# Dirichlet Process Prior for Student's t Graph Variational Autoencoders
## 5 Experiments
### Link Prediction  
To assess our model's ability to perform link prediction tasks, we compared it with two algorithms: GVAE [3] and standard tGVAE [4]. Our model improves the problem that the standard St distribution as a prior can not fully discover the latent information for a large portion of nodes in networks, and in our experiments, it is applied to the network data, whose encoder and decoder are changed to use the same settings as our method, then we denoted it as St GVAE. For this task, we will follow the settings of GVAE and make the encoder use GCN of two layers to conduct four groups of comparative experiments, the dimensions of latent space are 8, 16, 32, and 64, and the corresponding GCN hidden layer sizes are 16, 32, 64, and 128 respectively. All experiments use a learning rate of 0.01. When the learning rate is 0.1, it is difficult for the model to converge in training. When the learning rate is 0.001, the model converges very slowly, and its performance in learning tasks is lower than that in the learning rate of 0.01. The validation set and the test set contain 5% and 10% of the network edges. AUC (area under ROC curve) and AP (average accuracy) are used as the assessment criteria for the correct classification of edge types in the networks. We show link prediction performance on three citation datasets in Tables 2-4, and our model is almost better than the contrastive approaches. As we can see from the experimental results, with the augment of the latent space dimension, the predictive performances of GVAE and St GVAE models are increasing, and our model presents a trend like a parabola. This is because our model can automatically select the most appropriate latent dimension, and the latent features under this dimension are conducive to the reconstruction of network structure. Moreover, there are St GVAE with a large predicted improvement span in the low-dimension interval, and GVAE with a uniform rising trend about the dimension. When the dimension of latent space is low, such as 8, the performance of St GVAE is the weakest among the three models, because, in the case of fewer latent features, the use of heavy-tailed St distribution can, to some extent, obscure the differences between various features. This indicates the importance of constructing the St distribution with DP because DP can help find the most critical features for each node among these few latent features. This ranking of importance can digest the disadvantage of heavy-tailed distribution in low-dimensional latent space. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Cora** & **Citeseer** & **PubMed** \\ \hline
**Nodes** & 2708 & 3327 & 19,717 \\
**Edges** & 5429 & 4732 & 44,338 \\
**Features** & 1433 & 3703 & 500 \\
**Labels** & 7 & 6 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the datasets. Now, to understand the latent representation \(\mathbf{Z}\), we visualize its posterior probability, \(q_{\phi}(\mathbf{Z})\), for GVAE and DP-St GVAE models on Cora and Citeseer datasets. With regard to the node selection for visualization, we first randomly select ten nodes with the most and the least number of latent features with high probability respectively, and then randomly choose 10 nodes in the remaining node-set. In addition, the dimensions of latent variables in the DP-St GVAE model are automatically determined, and for the convenience of comparison, we select similar dimensions for the GVAE model. From Figures 4a and 5a, we can see that many nodes have multiple latent features with high probability, and the latent representation contains rich information and complex correlation. However, in Figures 4b and 5b, the latent representation has higher sparsity, and the latent features of each node are more explicit. In the same dimension of latent space, the latent representation generated by GVAE will bring more disturbing information and severely restrict the nodes to find the most representative latent features.