## 3 Results
### Overall Performance of LSTM and DNN Models with the Network Method  
The performance of the LSTM model depends on the input data, and it is determined by the parameters constituting the model. The weights and biases for model learning are called parameters. The parameters included activation, time period, optimizer, learning rate, and loss. The modeling performance of DNN models depends on the input data, and optimal values are determined by the hyperparameters constituting the model. The weights and biases that the models learn are called hyperparameters. Hyperparameters include the learning rate, hidden layer, hidden nodes, drop-out, and time period. Depending on the user, parameters and hyperparameters must be manually set for the best combination for the model. In addition, since the hyperparameter value for each model differs depending on the input and output variables, a specific value cannot be defined as an optimal value. Therefore, it is necessary to derive the optimal hyperparameter value using the random search method. The optimal parameter settings used in this study are listed in Table 2. The rectified linear unit (ReLU) is one of the most frequently used activation functions. It is a function to solve the gradient vanishing problem of sigmoid and tanh. Adaptive moment estimation (Adam) is a method for adaptively adjusting the updated intensity of learning by reducing the learning rate and calculating the rate. The mean squared error (MSE) is the average value after squaring the difference between the predicted value and the actual value. The DNN model also needs to derive the optimal hyperparameter values using a random search method. The optimal hyperparameter settings used in this study are listed in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & \begin{tabular}{c} **Values** \\ **(PM\({}_{10}\) Prediction Model (1))** \\ \end{tabular} & \
\begin{tabular}{c} **Values** \\ **(PM\({}_{2.5}\) Prediction Model (2))** \\ \end{tabular} &
\begin{tabular}{c} **Values** \\ **(O\({}_{3}\) Prediction Model (3))** \\ \end{tabular} \\ \hline Activation & ReLU & ReLU & ReLU \\ \hline Time period & 14 & \(11\) & 27 \\ \hline Optimizer & Adam & Adam & Adam \\ \hline Learning-rate & 0.01 & 0.01 & 0.01 \\ \hline Loss & MSE & MSE & MSE \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Setting of parameters in LSTM. Each of the six pollutants from the station is predicted using each of the six pollutants’ data as an independent variable (pollutant prediction models). The six pollutants are fine dust (PM\({}_{10}\)), fine particulate matter (PM\({}_{2.5}\)), ozone (O\({}_{3}\)), sulfurrous acid gas (SO\({}_{2}\)), nitrogen dioxide (NO\({}_{2}\)), and carbon monoxide (CO). Figure 6: Construction of links in station network. Black pentagonal points represent six pollutant stations located in a neighboring city, and black lines represent six pollutant stations connected in neighboring stations. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Models**} & **Correlation Coefficient** & **Normalized Root Mean** & **Nash–Sutcliffe** \\  & **Coefficient** & **Squared Error (\%)** & **Efficiency Coefficient** \\ \hline PM\({}_{10}\) & 0.88 & 0.16 & 0.93 \\ prediction model (1) & 0.90 & 0.12 & 0.95 \\ \hline PM\({}_{2.5}\) & 0.90 & 0.12 & 0.95 \\ prediction model (2) & 0.85 & 0.19 & 0.91 \\ \hline O\({}_{3}\) & 0.85 & 0.19 & 0.91 \\ prediction model (3) & 0.86 & 0.18 & 0.92 \\ \hline SO\({}_{2}\) & 0.88 & 0.16 & 0.93 \\ prediction model (5) & & & \\ \hline CO & 0.90 & 0.12 & 0.95 \\ prediction model (6) & & & \\ \hline CAI & 0.91 & 0.10 & 0.96 \\ prediction model (7) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation of predictive power by the LSTM and DNN models.