# Session-Based Recommendations for e-Commerce with Graph-Based Data Modeling
## 5 The Experimentation Procedure and Results
### Results and Discussion
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Dataset** & **Method** & **Rec@10** & **MRR@10** & **Rec@20** & **MRR@20** & **Rec@30** & **MRR@30** \\ \hline \multirow{8}{*}{Leather} & SR-GNN & 0.5007 & 0.2723 & 0.6028 & 0.2793 & 0.6574 & 0.2814 \\  & GCE-GNN & **0.5391** & 0.2686 & **0.6452** & 0.2760 & **0.6994** & 0.2781 \\  & IC-GAR & 0.4744 & 0.2675 & 0.5654 & 0.2734 & 0.6171 & 0.2754 \\  & Pair Popularity & 0.4776 & 0.2605 & 0.5678 & 0.2667 & 0.6206 & 0.2688 \\  & HSP & 0.4878 & 0.2837 & 0.5632 & 0.2892 & 0.6028 & 0.2905 \\  & RIC CiL & 0.5308 & **0.2986** & 0.6175 & **0.3046** & 0.6683 & **0.3066** \\  & RIC plain & 0.5083 & 0.1984 & 0.6062 & 0.2053 & 0.6594 & 0.2074 \\ \hline \multirow{8}{*}{Yoochoose1/64 Pair Popularity} & SR-GNN & 0.6013 & **0.2990** & 0.7059 & **0.3070** & 0.7546 & **0.3080** \\  & GCE-GNN & **0.6113** & 0.2966 & **0.7117** & 0.3040 & **0.7660** & 0.3060 \\  & IC-GAR & 0.5776 & 0.2947 & 0.6803 & 0.3018 & 0.7310 & 0.3039 \\  & Pair Popularity & 0.4266 & 0.2108 & 0.5227 & 0.2176 & 0.5715 & 0.2196 \\  & HSP & 0.5455 & 0.2766 & 0.6409 & 0.2833 & 0.6835 & 0.2850 \\  & RIC CiL & 0.4365 & 0.2147 & 0.5366 & 0.2217 & 0.5865 & 0.2237 \\  & RIC plain & 0.5693 & 0.2755 & 0.6791 & 0.2832 & 0.7307 & 0.2853 \\ \hline \multirow{8}{*}{Diginetica} & SR-GNN & 0.3877 & 0.1697 & 0.5160 & 0.1788 & 0.5945 & 0.1819 \\  & GCE-GNN & **0.4104** & **0.1812** & **0.5426** & **0.1900** & **0.6193** & **0.1932** \\ \cline{1-1}  & IC-GAR & 0.3581 & 0.1572 & 0.4838 & 0.1659 & 0.5631 & 0.1691 \\ \cline{1-1}  & Pair Popularity & 0.2664 & 0.1078 & 0.3685 & 0.1149 & 0.4271 & 0.1173 \\ \cline{1-1}  & HSP & 0.2742 & 0.1225 & 0.3414 & 0.1273 & 0.3692 & 0.1283 \\ \cline{1-1}  & RIC CiL & 0.3190 & 0.1406 & 0.4295 & 0.1483 & 0.4944 & 0.1509 \\ \cline{1-1}  & RIC plain & 0.3931 & 0.1777 & 0.5134 & 0.1860 & 0.5806 & 0.1868 \\ \hline \multirow{8}{*}{eElectronics} & SR-GNN & 0.4041 & 0.1958 & 0.4957 & 0.2023 & 0.5453 & 0.2043 \\ \cline{1-1}  & GCE-GNN & **0.4553** & 0.2116 & **0.5555** & 0.2185 & **0.6037** & 0.2204 \\ \cline{1-1}  & IC-GAR & 0.3868 & 0.2004 & 0.4730 & 0.2057 & 0.5188 & 0.2075 \\ \cline{1-1}  & Pair Popularity & 0.3842 & 0.1872 & 0.4697 & 0.1931 & 0.5100 & 0.1948 \\ \cline{1-1}  & HSP & 0.3668 & 0.2068 & 0.4243 & 0.2109 & 0.4491 & 0.2119 \\ \cline{1-1}  & RIC CiL & 0.4525 & **0.2382** & 0.5421 & **0.2444** & 0.5892 & **0.2463** \\ \cline{1-1}  & RIC plain & 0.4390 & 0.1685 & 0.5356 & 0.1752 & 0.5854 & 0.1772 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison results of our methods against three state-of-the-art Graph Neural Network recommendation models. The MRR@[10,20,30] and Recall@[10,20,30] are used as evaluation metrics. The best performance for each dataset and corresponding metric is marked by bold-face numbers. Additionally, our experiments show that the GCE-GNN model achieves the best Recall@\(k\) for any \(k\) in all the datasets. In combination with the previous observations, we conclude that the GCE-GNN model is the most efficient one in finding the next item somewhere in the top-\(k\) list. However, it has still some difficulty in placing the next item in a high ranking position unless it is the same item as the current one. This is more obvious when studying the top 10 recommendations in the Leather and eElectronics datasets. In this case, we note that, although Rec@10 is almost identical for GCE-GNN and RIC-CiL, GCE-GNN has a significantly lower MRR@10 (between 2.5-3%)  
Comparing HSP and RIC with each other, we find that HSP is inferior to RIC-CiL in the case of the non-repeating datasets (Leather and eElectronics) and inferior or very close to the performance of RIC-plain in the item-repeating datasets (Diginetica and Yoochoose1/64). Especially in the case of Yoochoose1/64, the HSP and RIC-plain are almost equivalent in terms of MRR performance although HSP is inferior in terms of the Rec@\(k\) metric. In the case of the Diginetica dataset, the performance of HSP is inferior to both versions of RIC.