## 3 Result And Discussion
### Predictive Models
#### 3.1.3 Demand Prediction  
The effectiveness of the demand prediction model is presented below. In our experiment, the dataset is split into three groups: training, validation, and testing, with a ratio of 6:3:1. The training set is used during the training phase; the validation set is used for model selection and hyper-parameter tuning; the testing set is used for evaluation purposes.  
Here, we conduct an independent evaluation of the proposed model, examining its performance with respect to both the LSTM and MLP-MDN models. For LSTM, we tested  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Baseline**} & \multicolumn{2}{c}{**Proposed**} \\ \cline{2-5}  & LR & RF & MLP & **Ensemble Model** \\ \hline RMSE for 14 features & 0.32 & 0.59 & 0.25 & 0.098 \\ RMSE for 6 features & 3.61 & 3.44 & 3.33 & 3.26 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison of the proposed model and baseline models.  
Figure 5: Fare prediction testing results under different testing set sizes.  
three structures, namely, one layer, two layers, and three layers, with different numbers of hidden neurons and dropouts. Based on the testing results, the LSTM with a two-layer structure had the best performance. Therefore, we evaluate different numbers of hidden neurons and dropouts in the two-layer model. Table 2 shows the comparison of LSTM under different setups.  
As shown in the table, the LSTM with the \(n1,n2=600,600\) setup has the best performance. Furthermore, the inclusion of a dropout layer has minimal impact on the accuracy of the model. Here, we further compare our proposed LSTM model with four baseline models, namely, multilayer perceptron, ridge regression, lasso, and elastic net. We use the LSTM with \(n_{1},n_{2}=600,600\) setup for the comparison as it has the best performance. Table 3 presents the comparison of them.  
Based on the presented results, it is evident that our proposed model exhibits superior performance when evaluated using the RMSE metric. What is more, our model shows comparable performance in terms of the MAE metric compared to the other baseline models. Despite not attaining the highest performance in the MAE metric, the noteworthy achievement in the RMSE underscores the resilience of our proposed model in handling outlier scenarios. This advantage is expected to be further amplified with the inclusion of additional data from diverse time ranges.  
For MLP-MDN, we tested different numbers of hidden neurons. Table 4 presents a comparison of MDN under different setups. It is found that the model with the \(n_{1},n_{2}=200,200,M=40\) setup has the best performance.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Neg. Log-Likelihood** \\ \hline \(n_{1},n_{2}=100,100,M=20\) & \(-3.7557\) \\ \(n_{1},n_{2}=100,100,M=40\) & \(-3.7552\) \\ \(n_{1},n_{2}=100,100,M=80\) & \(-3.7999\) \\ \(n_{1},n_{2}=200,200,M=20\) & \(-3.7533\) \\ \(n_{1},n_{2}=200,200,M=40\) & \(-3.8394\) \\ \(n_{1},n_{2}=200,200,M=60\) & \(-3.7533\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance comparison of the MDN model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**2-Layer LSTM without Dropout**} & \multicolumn{2}{c}{**2-Layer LSTM with 0.1 Dropout**} \\ \cline{2-5}  & RMSE & MAE & RMSE & MAE \\ \hline \(n_{1},n_{2}=100,100\) & 4.7018 & 0.3104 & 4.8328 & 0.3474 \\ \(n_{1},n_{2}=200,200\) & 3.5504 & 0.2438 & 3.4462 & 0.3359 \\ \(n_{1},n_{2}=400,400\) & 3.3746 & 0.2413 & 3.4227 & 0.3370 \\ \(