# Multi-Scale Recurrence Quantification Measurements for Voice Disorder Detection
## 4 Results and Discussion  
Although some recurrence states of pathological voice can be obtained by recurrence quantification analysis, the dynamic recurrence characteristics of voice signals cannot be described comprehensively. From the recurrence plot's definition, the recurrence threshold selection plays a vital role in extracting MRQMs. When a larger or smaller recurrence threshold is selected, the state in RP will change, which is not conducive to the practical analysis of the system, thus affecting the recognition results. This paper sought a more appropriate threshold to make distinguishing the diagonal and vertical recurrence structures of pathological voices easier. Table 5 adopted four machine learning algorithms in different thresholds to detect pathological voice: SVM, RF, BN and LWL. It could be found from the table that the accuracy of pathological voice detection under the four machine learning classifiers had different results under different recurrence thresholds. However, the overall accuracy was considerable. It showed extensive and effective thresholds of multi-scale recurrence quantification measurements in pathological voice detection. The average accuracy showed an upward trend from 1%rr to 40%rr and a downward trend from 40%rr to 99%rr. In the case of 40%rr, the average accuracy of pathological voice detection under the four machine learning classifiers reached 99.45%, which reached the optimal result in different classifiers. Therefore, this article selected 40%rr as the recurrence threshold. In order to further explore in detail that the recurrence threshold at 40%rr is more suitable for pathological voice detection than the other recurrence threshold, the first three multi-scale recurrence quantification measurements ranked by the FDR algorithm were selected to draw three-dimensional scatter plots. It was obvious to find that the first three multi-scale recurrence quantification measurements ranked by the FDR algorithm of the two types of samples can be highly differentiated from Figure 4. The blue circles represented samples of normal voices, and the red crosses represented samples of pathological voice. When the recurrence threshold was 40%rr, the samples had a slight overlap. However, when the recurrence threshold was 1%rr, 80%rr or 99%rr, the degree of overlap was significantly more than 40%rr. It proved that the method proposed in this article could effectively separate the normal samples from the pathological samples, and the dichotomous classification performance was superior. The RP structure of multi-scale recurrence quantification measurements also illustrated the difference when the threshold is 40%rr. Figure 5 shows the RP of the normal and pathological glottal signals in the tenth frequency band. Among them, the diagonal recursion of the normal glottal source signal was obvious. The diagonals were parallel, without vertical and horizontal lines and no scattered points, indicating that the signal had periodicity. Pathological glottal source signals were mainly parallel to the diagonal, but there were some isolated dispersion points. Massive recurrence points on the diagonal indicate that the pathological voice still had a certain periodicity, but its vibration was \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\epsilon\)(rr)\textbackslash{}Classifiers & **SVM** & **RF** & **BN** & **LWL** & **Average** \\ \hline
1\% & 95.56 & 98.22 & 97.33 & 98.67 & 97.45 \\
10\% & 96.44 & 98.22 & 99.11 & 97.33 & 97.78 \\
20\% & 99.11 & 97.78 & 99.56 & 98.22 & 98.67 \\
30\% & 98.22 & 99.11 & 99.11 & 98.67 & 98.78 \\
40\% & 99.11 & 99.56 & 99.56 & 99.56 & 99.45 \\
50\% & 99.11 & 99.11 & 99.11 & 99.11 & 99.11 \\
60\% & 98.22 & 99.11 & 99.56 & 98.67 & 98.89 \\
70\% & 98.22 & 99.56 & 99.56 & 99.56 & 99.23 \\
80\% & 98.67 & 98.22 & 99.56 & 99.11 & 98.89 \\
90\% & 96.00 & 99.11 & 99.11 & 98.67 & 98.22 \\
99\% & 97.78 & 98.22 & 99.11 & 97.78 & 98.22 \\ \hline \hline \end{tabular}
\end{table}