## 5 Experiments
### Symbol and Note Component Detection
#### 5.3.6 Error Analysis  
Regarding the error analysis, we compare the predicted and GT sequences and count how many deletions or insertions of a specific type are required to gain the GT. We use the model, when training and evaluating a cross fold comprising all data, which yields a dSAR of 87.1% (compare Table 6). Note that in this section replacements are treated as two errors: one insertion and one deletion. Table 9 lists eight groups of errors and their relative impact on the total dSAR whereas Figure 14 shows examples for the errors.  
The first result is that the combined amount of FPs and FNs are balanced (48% vs. 52%). Notes are missed (1) most often if the contrast between notes and background is too low or if neumes are written very dense, which also significantly affects the prediction accuracy of connection types (2). Wrong note positions (3) occur only at locations where even for a human it is difficult to decide whether the NC is located on a line or in a space. Mainly neumes with stacked NCs, such as a so-called pes (first neume in Figure 1) or scanduc  
Figure 14: The three lines exemplarily show typical errors of the symbol detection algorithm. Refer to Table 9 for the definition of the numbers indicating different groups. The yellow boxes mark single NCs, solid lines between two NCs indicate that the second note is graphically connected to the previous. The dashed vertical lines separate single neumes and therefore represent logical connections. The cyan symbols denote clefs. The connecting thin dotted line represents the reading order of the symbols.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Group** & **Error** \\ \hline _False Negatives_ & & 51.7\% \\
1. & Missing Note & 21.2\% \\
2. & Wrong Connection & 10.8\% \\
3. & Wrong Location & 14.3\% \\
4. & Missing Clef & 3.5\% \\
5. & Missing Accidental & 1.9\% \\ \hline _False Positives_ & & 48.3\% \\
6. & Additional Note & 20.6\% \\
2. & Wrong Connection & 10.8\% \\
3. & Wrong Location & 14.3\% \\
7. & Additional Clef & 2.6\% \\
8. & Additional Accidental & 0.0\% \\ \hline \hline  & Total & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 9: Error analysis: The relative amount of errors of the output sequence is categorised.  
order which is only captured by SAR metrics. Since the NCs are ordered left to right based on their prediction position, it happens that the upper note, which should be sung later, is predicted a little to far to the left compared to the lower note. Observations show that the first clef in a staff was almost always detected, whereas a clef in a line was very often missed (4) and sometimes misrecognised as two notes. Accidentals are not detected at all (5) possibly due to their underrepresentation in the available data set.  
Additional notes (6) mostly occur if clefs or accidentals are labeled as two notes or if noise or bleeding is falsely detected as symbols. Wrong connections and locations count also as FP which is why their ratio is the same. The amount of FPs that are clefs (7) is very low and since no accidentals are predicted at all no FPs (8) can occur.  
In conclusion, it can be observed that the majority of errors are, as expected, note related; however, missing (21.2%), additional (20.6%), wrong connection (21.6%) and wrong location (28.6%) errors are roughly balanced.