## 5 Experiments
### Results  
First, we show the normalized training loss for RLC-GNN with 4, 6, 11, 19, and 27 layers in Figure 12. As the number of layers increases, the overall normalized training loss goes down. As we have discussed above, the final loss, \(Loss_{\Sigma}\), consists of the loss of similarity measure modules from every layer. In other words, \(Loss_{\Sigma}\) contains more items as the number of layer increases. However, we note that more layers leads to greater loss reduction ratio on the contrary. Tendency of training loss of each layer in Figure 13 shows that latter layer can make better inferences based on inherited knowledge of previous layers, which shows the effectiveness of proposed method on dealing with the single-layer learning problem. Moreover, we notice that the second layer makes the greatest improvement. Although the latter layers do not obtain as much improvement as the second layer, they indeed perform better layer by layer. Here we give the empirical analysis. As the number of layers increases, the problems to be solved for each layer become simpler. For instance, the single-layer model has to solve the entire problem alone. There is no other layers to share its learning pressure and to correct its mistakes. When we add more layers, each layer only needs to deal with partial problems (i.e., problems become easier for every layer). The remaining problems and the mistakes made by previous layers will be solvedand corrected by subsequent layers. More precisely, because of the input of each layer consisting of original dataset, aggregated information and progress already made, each layer has sufficient information to judge the correctness of inferences (i.e., giving higher confidence to correct inferences, and correcting the wrongs). Furthermore, if a layer has not yet been trained well, input features can skip the layer by passing through shortcut connection. The training will not be interrupted, and the problem will be directly handed over to the next layer for processing. With such cooperation mechanism, the whole problem can be solved more smoothly. We show the performance of RLC-GNN and various GNNs on the fraud detection tasks on Yelp and Amazon datasets in Table 2. GCN, GAT, GraphSAGE, and GeniePath are designed to run on homogeneous graphs. Multiple relations are merged into a single relation (i.e., heterogeneous to homogeneous) in the experiments of these GNNs [2]. Compared with the single-relation GNNs, we can see that multi-relation GNNs have great advantages on tasks based on heterogeneous graphs. Furthermore, it might point out a direction for future development of GNNs. Moreover, based on this superiority, proposed RLC-GNN introduces the mechanism of progressive-learning and self-correcting, which makes the use of neighboring information as more effective as possible and once again achieves significant improvements. Figure 12: The normalized training loss for RLC-GNN with varying depth on Amazon dataset (**a**) and Yelp dataset (**b**). As it can be seen, an obvious characteristic on both dataset is that the overall training loss is lower with the increasing of layers. Table 3 shows the experiment results of RLC-GNN with various depth. According to the experimental results, RLC-GNN outperforms CARE-GNN significantly, especially on the more complex Yelp dataset. On the Yelp dataset, the model with 27 layers achieves the best performance in our experiments, and recall, AUC, and F1-score increase by 5.66%, 7.72%, and 8.90%, respectively. On the Amazon dataset, when RLC-GNN has 11 layers, overall results outperform other settings, which Recall, AUC and F1 increase by 3.22%, 4.05%, and 3.25%, respectively. The original feature dimension size of Yelp dataset and Amazon dataset are 32 and 25, respectively. Generally, the more complex the features are, the more complex model we will need to fit data.