## 2 Methods
### Graph Embedding
The Massachusetts Eye and Ear Infirmary (MEEI) [32] database consists of English voices from 53 healthy and 657 pathological speakers, which are sustained vowels /a/. The healthy speech recordings in the MEEI are sampled at 50 kHz, while the pathological ones are sampled at 25 kHz. The Saarbruecken Voice Database (SVD) [33] includes 687 healthy and 1356 pathological voice samples, which are all sampled at 50 kHz. The voices for each speaker consist of vowels /a/, i/, and /u/. The Hospital Universitario Principe de Asturias (HUPA) [34] database consists of 239 healthy and 169 pathological voice samples. Each voice is sampled at 25 kHz with the sustained vowels /a/. The diseases, which are clinically common and widely studied, were selected and divided into two categories. Neuromuscular voices consist of vocal fold paralysis and Parkinsonian disease, while structural voices include vocal fold polyps, nodules, edema, and vocal leukoplakia. The healthy and pathological samples from three different databases are presented in Table 2. We conduct the following six cross-database recognition settings for evaluation, which can be seen in Table 3.

We conducted the following six cross-database experiment settings for evaluation:

### Feature Set

The IS09 feature set in OpenSmile [35] was utilized to extract the features. A total of 384 dimensional features were obtained by calculating the first-order difference and second-order difference of 16 LLDS. The details are presented in Table 4.

We chose the INTERSPEECH 2009 feature set because the features in IS09, including the MFCC [36], HNR [37], and F0 [38] are often used in pathological voice research. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Database** & **Healthy** & **Neuromuscular** & **Structural** \\ \hline MEEI & 53 & 67 & 82 \\ SVD & 200 & 64 & 130 \\ HUPA & 239 & 31 & 128 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Voice samples selected from the pathological voice database. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **M-S** & **M-H** & **S-M** & **S-H** & **H-M** & **H-S** \\ \hline Training set & MEEI & MEEI & SVD & SVD & HUPA & HUPA \\ Testing set & SVD & HUPA & MEEI & HUPA & MEEI & SVD \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cross-database experiment settings. ### Feature Selection

According to [27], a feature set consists of important and unimportant features. Unimportant features will affect the result of experiments and increase the time complexity of the model construction. Therefore, feature selection should be used to choose the useful features for classification. The FDR value is used to rank the selected features, which is computed as follows

\[FDR(k)=\frac{\left(\mu_{n,k}-\mu_{p,k}\right)^{2}}{\sigma_{n,k}^{2}+\sigma_{p,k} ^{2}},k=1,2,3\ldots \tag{19}\]

where \(k\) is the number of features, \(\mu_{n,k}\) and \(\mu_{n,p}\) are the means of the \(k\)-th feature for classes of normal and pathological voices, respectively. \(\sigma_{n,k}\) and \(\sigma_{n,p}\) are the variances of \(k\)-th feature for classes of normal and pathological voices, respectively. For a certain feature, the more satisfactory results obtained, the higher the FDR. After the FDR, the 384 dimensions were reduced to 160 dimensions. From Figure 2, it can be found that after the FDR method, the feature set performs better. \begin{table}
\begin{tabular}{c c c} \hline \hline
**LLD** & **Number** & **Functionals (12)** \\ \hline ZCR & 1 & mean \\ \(\Delta\)ZCR & 1 & Energy standard deviation \\ RMS & 1 & kurtosis, skewness \\ F0 & 1 & Extremes: Value, rel. position, range \\ \(\Delta\)HNR & 1 & \\ MFCC1-12 & 12 & linear regression: offset, slope, MSE \\ AMFC1-12 & 12 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Features in INTERSPEECH 2009 Emotion Challenge. Figure 2: The results of the experiments for the FDR and non-FDR. ## 4 Results and Discussion

### Cross-Database Experiments

In this section, we compared our method with traditional methods and other transfer learning methods.