## 4 Experimental Results Analysis and Discussion
### Ablation Experiment
For models (A) and (B) without SSL or VAT, the clusters show obvious overlap and relatively poor intra-class compactness, indicating limited discriminative ability. After the introduction of self-supervised learning, (C) and (D) exhibit a more compact intra-class distribution and better inter-class separation, indicating that the SSL framework effectively guides the encoder to learn semantically meaningful representations. With the introduction of VAT, it was observed that (E) further demonstrated clearer class boundaries and a more compact intra-class distribution than the model using only SSL. Finally, the complete Model (F) achieves the best visualization quality, featuring highly compact intra-class clusters and minimal inter-class overlap. This clear and well-separated feature distribution reflects the effectiveness of each component and proves that the proposed complete framework not only achieves high precision but also learns a highly discriminative feature space. Table 8 further quantitatively analyzes the silhouette coefficient and separation ratio. Specifically, we use the silhouette coefficient and separation ratio to measure the distribution of class representations. The silhouette coefficient measures separation quality between clusters, and the higher values (closer to 1) indicate better clustering, which is defined as:  
\[s=\frac{1}{n}\sum_{i=1}^{n}\frac{b(i)-a(i)}{\max\{a(i),b(i)\}} \tag{24}\]  
where \(a(i)\) represents average Euclidean distance between sample \(i\) and all other points in the same cluster, \(b(i)\) represents the smallest average Euclidean distance between sample \(i\) and points in any other cluster, and \(n\) is total number of samples. The separation ratio is the ratio of inter-cluster separation to intra-cluster compactness. Higher values indicate superior clustering (well-separated and tight clusters). The separation ratio is defined as:  
\[SepRatio=\frac{InterSep}{IntraCompact+\epsilon} \tag{25}\]where \(\epsilon\) is a small constant to prevent division by zero. Intra-class compactness and inter-class separation, respectively, represent the average distance of samples within the cluster and the average distance of the cluster centroids, and are defined as:  
\[IntraCompact=\frac{1}{N_{p}}\sum_{k=1}^{K}\sum_{ \begin{subarray}{c}i,j\in C_{k} \\ i<j\end{subarray} }d(\mathbf{x}_{i},\mathbf{x}_{j}) \tag{26}\]  
\[InterSep=\frac{1}{M_{p}}\sum_{1\leq p<q\leq K}d(\mathbf{\mu}_{p},\mathbf{\mu}_{q}) \tag{27}\]  
where \(C_{k}\) is the set of samples in cluster \(k\) (\(k=1,\ldots,K\)), \(d(\mathbf{x}_{i},\mathbf{x}_{j})\) is the Euclidean distance between samples \(\mathbf{x}_{i}\) and \(\mathbf{x}_{j}\), \(N_{p}\) is the total intra-cluster pairs, \(\mathbf{\mu}_{k}\) is the centroid of cluster \(k\), \(d(\mathbf{\mu}_{p},\mathbf{\mu}_{q})\) is the Euclidean distance between centroids, and \(M_{p}\) is the total cluster pairs. As shown in Table 8, (A) and (B) yield the lowest silhouette coefficients and separation ratios, indicating poor feature discrimination and clustering quality. The incorporation of self-supervised learning in (C) and (D) leads to consistent improvements across both metrics, demonstrating the effectiveness of contrastive pretraining in enhancing representation learning. Further performance gains are achieved with the addition of VAT in Model (E), highlighting its role in improving robustness and inter-class separability under limited  
Figure 6: Visualization of feature embeddings extracted by different model variants. (**a**) Supervised model with ResNet encoder. (**b**) Supervised model with a hybrid encoder. (**c**) SSL framework with ResNet encoder. (**d**) SSL framework with a hybrid encoder. (**e**) SSL framework with ResNet encoder and VAT. (**f**) The proposed method. supervision. The complete Model (F) achieves the highest silhouette coefficient of 0.8859 and a separation ratio of 11.3587, significantly outperforming all other variants. These results collectively validate the effectiveness of the proposed SSL-SEI framework.