## 4 Experiments
### Complexity Analysis  
The computation time of the proposed ATKGRM framework is mainly determined by evaluating the objective functions L in (21), (23), and gradients against feature vectors (variables). The time complexity of negative sampling optimization algorithms is O (log W), where W is the size of vocabulary for users and items. The computational complexity of gradients \(\partial\)L/\(\partial\)u, \(\partial\)L/\(\partial\)i, \(\partial\)L/\(\partial\)i in (21) is O (k \(\mid\)\(\Omega\)\(\mid\)), where k is the dimension of the latent vector, and \(\mid\)\(\Omega\)\(\mid\) is the number of users and items observed. The computational complexity of gradients \(\partial\)L/\(\partial\)u and \(\partial\)L/\(\partial\)vp, \(\partial\)L/\(\partial\)vc, \(\partial\)L/\(\partial\)vn in (23) is O (k (r + 1) \(\mid\)\(\Omega\)\(\mid\)), where r is the number of negative samples per positive instance. Therefore, the overall computational complexity of T iterations is O (k (r + 1) \(\mid\)\(\Omega\)\(\mid\)T + log W) for implicit feedback. On the other hand, since explicit feedback does not require negative sampling, r = 0 is used to compute explicit feedback. The overall computation time is linear with the observations of rating matrices. Then, we carry out a performance comparison and discussion. As shown in Table 9, our method has more parameters than NESVD and KGCN, but it corresponds to the best RMSE results on both datasets. As for NESVD, it only uses interactive data, and our model uses not only interactive data but also knowledge graph information, which increases the complexity of the model in the process of knowledge graph aggregation. Compared with KGCN, we have extra MLP layers, which increases the complexity of the model. However, the overall performance of ATKGRM is better than that of the baseline model, GCGAN. To sum up, ATKGRM does have higher complexity, but our model has achieved a good result on the value of RMSE. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**H**} & \multicolumn{2}{c}{**MovieLens-20M**} & \multicolumn{2}{c}{**Book-Crossing**} & \multicolumn{2}{c}{**Last. FM**} \\ \cline{2-6}  & **AUC** & **F1** & **AUC** & **F1** & **AUC** & **F1** \\ \hline
1 & 0.981 & 0.946 & 0.782 & 0.723 & 0.857 & 0.776 \\
2 & 0.984 & 0.954 & 0.773 & 0.715 & 0.850 & 0.773 \\
3 & 0.983 & 0.952 & 0.769 & 0.708 & 0.844 & 0.769 \\
4 & 0.980 & 0.948 & 0.764 & 0.701 & 0.840 & 0.760 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Experimental performance of ATKGRM with different H values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**MovieLens-1M**} & \multicolumn{2}{c}{**MovieLens-10M**} \\ \cline{2-5}  & **Parameters** & **RMSE** & **Parameters** & **RMSE** \\ \hline NESVD & 4.75 M & 0.826 & 39.3 M & 0.762 \\ KGCN & 3.4 M & 0.517 & 20 M & 0.446 \\ GCGAN & 30 M & 0.599 & 52 M & 0.525 \\ ATKGRM & 16 M & 0.511 & 49 M & 0.441 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The number of parameters and the results of RMSE on different models (M denotes “million”). The results show that our method has more parameters than NESVD and KGCN, but it corresponds to the best RMSE results on both datasets. As for NESVD, it only uses interactive data, and our method uses not only interactive data but also knowledge graph information, which increases the complexity of the model in the process of knowledge graph aggregation. Compared with KGCN, we have extra MLP layers, which increases the complexity of the model. Moreover, the overall performance of ATKGRM is better than that of the baseline model, GCGAN, and we have advantages in both the number of parameters and RMSE. At the same time, to verify the scalability of the model ATKGRM on large-scale data, we also expand the comparison of our model to different aggregation layers (H) and training data ratios (D). As shown in Table 10, the overall computation time is linear with the observations of rating matrices. Our proposed ATKGRM has good potential to scale to large-scale datasets.