## 4 Methodology
Moreover, then we calculate losses of similarity measure modules and RLC-GNN (Equations (13) and (14)), and do backpropagation to update trainable parameters. At last, we use the reinforcement learning modules to update selector thresholds. ```
Input: Graph with features: \(\mathcal{G}=\{V,X,E\}\); Number of layers, epochs, batches and relationships: \(L,E,B,R\); Similarity measures: \(\{S^{(k)}\}_{k=1}^{L}\); Selector thresholds: \(\{p_{1}^{(k)},p_{2}^{(k)},...,p_{R}^{(k)}\}_{k=1}^{L}\); Inter-relation AGGs: \(\{AGG^{k}\}_{k=1}^{L}\); Intra-relation AGGs: \(\{AGG^{k}_{1},AGG^{k}_{2},...,AGG^{k}_{R}\}_{k=1}^{L}\) Output: Nodes embeddings after last layer: \(\omega_{v},v\in V\)
```  
```
for\(e=1\) to \(E\)do for\(b=1\) to \(B\)do for\(k=1\) to \(L\)do if\(k=1\)then /* Layered structure */ \((h_{v}^{(1)},h_{u})\leftarrow(x_{v},x_{u}),x\in X,v\in V_{b},u\in V\); else \((h_{v}^{(k)},h_{u})\leftarrow(\omega_{v}^{(k-1)},x_{u}),v\in V_{b},u\in V\);  end for for\(r=1\) to \(R\)do \(D^{(k)}\leftarrow\) Equation (8), \(v\in V_{b}\); \(S^{(k)}\leftarrow\) Equation (5), \(v\in V_{b}\) ; /* Similarity measure */ \(X^{(k)}_{v\in V}\leftarrow\) top-p sampling ; /* Select neighbors */ \(h_{v,r}^{(k)}\leftarrow\) Equation (6), \(v\in V_{b}\); /* Intra-relation aggregate */  end for \(h_{v}^{(k)}\leftarrow\) Equation (7), \(v\in V_{b}\) ; /* Inter-relation aggregate */ if\(d_{i}=d_{o}\)then /* Residual structure */ \(o^{(k)}\leftarrow\) Equation (11), \(v\in V_{b}\) ; /* Dimensions match */  else \(o^{(k)}\leftarrow\) Equation (12), \(v\in V_{b}\) ; /* Dimensions not match */  end for \(\mathcal{L}_{Simi}^{(k)}\leftarrow\) Equation (14), \(v\in V_{b}\);  end for \(\mathcal{L}_{GNN}\leftarrow\) Equation (14), \(v\in V_{b}\); \(\mathcal{L}_{\Sigma}\leftarrow\) Equation (13), \(v\in V_{b}\); for\(k=1\) to \(L\)do for\(r=1\) to \(R\)do  update \(p_{r}^{(k)}\) ; /* See [2] Section 3.3 for more details */  end for  end for  end for  end for
```  
**Algorithm 1**RLC-GNN  
When the node embeddings are input to a layer, there may be the case that the current layer has not been properly trained and the benign samples cannot be effectively filtered out during the similarity measure, which results in the features of fraudsters being covered up by benign samples' features. After the introduction of residual structure to the model, if the current layer causes an adverse effect on the classification, the input embeddings passing through the shortcut connection will reduce the losses during the propagation. Therefore, RLC-GNN has the ability to skip the layers which have not been trained well and perform the rollback of embeddings (i.e., we avoid \"bad\" layers blocking normal training of subsequent layers). The model will have opportunities to further learning the characteristics of fraudsters based on the knowledge that has been acquired by previous layers. Thus, as the learning process progresses layer by layer, more information will be taken into account and better selection will be made. In Figure 11, we show our implementation for RLC-GNN with various number of layers. If dimensions of input and output not match, we adopt a linear projection \(W_{s}\) to match the dimensions. Moreover, we show details of the architecture for RLC-GNN with various number of layers in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **4-Layers** & **6-Layers** & **11-Layers** & **19-Layers** & **27-Layers** \\ \hline \(N_{64}\) & 1 & 2 & 3 & 3 & 5 \\ \(N_{48}\) & 0 & 0 & 3 & 5 & 7 \\ \(N_{32}\) & 1 & 2 & 3 & 6 & 10 \\ \(N_{16}\) & 2 & 2 & 2 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Implementations for RLC-GNN with various number of layers. \(N_{d}\) denotes the number of layers whose dimension of input node embeddings is \(d\). Figure 11: Our implementation for RLC-GNN architecture in experiments. \(d_{i}\) and \(d_{o}\) denote dimensions of input and output, respectively. See Table 1 for details of architectures. Figure 10: Proposed RLC-GNN architecture.