## 3 Experimental Results and Analysis
### Vowel Classification Results and Analysis Based on ID3 Algorithm  
The ID3 algorithm is a classification prediction algorithm in machine learning. This algorithm uses information entropy and information gain as measurement criteria to further achieve data induction and classification [31; 32]. The core of this algorithm is information entropy, which is the information contained in a set of data, a measure of probability. Suppose a set of data consists of {d1, d2,..., dn} and its sum is represented by Sum, then the formula for calculating information entropy is as follows:  
\[Entropy(D)=-\sum_{x=1}^{n}\frac{d_{x}}{sum}log\frac{d_{x}}{sum} \tag{7}\]  
where \(\frac{dx}{sum}\) is the probability of class \(d_{x}\) appearing in the sample \(D\). In the ID3 algorithm, information gain is denoted by Gain(D), which refers to the effective reduction in information entropy or the change in entropy before and after partitioning. The higher this value, the more information entropy the target attribute loses in that reference attribute. Information gain, Gain(D), can be represented by the following formula:  
\[Gain(D,A)=Entropy(D)-\sum_{V\in Value(A)}\frac{D_{V}}{D}Entropy(D_{V}) \tag{8}\]  
where \(A\) represents the attributes of the sample, \(Value(A)\) is the set of all values of attribute \(A\), \(V\) is one of the attribute values of \(A\), and \(D_{V}\) is the set of samples where the value of \(A\) in \(D\) is \(V\). From the results in Figure 4, it can be observed that the average classification accuracy of vowels based on the ID3 algorithm for learners at different levels can reach 90.04%. This is 2.04% lower than the vowel classification accuracy of SVM. This is because SVM better handles the classification features selected in this study, namely formant patterns and the distances between them, while exhibiting better classification performance. The specific results are summarized in Table 3.  
As shown in Table 3 above, there are certain differences in vowel pronunciation accuracy and recall among Mandarin learners at different proficiency levels, but the overall performance is slightly lower than the SVM algorithm. The UCA has an average accuracy of 90.4% and a recall of 89.6%, with vowel \"\(\chi\)\" performing the best (accuracy 94%, recall 91%), indicating that advanced learners have relatively stable tongue position control. However, the accuracy and recall for vowel \"\(\chi\)\" are lower (88% and 85%, respectively), possibly related to the complexity of lip shape control. The UCI has an average accuracy of 90.8% and a recall of 90.1%, with vowel \"o\" showing outstanding performance (accuracy 94%, recall 92%), but the classification performance for vowels \"y\" and \"z\" decreases (accuracy \(\leq\) 90%), reflecting the pronunciation instability of intermediate learners in some complex vowels. The UCB has an average accuracy of 89.0% and a recall of 87.9%, with vowels \"x\" and \"o\" performing relatively well (accuracy \(\geq\) 90%), but the accuracy and recall for apical vowels \"z\" and \"z\" are significantly lower (87-88% and 85-86%, respectively), indicating that elementary learners have obvious difficulties in pronouncing these vowels, possibly related to native language interference or the specificity of the pronunciation position. Combining the analyses of Tables 2 and 3 above, the SVM algorithm generally outperforms the ID3 algorithm in vowel classification accuracy and recall, regardless of whether the learners are in the advanced, intermediate, or elementary level group. The SVM algorithm, due to its advantages in handling complex data and non-linear problems, is more effective and reliable for the objective testing of learners' vowel pronunciation proficiency. Therefore, the SVM-based vowel classification method is considered superior in this study and more suitable for evaluating learners' vowel pronunciation ability at different levels.