## 3 Experiments
### Ablation Study  
We conducted an ablation study to verify the effectiveness of the proposed model. We experimented with the following settings to investigate the model. The architectures of each model used in the experiments are illustrated in Figure 2.  
* **The effect of the auxiliary network**: The proposed JDC network model was compared to the main network only (without the auxiliary network). They are denoted by \(JDC_{S}\) and \(Main\), respectively.
* **The effect of the combined voice detection in calculating the loss function**: The proposed model used the sum of the outputs from both the main and auxiliary networks (Equation (3)) in calculating the voice loss function. This was compared to the case where only the output of auxiliary network, \(o_{v}\), was used in calculating the loss function, which is denoted by \(JDC_{A}\).
* **The effect of the combined voice detection in predicting singing voice**: The JDC network can detect singing voice with three possibilities in the test phase: \(o_{mv}\) from the main network, \(o_{v}\) from the auxiliary network, and \(o_{sv}\) the sum of the two outputs. We compared the performance of the three melody extraction outputs and evaluated them for each of the two loss functions above. As a result, we had a total of six outputs, which are denoted by \(JDC_{S}(o_{mv})\), \(JDC_{S}(o_{v})\), \(JDC_{A}(o_{mv})\), \(JDC_{A}(o_{v})\), and \(JDC_{A}(o_{sv})\).  
To demonstrate the effectiveness of the JDC network, we also examined the performances of the model \(Main(AUX)\) and \(Main(SVD)\). In both models, the networks for pitch estimation and singing voice detector (SVD) were trained separately. Both networks for melody extraction were identical to \(Main\), but only the labels corresponding to the pitches were used as the target labels. The architecture of SVD for \(Main(AUX)\) was identical to the auxiliary network. Following [38], we implemented the SVD for \(Main(SVD)\). For fair comparison, the same training datasets were used in all training phases.  
The models and voice detection outputs on the four test datasets were evaluated for melody extraction as mentioned in Section 3.1.2. We carried out five runs of training with different initializations and analyzed the results across different metrics of melody extraction evaluation and different test sets, respectively. To further validate the effectiveness of the models, a \(t\)-test between the \(Main\) and each JDC network to  
Figure 2: Architectures of melody extraction used for performance comparison in this paper. In the model name, the subscript refers to the type of JDC network, and parentheses refer to the source of voice detection output. The black and red solid arrows indicate the paths used for training and training/testing, respectively. The red dotted arrows indicate the path used for the test, although it was not used for training.  
compute the statistical significance on the results (the results were normally distributed (Shapiro-Wilk test: \(p>0.05\))) of the five trials was performed.  
In addition, we examined their singing voice detection capability using the Jamendo dataset, which was dedicated to the voice detection task (there was no annotation on the pitch of the melody). Because this was for the voice detection task, we report only VR and VFA. In addition to the models and voice detection outputs in the ablation study, we also compared out best model to other state-of-the-art singing voice detection algorithms [38; 44; 45].