## 4 Results and Discussion
### Comparisons with Other Multiple Instance Methods
\[\text{MIP}(\text{max}):\ \mathbf{z}=\text{max}\big{(}\mathbf{h_{j}}\big{)}\ j=1,2, \ldots,K \tag{14}\]  
\[\text{MIP}(\text{mean}):\ \mathbf{z}=\frac{1}{K}\sum_{j=1}^{K}\mathbf{h_{j}}\ j=1,2, \ldots,K \tag{15}\]  
\[\text{MIP}(\text{attention}):\ \mathbf{z}=\sum_{j=1}^{K}a_{j}\mathbf{h_{j}}\ a_{j}= \frac{\exp\Big{\{}\mathbf{w}^{\text{T}}\text{tan}\,\text{h}\Big{(}\mathbf{V} \mathbf{h_{j}^{\text{T}}}\Big{)}\Big{\}}}{\sum_{i=1}^{K}\exp\Big{\{}\mathbf{w} ^{\text{T}}\text{tan}\,\text{h}\Big{(}\mathbf{V}\mathbf{h_{i}^{\text{T}}} \Big{)}\Big{\}}} \tag{16}\]  
As mentioned in Section 2.2, pooling methods in the graph classification task include standard global pooling and hierarchical pooling methods. In order to compare with the GCN model with the standard global pooling method, extra experiments were conducted. As shown in Tables 3 and 4, GCN (mean_pool/max_pool) and GCN+DIFFPOOL methods refer to introducing a graph structure to solve the histopathological image classification problem. The former is based on a graph classification model with global pooling, which consists of three GCN layers and one global pooling layer, specifically. The latter adopts the network architecture proposed in the previous experiments, which is based on a graph classification model with DIFFOOL module, one hierarchical pooling method. Similarly, fully connected layers were added for final bag level classification. Experimental results show that classification performance of the proposed method has been evaluated. The proposed graph-based method showed superior performance compared with several MIL methods on two different gastric cancer pathological image datasets. Compared to the RMDL method, the graph-based method (GCN+DIFFPOOL) showed at least an increase of 4.5% in the final classification indicators. The proposed GCN+DIFFPOOL method achieved an average _F1_score_ of 90.75% and 98.24% on the SRS and Mars datasets, respectively. When applying MIL to the pathological image analysis tasks, the overlapping patches were viewed as instances in bags. Therefore, there must exist underlying structural information between instances in the same bag. The structure of the graph can model the relationships between the instances, and the GNNs can capture this \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall (\%)** & **Precision (\%)** & _F1\_Score (\%)_ \\ \hline MIP (mean) & 92.40 \(\pm\) 0.013 & 92.45 \(\pm\) 0.013 & 92.40 \(\pm\) 0.014 \\ MIP (max) & 95.48 \(\pm\) 0.011 & 95.52 \(\pm\) 0.011 & 95.45 \(\pm\) 0.011 \\ MIP (attention) & 93.11 \(\pm\) 0.009 & 93.15 \(\pm\) 0.009 & 93.13 \(\pm\) 0.009 \\ RMDL & 93.76 \(\pm\) 0.008 & 93.81 \(\pm\) 0.008 & 93.74 \(\pm\) 0.009 \\ GCN(mean_pool) & 95.81 \(\pm\) 0.008 & 95.83 \(\pm\) 0.008 & 95.81 \(\pm\) 0.008 \\ GCN (max_pool) & 97.70 \(\pm\) 0.007 & 96.73 \(\pm\) 0.007 & 97.70 \(\pm\) 0.007 \\ GCN + DIFFOOL} & 98.24 \(\pm\) 0.004 & 98.26 \(\pm\) 0.004 & 98.24 \(\pm\) 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of different MIL methods on Mars dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall (\%)** & **Precision (\%)** & _F1\_Score (\%)_ \\ \hline MIP (mean) & 82.10 \(\pm\) 0.051 & 82.70 \(\pm\) 0.051 & 81.83 \(\pm\) 0.051 \\ MIP (max) & 83.65 \(\pm\) 0.044 & 84.82 \(\pm\) 0.041 & 83.81 \(\pm\) 0.046 \\ MIP (attention) & 84.37 \(\pm\) 0.042 & 85.34 \(\pm\) 0.038 & 84.47 \(\pm\) 0.041 \\ RMDL & 84.47 \(\pm\) 0.044 & 85.29 \(\pm\) 0.042 & 84.23 \(\pm\) 0.045 \\ GCN (mean_pool) & 89.08 \(\pm\) 0.038 & 89.88 \(\pm\) 0.033 & 89.67 \(\pm\) 0.033 \\ GCN (max_pool) & 89.13 \(\pm\) 0.046 & 90.20 \(\pm\) 0.042 & 88.96 \(\pm\) 0.049 \\ GCN + DIFFOOL} & 90.40 \(\pm\) 0.032 & 91.16 \(\pm\) 0.032 & 90.75 \(\pm\) 0.034 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of different MIL methods on SRS dataset. structure information better in a non-independent, identically distributed MIL problem.