# Margin and Shared Proxies: Advanced Proxy Anchor Loss for Out-of-Domain Intent Classification
## 4 Experiments
### Cluster Analysis  
The analysis involves embedding the test set through the trained model and examining the distribution of these vectors in the embedding space. As the model was trained with distance-based functions, clusters are expected to form in the embedding space for each intent. To evaluate the quality of these clusters, a Silhouette analysis [43] and the average separation [44] of clusters are utilized. The silhouette coefficient used in the silhouette analysis ranges from \(-1\) to \(1\), where values closer to \(1\) indicate more successful clustering. The separation metric, which also ranges between \(0\) and \(1\), is considered to be successful when it is close to \(0\). Table 4 presents the silhouette coefficients and separation values for the proposed method and variant models. Bolded values mark indicate the highest performance, while underlined values mark represent the second-highest performance. The evaluation results show that the proposed method outperforms other models in silhouette coefficients and separation metrics across most configurations. This suggests that the proposed method is effective in embedding data samples based on semantic distances. Moreover, models without margin proxies (w/o Margin) and model without all proxies (w/o ALL) exhibit significantly lower separation values compared to models utilizing margin proxies, thus indicating the effectiveness of margin proxies in separating intents. Despite the fact that the w/o Margin model shows a much lower separation than the w/o Shared model, there are cases where it surpasses it in the silhouette coefficient. This implies that shared proxies can help distinguish OOD and enhance cohesion within OOD classes. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**CLINC**} & \multicolumn{2}{c}{**StackOverflow**} & \multicolumn{2}{c}{**BANKING**} \\  & **Methods** & **Silhouette** & **Separation** & **Silhouette** & **Separation** & **Silhouette** & **Separation** \\ \hline \multirow{4}{*}{25\%} & w/o Shared & \(-0.1315\) & \(0.2847\) & \(-0.1240\) & \(0.4318\) & \(-0.1682\) & \(\mathbf{0.3024}\) \\  & w/o Margin & \(-0.1526\) & \(0.6618\) & \(-0.0729\) & \(0.7193\) & \(-0.1324\) & \(0.6441\) \\  & w/o ALL & \(-0.1395\) & \(0.6251\) & \(0.0535\) & \(0.4834\) & \(-0.1358\) & \(0.5926\) \\  & Ours & \(-\mathbf{0.1137}\) & \(\mathbf{0.2736}\) & \(\mathbf{0.0770}\) & \(\mathbf{0.3132}\) & \(-\mathbf{0.0735}\) & \(0.3273\) \\ \hline \multirow{4}{*}{50\%} & w/o Shared & \(0.0419\) & \(0.3509\) & \(0.2494\) & \(0.4749\) & \(0.1028\) & \(0.3306\) \\  & w/o Margin & \(0.0471\) & \(0.6876\) & \(0.1887\) & \(0.6814\) & \(0.0152\) & \(0.6704\) \\  & w/o ALL & \(-0.0191\) & \(0.6457\) & \(0.2377\) & \(0.4417\) & \(-0.0290\) & \(0.5934\) \\  & Ours & \(\mathbf{0.0689}\) & \(\mathbf{0.3096}\) & \(\mathbf{0.2813}\) & \(\mathbf{0.4267}\) & \(\mathbf{0.1246}\) & \(\mathbf{0.3277}\) \\ \hline \multirow{4}{*}{75\%} & w/o Shared & \(0.2024\) & \(0.4327\) & \(0.4515\) & \(0.4251\) & \(0.2974\) & \(0.4289\) \\  & w/o Margin & \(0.2563\) & \(0.6993\) & \(0.3783\) & \(0.6556\) & \(0.2798\) & \(0.7062\) \\ \cline{1-1}  & w/o ALL & \(0.1122\) & \(0.6502\) & \(0.3428\) & \(\mathbf{0.3927}\) & \(0.1184\) & \(0.5968\) \\ \cline{1-1}  & Ours & \(\mathbf{0.2759}\) & \(\mathbf{0.3702}\) & \(\mathbf{0.4748}\) & \(0.4173\) & \(\mathbf{0.3655}\) & \(\mathbf{0.3629}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Clustering performances of proposed method and ablation models. The best performances are indicated in bold letters and the second-highest performances are underlined.