# Design of a Semantic Understanding System for Optical Staff Symbols
## 4 Results
### Experiment and Analysis
#### 4.4.2 Experiment with HSUS  
The accuracy of the HSUS is related to the accuracy of the output of the LSUS and the stability and accuracy of the NERA. To verify the accuracy of the NERA, using the ideal data (manual annotation) and the practical data (the output of the LSUS) as inputs--named ideal input and practical input, respectively--the error rate and the omission rate of the output results are calculated as follows:  
* When the input is ideal, the error rate and the omission rate of the output result are the performance indexes of the NERA;
* The error and omission rates are the performance indexes of the whole system when the output is practical. Figure 5: Complexity variable correlation coefficient. Figure 6: For LSUS visualization, the diagram shows the staff of _Oboe String Quartet in C Minor, Violin Concerto_ (JS BACH BWV 1060), page 5, lines 1 and 2. The characters in each box indicate the semantics of the corresponding symbol. In the diagram, green boxes indicate incorrectly identified symbols, and the symbols without boxes are the missed notes. Tests were conducted on the test set, and the experimental results are shown in Table 5. The specific analysis is as follows:  
(1) HSUS output error  
As shown in Table 4, the ideal data as the input of HSUS have a zero omission rate, which indicates that the NERA has performed the HSUS for each note input, thus proving its stability. The error is mainly caused by the deviation of the range of accidentals. The accidentals are defined in music theory to work for the notes with the same height within a bar; however, in this paper, the note reconstruction does not extend the effective range of accidentals to other symbols within the bar, which leads to the error in the HSUS, as shown in Figure 7.  
(2) Scope of application of NERA  
The NERA proposed in this paper can only be applied to the general rules of staff notation whose expression is notation, i.e., the rules described in Section 2.3. Additionally, due to the ambiguous restriction that the author may want to express the content using symbols, there will be some special rules of note expressions [5], and then the output of the HSUS will be very different from what the author expresses, as in the example shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Staff**} & \multicolumn{2}{c}{**Ideal Input**} & \multicolumn{2}{c}{**Practical Input**} \\ \cline{2-5}  & **Error Rate** & \begin{tabular}{c} **Omission Rate** \\ \end{tabular} & \
\begin{tabular}{c} **Error Rate** \\ \end{tabular} &
\begin{tabular}{c} **Omission Rate** \\ \end{tabular} \\ \hline Staff 1 & 0.006 & 0.000 & 0.052 & 0.044 \\ Staff 2 & 0.011 & 0.000 & 0.016 & 0.010 \\ Staff 3 & 0.010 & 0.000 & 0.020 & 0.006 \\ Staff 4 & 0.019 & 0.000 & 0.027 & 0.020 \\ Staff 5 & 0.013 & 0.000 & 0.044 & 0.014 \\ Staff 6 & 0.005 & 0.000 & 0.020 & 0.008 \\ Staff 7 & 0.000 & 0.000 & 0.004 & 0.010 \\ Staff 8 & 0.020 & 0.000 & 0.055 & 0.053 \\ Staff 9 & 0.022 & 0.000 & 0.037 & 0.021 \\ Staff 10 & 0.000 & 0.000 & 0.036 & 0.019 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental results for HSUS. Figure 7: The pitch-shifting notation leads to HSUS errors. The sharp should be applied to notes of the same height in the bar, but the NERA only applies it to the first note after the sharp. (3) LSUS as input  
The average error rate of the HSUS is 0.031, and the omission rate is 0.021 when the input is the system's practical data. Among numerous replicate experiments, we found that, despite the high overall accuracy of the system output, some errors with very low probability still occur. After analysis, we found that these errors are caused by LSUS errors, as shown in Figure 9, mainly as follows:  
* Misidentification of the pitch and duration of natural scales can lead to errors during HSUS;
* Misidentification or omission of accidentals (sharp, flat, natural, dot) acting on natural scales can lead to errors during HSUS;
* Omission of a note affects the HSUS of the note or the preceding and following notes.