## 5 Experiments
### Symbol and Note Component Detection
#### 5.3.4 Varying the Number of Training Examples  
In this section, we also train on two parts and test on the remaining part, however actual data of the target part is included. Table 8 lists the results when using 0, 1, 2, 4, or finally all pages. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & \multicolumn{2}{c}{**Detection**} & \multicolumn{2}{c}{**Type**} & \multicolumn{2}{c}{**Position in Staff**} & \multicolumn{2}{c}{**Sequence**} \\  & **Test** & **Train** & \(\mathbf{F_{1}^{\text{all}}}\) & \(\mathbf{F_{1}^{\text{note}}}\) & \(\mathbf{F_{1}^{\text{def}}}\) & \(Acc_{\text{type}}^{\text{note}}\) & \(Acc_{\text{type}}^{\text{clef}}\) & \(Acc_{\text{pos}}^{\text{note}}\) & \(Acc_{\text{pos}}^{\text{clef}}\) & **hSAR** & **dSAR** \\ \hline \multirow{4}{*}{Def.} & 1 & 2, 3 & 0.956 & 0.965 & 0.782 & 0.914 & 1.000 & 0.981 & 0.993 & 0.906 & 0.860 \\  & 2 & 1, 3 & 0.912 & 0.916 & 0.638 & 0.928 & 0.975 & 0.955 & 0.990 & 0.797 & 0.757 \\  & 3 & 1, 2 & 0.950 & 0.952 & 0.907 & 0.958 & 0.968 & 0.981 & 1.000 & 0.895 & 0.867 \\  & Mean & 0.939 & 0.944 & 0.776 & 0.933 & 0.981 & 0.972 & 0.994 & 0.866 & 0.828 \\ \hline \multirow{4}{*}{Aug.} & 1 & 2, 3 & 0.958 & 0.964 & 0.822 & 0.914 & 1.000 & 0.980 & 0.990 & 0.907 & 0.862 \\  & 2 & 1, 3 & 0.939 & 0.945 & 0.699 & 0.947 & 0.975 & 0.965 & 0.990 & 0.848 & 0.817 \\ \cline{1-1}  & 3 & 1, 2 & 0.943 & 0.945 & 0.901 & 0.959 & 0.956 & 0.981 & 1.000 & 0.886 & 0.859 \\ \cline{1-1}  & Mean & 0.946 & 0.951 & 0.807 & 0.940 & 0.977 & 0.976 & 0.993 & 0.881 & 0.846 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Symbol detection scores when testing on one and training on the remaining parts. The upper and lower rows show the results without and with data augmentation, respectively. Padding and a line height of 80 px are used for all experiments. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & \multicolumn{2}{c}{**Detection**} & \multicolumn{2}{c}{**Type**} & \multicolumn{2}{c}{**Position in Staff**} & \multicolumn{2}{c}{**Sequence**} \\  & \(\mathbf{N_{train}}\) & \(\mathbf{F_{1}^{\text{all}}}\) & \(\mathbf{F_{1}^{\text{note}}}\) & \(\mathbf{F_{1}^{\text{def}}}\) & \(Acc_{\text{type}}^{\text{note}}\) & \(Acc_{\text{type}}^{\text{clef}}\) & \(Acc_{\text{pos}}^{\text{note}}\) & \(Acc_{\text{pos}}^{\text{clef}}\) & **hSAR** & **dSAR** \\ \hline CT. & 0 & 0.946 & 0.951 & 0.807 & 0.940 & 0.977 & 0.976 & 0.993 & 0.881 & 0.846 \\ \hline \multirow{4}{*}{Default} & 1 & 0.846 & 0.854 & 0.533 & 0.862 & 0.963 & 0.954 & 0.986 & 0.730 & 0.661 \\  & 2 & 0.899 & 0.905 & 0.706 & 0.901 & 0.989 & 0.962 & 0.998 & 0.806 & 0.749 \\  & 4 & 0.926 & 0.930 & 0.775 & 0.927 & 0.982 & 0.970 & 0.990 & 0.846 & 0.804 \\  & All & 0.954 & 0.958 & 0.861 & 0.945 & 0.987 & 0.977 & 0.998 & 0.897 & 0.867 \\ \hline \multirow{4}{*}{PT.} & 1 & 0.925 & 0.929 & 0.760 & 0.907 & 0.978 & 0.956 & 0.992 & 0.834 & 0.777 \\  & 2 & 0.939 & 0.942 & 0.796 & 0.928 & 0.981 & 0.966 & 0.999 & 0.862 & 0.821 \\ \cline{1-1}  & 4 & 0.953 & 0.956 & 0.871 & 0.944 & 0.987 & 0.972 & 0.996 & 0.890 & 0.858 \\ \cline{1-1}  & All & 0.969 & 0.971 & 0.910 & 0.950 & 0.989 & 0.975 & 0.997 & 0.916 & 0.888 \\ \hline \multirow{4}{*}{Inc.} & 1 & 0.948 & 0.953 & 0.808 & 0.936 & 0.982 & 0.977 & 0.997 & 0.882 & 0.846 \\ \cline{1-1}  & 2 & 0.952 & 0.958 & 0.793 & 0.939 & 0.978 & 0.976 & 0.997 & 0.887 & 0.854 \\ \cline{1-1}  & Mean & 0.959 & 0.964 & 0.817 & 0.948 & 0.980 & 0.976 & 0.996 & 0.900 & 0.870 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Symbol detection scores when varying the number of training examples. The first line is the average of the cross-part training (CT.) experiment of Table 7 where no pages of the target part are used. The next rows (Default) only use \(N_{\text{train}}\) of the target data set for training. Afterwards, a pretrained model is used (PT) or the additional part data is included (Inc.). As expected, an increasing number of training examples leads in general to improve recognition rates and thus higher scores in any experiment.