0.944 & 0.911 & 0.968 & 0.994 & 0.877 & 0.844 \\ \(h_{\text{staff}}=80\) & **0.956** & 0.964 & **0.693** & 0.949 & 0.897 & **0.970** & 0.990 & **0.885** & **0.856** \\ \(h_{\text{staff}}=100\) & **0.956** & **0.965** & 0.673 & **0.950** & 0.911 & **0.970** & **0.995** & 0.884 & **0.856** \\ \hline Pad & 0.962 & 0.966 & **0.829** & 0.949 & **0.982** & 0.967 & 0.990 & 0.893 & 0.866 \\ Dewarp & 0.952 & 0.959 & 0.708 & 0.946 & 0.873 & 0.969 & 0.987 & 0.877 & 0.845 \\ Aug. & 0.959 & 0.968 & 0.671 & **0.953** & 0.912 & 0.970 & **0.992** & 0.889 & 0.862 \\ Pad, Aug. & **0.964** & **0.969** & 0.818 & **0.952** & **0.982** & **0.971** & **0.992** & **0.898** & **0.871** \\ \hline \hline \end{tabular}
\end{table}
Table 6: Metrics of various hyperparameter settings for the symbol detection. All experiments were conducted using a cross-fold of size five using all available data. The best values for each metric are highlighted.  
The dSAR of any part is considerably lower than the value of 86.6% and 87.1% yielded when training on all data (compare Table 6) with and without data augmentation, respectively. Also the ratio of detected symbols \(F_{1}^{\text{all}}\) is significantly lower, due to the variations in style across the parts. \(Acc_{\text{pos}}^{\text{note}}\) and \(Acc_{\text{pos}}^{\text{clef}}\) are similar to training on all data which shows that if a symbol is correctly detected, its position on the staff lines is usually correct. This behavior is expected because these errors are almost always intrinsic ambiguities which are independent of the layout. Furthermore, the average clef type accuracy \(Acc_{\text{type}}^{\text{clef}}\) of 97.7% in average is also very high. Therefore the network is mostly certain if a C- or F-clef is written even though they share similarities. The decision whether a NC is graphically or logically connected is correct in only 94.0% of all detected notes and slightly lower than the 95.2% reported in Table 6. This shows that the FCN can transfer information about the arrangement of NCs that build typical neunes.