## 3 Experimental Results and Analysis
### Classification Results and Analysis Based on Support Vector Machine
However, the classification performance is unbalanced for some vowels. Conducting a classification analysis of vowels based on formant patterns has the following research values: it can be used to examine which vowels are easily confused in the data and it can be used to establish a more reliable acoustic model for automatic vowel recognition. The results indicate that using formant features can separate standard and non-standard pronunciations, suggesting that employing formant structural information for pronunciation evaluation is reasonable. The specific results are summarized in Table 2.  
Figure 2: Formant patterns of different vowels. \(Y\)-axis: formant frequency (Hz); \(X\)-axis: time (ms). The top graph shows the formant pattern of vowel a, the middle graph shows the formant pattern of vowel i, and the bottom graph shows the formant pattern of vowel u. UC represents learners, MC represents Mandarin speakers, F1 represents the first formant, and F2 represents the second formant. The classification results based on SVM indicate significant differences in vowel pronunciation accuracy and recall among Mandarin learners at different proficiency levels. The advanced level group (UCA) demonstrates excellent classification performance across all vowels, with an overall average accuracy of 93.1% and a recall of 91.6%. Notably, the accuracy and recall for vowels \"x\" and \"u\" both reach 94%, suggesting that advanced learners exhibit highly stable acoustic features in their pronunciation of these vowels, with concentrated formant (F1, F2) distributions close to standard pronunciation. However, the accuracy and recall for apical vowels \"z\" and \"z\" are slightly lower (90% and 88-90%, respectively), possibly related to the specificity of the pronunciation position, but their performance remains significantly better than the elementary level group. The overall classification performance of the intermediate level group (UCI) is close to that of the advanced group, with an average accuracy of 92.9% and a recall of 91.5%. The performance for vowel \"o\" is the most outstanding, with accuracy and recall reaching 95% and 93%, respectively, indicating that the pronunciation of rounded vowels by intermediate learners is approaching the advanced level. However, the classification performance for vowels \"i\" and \"z\" is slightly lower (accuracy of 91% and 89%, respectively), possibly due to the complexity of tongue position control. Overall, the intermediate level group demonstrates stable performance for most vowels, but there is still room for improvement in apical vowels and high front vowels. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Vowel**} & \multicolumn{2}{c}{**UCA (Advanced Level**} & \multicolumn{2}{c}{**UCI (Intermediate**} & \multicolumn{2}{c}{**UCB (Elementary**} \\  & **Group)** & & **Level Group)** & & **Level Group)** \\ \cline{2-7}  & **Accuracy** & **Recall** & **Accuracy** & **Recall** & **Accuracy** & **Recall** \\ \hline a & 92\% & 91\% & 92\% & 90\% & 93\% & 91\% \\ o & 93\% & 90\% & 95\% & 93\% & 92\% & 90\% \\ x & 94\% & 91\% & 94\% & 92\% & 95\% & 94\% \\ u & 94\% & 91\% & 94\% & 91\% & 93\% & 94\% \\ y & 93\% & 91\% & 93\% & 92\% & 94\% & 93\% \\ i & 93\% & 92\% & 91\% & 91\% & 91\% & 90\% \\ z & 90\% & 88\% & 90\% & 89\% & 87\% & 88\% \\ z & 90\% & 90\% & 89\% & 88\% & 88\% & 85\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification accuracy and recall of vowels for learners at different levels based on SVM. Figure 3: Vowel classification results based on SVM. The left figure (**a**) shows accuracy, and the right figure (**b**) shows recall. UCA (black line) represents advanced learners, UCI (blue line) represents intermediate learners, and UCB (black dashed line) represents elementary learners. The classification performance of the elementary level group (UCB) is relatively lower, with an average accuracy of 91.9% and a recall of 90.4%.