# Visual Analysis of Spatiotemporal Data Predictions with Deep Learning Models
## 5 System Evaluation with Air Pollutant Prediction Models
### Analysis Based on Different Feature Selection  
When we reconsider the feature selection, we need to identify the problem with the selected features. The selected features, PM\({}_{10}\) and PM\({}_{2.5}\), have a strong linear relationship. Therefore, the PM\({}_{10}\) information is almost similar to the PM\({}_{2.5}\) information. If duplicate or nearly similar information is included in the input, the information may be insignificant in  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Selected Features** & **Model** & **Time Lag (h)** & **MAPE (\%)** \\ \hline \multirow{3}{*}{PM\({}_{2.5}\)} & \multirow{3}{*}{GRU} & 6 & 69.4 \\ \cline{3-4}  & & 24 & 89.6 \\ \cline{3-4}  & & 72 & 72.9 \\ \hline \multirow{3}{*}{PM\({}_{10}\)} & \multirow{3}{*}{LSTM} & 6 & 70.5 \\ \cline{3-4}  & & 24 & 83.0 \\ \cline{3-4}  & & 72 & 72.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Prediction accuracy of different time lags and models with PM\({}_{2.5}\) and PM\({}_{10}\) for gated recurrent units (GRU) and long short term memory (LSTM) with mean absolute percentage error (MAPE).  
Figure 2: The temporal autocorrelations of all variables are visualized over time lags. Humidity, noise, and temperature tend to have high autocorrelations every 24 h. However, PM\({}_{2.5}\) and PM\({}_{10}\) do not have repeated temporal autocorrelations.  
the prediction. Therefore, we train PM\({}_{2.5}\) again with temperature and humidity features, which have high linear coefficients next to PM\({}_{10}\). The results are summarized in Table 2 and visualized in Figure 3. We observe that the model with PM\({}_{2.5}\), humidity, and temperature produces more accurate prediction than one with only PM\({}_{2.5}\) and PM\({}_{10}\) as presented in Figure 3a,b. The fixed model with the same features predict PM\({}_{2.5}\) differently according to the time lags, as shown in Figure 3c-e. Although the average MAPE with the time lag of 6 h is lower than one with the time lag of 24 h, we observe that the time lag of 24 h produces lower errors overall in the map visualizations.  
In the results after selecting the new feature set, we observe that the MAPE becomes smaller, compared to the previous feature selection. One reason for this is that duplicated  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Selected Features** & **Model** & **Time Lag (h)** & **MAPE (\%)** \\ \hline \multirow{4}{*}{\(\text{PM}_{2.5}\) Temperature Humidity} & \multirow{4}{*}{GRU} & 6 & 45.4 \\ \cline{3-4}  & & 24 & 43.0 \\ \cline{3-4}  & & 72 & 49.9 \\ \cline{3-4}  & & 6 & 49.1 \\ \cline{3-4}  & & 24 & 59.6 \\ \cline{3-4}  & & 72 & 82.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Prediction accuracy of different time lags and models with PM\({}_{2.5}\), temperature, humidity for gated recurrent units (GRU), long short term memory (LSTM) and mean absolute percentage error (MAPE).  
Figure 3: The visualizations of PM\({}_{2.5}\) predictions. (**a,b**) Visualizations of prediction results with different features. (**c–e**) Results with different time lags.  
information, as previously suspected, may somewhat degrade the prediction performance. We can also see that the model performance according to the time lag is stable in the case of GRU. However, in the case of LSTM, it can be seen that the accuracy decreases significantly as the time lag increases. Therefore, the GRU designed in this paper can be interpreted as being more robust to the past data than LSTM.