## 2 Methods
### Graph Embedding
KNN was chosen as the base classifier, since it does not require tuning cross-validation parameters [39]. The recognition rate is given in Table 5. From Table 5, it can also be observed that:

Firstly, compared with traditional machine learning methods such as NN and PCA, the transfer learning methods achieved a higher recognition rate, which demonstrates that the feature distributions were quite different leading to the low recognition in the cross-database experiment. Meanwhile, since transfer learning methods can eliminate the distribution divergence across databases, transfer learning methods performed better in the experimental results. Secondly, the SJDA method, which combined the MMD with intra-class distance and inter-class distance achieved higher accuracy than the TCA and JDA. This shows that, in the process of feature transformation, intra-class distance and inter-class distance as regularization can guarantee the maximum separability among different classes. Thirdly, compared with DSTL which also used a graph as a regularization but did not take conditional distribution into account, the method we proposed, which calculated the graph matrix and the MMD distance between different classes achieved higher accuracy. Accordingly, the improvement of the DSTL compared to other transfer learning was not significant, and there was even a decrease in some groups. This demonstrates that when eliminating the divergence between different databases, conditional distribution affects the effect of transfer learning methods. Fourthly, the JDA, which used the MMD function as the distance measurement and took conditional distribution into account did not show much advantage over the TCA. However, the method we proposed achieved the highest accuracy, because the graph matrix acting as a regularization improved the accuracy of the pseudo labels, which further constructed the graph matrix. Fifthly, the recognition rate of our method was higher than the other transfer learning methods, because our proposed method constructed a graph with true and pseudo labels, which eliminated the difference between the source and target domain well and retained the local structural consistencies on labels. Table 6 shows the average accuracy of different methods. Our proposed method achieved the highest recognition accuracy in the categories of healthy and structural. In particular, in the category of structural, the recognition accuracy of the proposed method was significantly higher than other methods. The reason why the accuracy of neuromuscular disease is lower than the other methods may be due to the nature of machine learning. As is known, when training the machine learning models, minority samples can be easily misclassified as majority samples. Table 3 shows that the number of neuromuscular disease samples was much smaller than other categories. After iteration in the algorithm, the model could not learn the characteristics of neuromuscular disease well, which led to the decrease in accuracy. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Cases** & **NN** & **PCA** & **TCA** & **JDA** & **GFK** & **SJDA** & **DSTL** & **JSTL** \\ \hline M-S & 40.10 & 35.28 & 48.48 & 46.70 & 38.07 & 49.75 & 45.18 & **52.03** \\ M-H & 42.71 & 38.44 & 51.26 & 54.02 & 41.21 & 54.52 & 51.51 &



Figure 3 shows the confusion matrices of our method. The healthy category was more easily recognized compared with other categories, which proves the performance of our method on the pathological voice detection among cross-database experiments. When the HUPA was used as the training set, the accuracy of the neuromuscular category was small compared to other categories, which tended to cause the mismatch of the machine learning model. From Figure 3e,f, when the HUPA was used as the training set, the accuracy of the neuromuscular disease was the lowest, which confirms what we noted. On the contrary, when the MEI and SVD were used as the training set, the confusion matrix was the most evenly distributed.