## 4 Results and Discussion  
### Comparison of Melody Extraction Performance  
Figure 3a shows the results of the five melody extraction evaluation metrics for the compared models and outputs. In general, \(JDC\) networks were superior to \(Main\) in terms of OA, and among the \(JDC\) networks, \(JDC_{S}\) networks that used the sum of the two outputs in the loss function were more accurate than \(JDC_{A}\) that used only the output of the auxiliary network. Both RPA and RCA increased significantly in all \(JDC\) networks, especially \(JDC_{S}(o_{v})\) and \(JDC_{S}(o_{sv})\). This is mainly attributed to the increase in VR. That is, the \(JDC\) networks detected the activity of singing voice more responsively, having fewer missing errors. The average RPA and RCA of \(Main\) were 76.1% and 78.1%, respectively, while those of \(JDC_{S}(o_{v})\) were 84.7% and 86.0%, respectively (\(p\)-value < 0.01). However, both VR and VFA were high due to their aggressiveness, and this led to degradation in OA. On the other hand, \(JDC_{S}(o_{mv})\) predicted the voice activity more reliably by significantly reducing VFA. The average VFA of \(JDC_{S}(o_{sv})\) was 17.7%, but that of \(JDC_{S}(o_{mv})\) was 9.0%. As a result, \(JDC_{S}(o_{mv})\) achieved the highest average OA (85.7%, \(p\)-value < 0.01), outperforming the two networks. This result indicates that the voice detection output of the main network was more conservative than the output of the auxiliary network. This is true because the main network had more classes (i.e., pitch labels) with which to compete. However, comparing \(JDC_{S}(o_{mv})\) to \(JDC_{A}(o_{mv})\), the main network in \(JDC_{S}(o_{mv})\) became more sensitive to voice activity due to the influence of the auxiliary network. This reveals that combining \(o_{mv}\) with \(o_{v}\) in calculating the voice detection loss function (Equation (4)) contributed to driving more tightly-coupled classification and detection, thereby improving the performance of melody extraction. The overall performance of \(Main(AUX)\) was generally higher than that of \(Main\), but it did not outperform \(JDC_{S}(o_{mv})\). The average OA of \(Main(SVD)\) was comparable to \(Main\), and the performance was lower than that of \(Main(AUX)\). Experimental results also showed that the deviations of RPA and RCA of the proposed models were high, except for \(Main(AUX)\) and \(Main(SVD)\). Since the proposed models were trained for both pitch estimation and voice detection at different levels of abstraction, they were sensitive to initialization. Figure 3b shows the results of overall accuracy (OA) on the four test sets for the compared models and outputs. The performance gap varied by up to 10% depending on the dataset, indicating that the models were affected by the characteristic that each test set had (e.g., genre). Again, we see that the performances of the JDC networks were generally superior to that of \(Main\) for all test datasets. Comparing \(JDC_{A}\) to \(JDC_{S}\) in each of the three cases (\(o_{mv}\), \(o_{v}\), and \(o_{sv}\)), the average of OA for three \(JDC_{A}\) and \(JDC_{S}\) networks were 83.5% and 84.9%, respectively. \(JDC_{S}\) networks were generally superior to \(JDC_{A}\) networks. The average OA of \(JDC_{S}(o_{mv})\) was improved by 3.17% over that of \(Main\). With regard to OA, a \(t\)-test revealed a statistical significance between \(Main\) and \(JDC_{S}(o_{mv})\). The results are as follows: ADC04 (0.025), MIREX05 (0.01), MedleyDB (0.027), and RWC (0.043). \(JDC_{S}(o_{mv})\) increased the average OA with respect to \(Main\) for ADC04, which is an especially challenging dataset. The average overall accuracy of \(JDC_{S}(o_{mv})\) is 83.7%, which was 6.1% higher than that of 77.6% of \(Main\). To summarize, in the training phase, the most effective models were \(JDC_{S}\) networks that used both the main and auxiliary outputs for voice detection in the loss function. In the inference stage, the most effective output was \(o_{mv}\), which used only the output of the main network.