# Prototypical Graph Contrastive Learning for Recommendation
## 4 Experiments
### Ablation Study (RQ3)  
In this section, we present several variants of ProtoRec to evaluate their recommendation performance. As shown in Table 3, the variant ProtoRec\({}_{\text{a}}\) uses the prototype-augmented embeddings for recommendation and performs contrastive learning with the embeddings learned by the first layer of the GNN, still achieving good performance. The variant ProtoRec\({}_{\text{c}}\) extends the prototype augmentation scheme to each layer of the GNN. While it achieves better performance on some metrics in the Yelp2018 dataset, it comes at the cost of increased complexity. The variant ProtoRec\({}_{\text{c}}\) replaces the Euclidean distance in the K-means algorithm with cosine similarity. Although different similarities are used to divide the clustering results and extract prototypes, good recommendation performance is still achieved. To investigate whether ProtoRec can adapt to different clustering algorithms, we replaced K-means with alternative clustering methods such as DBSCAN, hierarchical clustering, and Gaussian mixture models. The impact of these methods on the recommendation per formance is shown in the table as ProtoRec\({}_{dbscan}\), ProtoRec\({}_{hc}\), and ProtoRec\({}_{qmm}\). Across the three datasets, these variations still demonstrate good performance compared to ProtoRec. Although different clustering methods were employed, they all successfully extracted prototype information from the embedding space. ProtoRec effectively transformed this information into useful augmentation, thereby maintaining the stability of the model. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Dataset** & \multicolumn{2}{c}{**Yelp2018**} & \multicolumn{2}{c}{**Douban-Book**} & \multicolumn{2}{c}{**Amazon-Book**} \\ \hline
**Method** & **Recall@20** & **NDCG@20** & **Recall@20** & **NDCG@20** & **Recall@20** & **NDCG@20** \\ \hline ProtoRec\({}_{dbscan}\) & 0.0716 & 0.0591 & 0.1727 & 0.1482 & 0.0518 & 0.0412 \\ ProtoRec\({}_{hc}\) & 0.0718 & 0.0592 & 0.1732 & 0.1492 & 0.0514 & 0.0409 \\ ProtoRec\({}_{gmm}\) & 0.0719 & 0.0593 & 0.1731 & 0.1486 & 0.0515 & 0.0413 \\ \hline ProtoRec\({}_{hc}\) & 0.0689 & 0.0568 & 0.1706 & 0.1513 & 0.0472 & 0.0374 \\ ProtoRec\({}_{c}\) & 0.0723 & 0.0597 & 0.1783 & 0.1553 & 0.0516 & 0.0411 \\ ProtoRec\({}_{c}\) & 0.0722 & 0.0593 & 0.1774 & 0.1544 & 0.0511 & 0.0405 \\ \hline w/o-SIG & 0.0721 & 0.0594 & 0.1754 & 0.1543 & 0.0513 & 0.0406 \\ w/o-PFN & 0.0643 & 0.0530 & 0.1473 & 0.1266 & 0.0427 & 0.0343 \\ \hline ProtoRec & 0.0722 & 0.0598 & 0.1788 & 0.1566 & 0.0519 & 0.0413 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of different variants and ablation studies. Figure 4: The embedding distribution plots for the three datasets. The upper part of each plot shows the Gaussian and kernel density estimation (KDE) in \(\mathbb{R}^{2}\), where darker colors represent a higher density of points in the area. The lower part depicts the KDE on angles. A smooth curve indicates that the model has learned uniform features. Each row is sorted by the model performance on the corresponding dataset, allowing an observation of the relationship between embedding uniformity and recommendation performance from left to right. To explore the impact of certain modules in ProtoRec on recommendation performance, we present the results of ablation studies in Table 3. w/o-SIG examines the impact of adding irrelevant information in the prototype refinement module. Performance is slightly lower than ProtoRec across the three datasets. Although the model assigns less weight to this irrelevant information during training, directly removing these connections reduces the impact of noise. w/o-PFN removes the prototype filtering network (PFN), resulting in a significant drop in recommendation performance across all datasets. This is because assigning excessive weight to the prototype information can mislead the knowledge learned by the GNN. The PFN helps maintain a balance between the knowledge acquired by the GNN and the prototype information by adjusting the weight.