# Product Demand Prediction with Spatial Graph Neural Networks
## 4 Experiments
### Ablation Study (RQ2)  
To delve deeper into the intricacies of our Spatial Graph Neural Network model's architecture and to answer Research Question 2 (RQ2), we embarked on an exploratory journey to dissect the influence of individual components within our model. Specifically, we scrutinized the unique contributions of the spatial adjacency and attention-aware message propagation modules by systematically omitting each from the SGNN framework and observing the subsequent impact on prediction accuracy. This methodical approach allowed us to isolate and understand the value added by these critical modules. The results of this analysis are meticulously compiled in Table 2. In this table, \"spatial\" refers to the module that integrates spatial adjacency information, while \"attention\" corresponds to the module that facilitates attention-aware message propagation. The comparative performance metrics, including MAE, RMSE, and R\({}^{2}\), serve as clear indicators of each module's significance. Upon reviewing the table, it becomes apparent that the absence of either the spatial or attention module from the SGNN framework results in a marked reduction in predictive performance. This is evidenced by increased values of MAE and RMSE, alongside decreased R\({}^{2}\) scores, signaling a decline in the model's ability to predict product demand accurately. Such findings underscore the indispensable nature of both modules in our predictive framework. The spatial adjacency module, in particular, plays a pivotal role by embedding geographical information into the model, thereby allowing for a nuanced understanding of spatial relationships and their impact on product demand. The noticeable performance drop observed upon the removal of this module underscores its critical contribution to capturing the spatial dynamics integral to accurate demand prediction. Similarly, the attention-aware message-propagation module enriches the model by enabling it to selectively prioritize and learn from the information disseminated across neighboring nodes. This adaptability enhances the model's capacity to discern relevant patterns and relationships, further bolstering its predictive accuracy. In sum, the ablation study not only reaffirms the value of incorporating geographical information into demand prediction models but also highlights the synergistic effect of combining spatial adjacency with attention mechanisms. The discernible performance degradation observed upon excluding these modules validates our initial hypothesis and motivation for their integration, solidifying their status as cornerstone components of our SGNN framework. This insight not only propels our understanding of SGNN's inner workings but also paves the way for future enhancements and optimizations in geographical demand prediction methodologies. To further elucidate the impact of our proposed modules, we also evaluated a stripped-down version of SGNN without both the spatial adjacency and attention-aware message propagation modules. This basic GNN model achieved an MAE of 0.2103, RMSE of 0.2014, and R\({}^{2}\) of 0.8976. These results, which are notably inferior to the full SGNN model, underscore the significant contributions of \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Avito**} \\ \cline{2-4}  & **MAE** & **RMSE** & **R\({}^{2}\)** \\ \hline GLM & 0.3285 & 0.3172 & 0.7349 \\ \hline XGBoost & 0.2891 & 0.2587 & 0.8170 \\ \hline LightGBM & 0.2572 & 0.2312 & 0.8346 \\ \hline CatBoost & 0.2689 & 0.2563 & 0.8308 \\ \hline MLP & 0.2952 & 0.2951 & 0.7652 \\ \hline LSTM & 0.2491 & 0.2286 & 0.8569 \\ \hline GRU & 0.2438 & 0.2210 & 0.8625 \\ \hline CNN & 0.2347 & 0.2054 & 0.8901 \\ \hline SGNN & 0.1685 & 0.1504 & 0.9234 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The evaluation performance of various baselines and our SGNN on the Avito dataset for product demand prediction. both modules to the model's predictive performance.