# GRNN: Graph-Retraining Neural Network for Semi-Supervised Node Classification
## 5 Experiments and Discussion
### Result Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{4}{c}{**Label Rate**} \\  & **0.5\%** & **1\%** & **2\%** & **3\%** & **4\%** & **5\%** \\ \hline LP & 56.4 & 62.3 & 65.4 & 67.5 & 69.0 & 70.2 \\ GCN & 50.9 & 62.3 & 72.2 & 76.5 & 78.4 & 79.7 \\ Co-training [6] & 56.6 & 66.4 & 73.5 & 75.9 & 78.9 & 80.8 \\ Self-training [6] & 53.7 & 66.1 & 73.8 & 77.2 & 79.4 & 80.0 \\ Union [6] & 58.5 & **69.9** & 75.9 & 78.5 & 80.4 & 81.7 \\ InterSection [6] & 49.7 & 65.0 & 72.9 & 77.1 & 79.4 & 80.2 \\ MultiStage [50] & 61.1 & 63.7 & 74.4 & 76.1 & 77.2 & - \\ M3S [50] & 61.5 & 67.2 & 75.6 & 77.8 & 78.0 & - \\ \hline GRNN-0 & 55.4 & 65.0 & 75.3 & 75.7 & 79.9 & 81.0 \\ GRNN & **63.0** & 69.2 & **79.2** & **80.2** & **82.4** & **82.8** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of classification accuracy (%) results with fewer training samples on Cora. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{4}{c}{**Label Rate**} \\  & **0.5\%** & **1\%** & **2\%** & **3\%** & **4\%** & **5\%** \\ \hline LP & 34.8 & 40.2 & 43.6 & 45.3 & 46.4 & 47.3 \\ GCN & 43.6 & 55.3 & 64.9 & 67.5 & 68.7 & 69.6 \\ Co-training [6] & 47.3 & 55.7 & 62.1 & 62.5 & 64.5 & 65.5 \\ Self-training [6] & 43.3 & 58.1 & 68.2 & 69.8 & 70.4 & 71.0 \\ Union [6] & 46.3 & 59.1 & 66.7 & 66.7 & 67.6 & 68.2 \\ InterSection [6] & 42.9 & 59.1 & 68.6 & 70.1 & 70.8 & 71.2 \\ MultiStage [50] & 53.0 & 57.8 & 63.8 & 68.0 & 69.0 & - \\ M3S [50] & 56.1 & 62.1 & 66.4 & 70.3 & 70.5 & - \\ \hline GRNN-0 & 53.1 & 60.9 & 66.2 & 68.9 & 70.2 & 70.7 \\ GRNN & **60.0** & **66.0** & **69.4** & **70.8** & **71.5** & **71.7** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of classification accuracy (%) results with fewer training samples on Citeseer. of label rates across the three datasets. When the training size was small, the benchmark neural network GRNN-0, which is equivalent to the improved GCN, was much better than GCN in most cases. For example, GRNN-0 improved over GCN by 4.5% and 9.5%, with a labeling rate of 0.5%, on Cora and CiteSeer, respectively, and improved over GCN by 4.4%, with a labeling rate of 0.05% on PubMed. When the training size grew, GRNN-0 was still better than GCN in most cases, demonstrating the effectiveness of the multi-head operation and the dropout of edges as well as nodes. Moreover, GRNN was better than GRNN-0, especially when the training size was small. For example, GRNN improved over GRNN-0 by 7.6% and 6.9% with a labeling rate of 0.5% on Cora and CiteSeer, respectively, and improved over GRNN-0 by 6.9% with a labeling rate of 0.05% on PubMed. These also show that it is beneficial to reduce the global smoothing error over the graph by iteratively training the graph neural network. Analyzing Tables 7 and 8, with labeling rates of 3.5%, 7.0%, and 10.0% on Wiki, it can be inferred that GRNN improved over GRNN-0 by 2.9%, 2.5%, and 1.6%, respectively; GCN+GRNN improved over GCN by 3.6%, 2.8%, and 1.8%, respectively; and GCNII+GRNN improved over GCNII by 2.3%, 3.5%, and 1.7%, respectively. Moreover, GCN+GRNN only improved over GCN by 0.03% on Arxiv, which indicates that the global smoothing model is not effective when the label rate is large. Moreover, Figure 3 evaluating the contributions of GRNN with different layers shows that GRNN with two layers achieved stability and high accuracy in the standard citation network with the increase in the number of iterations. With the increase in the number of iterations, the effect of GRNN follows the law of diminishing marginal utility. Therefore, in the absence of current GPU computing capability integration, we recommend that the number of iterations be about four (and even only two).