## 5 Experiments
### Experimental Results
#### 5.3.4 Affection of Number of Labeled Grids  
Generally, errors are fewer when more labeled grids are selected. Missing observed values in a real case is usual. Hence, in our experimental settings in Section 5.2, the number  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**No. of Data** & \(\mathbf{T_{0}}\) & \(\mathbf{T_{1}-T_{6}}\) & \(\mathbf{T_{7}-T_{12}}\) & \(\mathbf{T_{13}-T_{18}}\) & \(\mathbf{T_{19}-T_{24}}\) \\ \hline Data 1 & 16.92 & 17.49 & 18.78 & 19.36 & 20.18 \\ Data 2 & 19.98 & 18.24 & 18.38 & 18.83 & 19.93 \\ Data 3 & 21.02 & 20.17 & 20.31 & 21.11 & 22.26 \\ Data 4 & 19.86 & 22.63 & 23.77 & 24.89 & 30.67 \\ Data 5 & 16.18 & 18.15 & 18.33 & 17.83 & 19.18 \\ Data 6 & 20.92 & 20.83 & 19.16 & 20.93 & 23.08 \\ Data 7 & 21.96 & 22.36 & 23.81 & 22.97 & 25.89 \\ Data 8 & 22.34 & 20.78 & 20.34 & 23.52 & 23.80 \\ Data 9 & 19.16 & 17.49 & 17.54 & 17.92 & 19.34 \\ Data 10 & 15.21 & 15.98 & 16.76 & 16.75 & 18.17 \\ \hline \hline \multirow{2}{*}{AVERAGE} & MAE & 19.35 & 19.41 & 19.72 & 20.41 & 22.25 \\  & RMSE & 33.78 & 32.08 & 33.14 & 35.88 & 39.95 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The detailed results of our proposed model with weighted summation for all 10 times. The values in the table are the MAE of AQI values.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**No. of Data** & \(\mathbf{T_{0}}\) & \(\mathbf{T_{1}-T_{6}}\) & \(\mathbf{T_{7}-T_{12}}\) & \(\mathbf{T_{13}-T_{18}}\) & \(\mathbf{T_{19}-T_{24}}\) \\ \hline Data 1 & 16.88 & 17.31 & 18.39 & 19.66 & 20.61 \\ Data 2 & 20.46 & 17.90 & 17.46 & 18.80 & 19.83 \\ Data 3 & 23.12 & 20.86 & 22.39 & 23.74 & 28.83 \\ Data 4 & 17.50 & 19.16 & 19.37 & 21.29 & 23.29 \\ Data 5 & 18.60 & 21.90 & 26.15 & 22.00 & 25.08 \\ Data 6 & 20.28 & 18.33 & 20.41 & 21.31 & 23.84 \\ Data 7 & 21.40 & 22.67 & 24.79 & 23.46 & 24.08 \\ Data 8 & 23.41 & 20.61 & 19.24 & 22.27 & 23.29 \\ Data 9 & 20.17 & 17.76 & 18.72 & 19.71 & 20.22 \\ Data 10 & 15.42 & 15.93 & 17.16 & 17.41 & 18.78 \\ \hline \hline \multirow{2}{*}{AVERAGE} & MAE & 19.72 & 19.24 & 20.41 & 20.97 & 22.78 \\  & RMSE & 33.90 & 32.76 & 34.76 & 37.46 & 41.71 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The results of aggregating two data flow with simple summation in all 10 times. The values in the table are the MAE of AQI values.  
of labeled grids might influence available data for training and testing. In other words, it is more difficult to have complete historical PM\({}_{2.5}\) data with at least 20 labeled grids than with at least 15 labeled grids. In this part, we experiment with the different numbers of labeled grids (k) to discuss the effect of k.  
To set up the experiment, we select the same amount (15,210) of data with different k. Namely, k as the only variation means that the result will not be influenced by the total amount of data or predicted target. We experiment with k at 10, 15, and 20 as appropriate values in our dataset. First, we randomly select 20 labeled grids from 35 grids with monitoring stations and collect all available data. Next, we randomly select 15 grids from the previously selected 20 as the labeled grids and with k = 15, and randomly select 10 from the selected 15 grids. We then filter the selected number of k stations in previously collected data. The predicted unlabeled grids, predicted values and the number of all collected available data are the same with a different k. The only difference is the set of labeled grids used for reference. We then repeat the steps to select grids and collect available data 10 times and also evaluate the effect of k with average MAE and RMSE in Table 7. As we expected, our model performs better with a larger k because there is more referable monitoring stations. However, a larger k is not feasible in real life due to the completeness of observed data stated in the previous section. Thus, we choose an appropriate k = 15 as our setting in this dataset.