# Novel MIA-LSTM Deep Learning Hybrid Model with Data Preprocessing for Forecasting of PM2.5
## 5 Results & Discussions
### Performance of Proposed Method
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**RAW Data (Removed Missing Values)**} & \multicolumn{4}{c}{**Imputed Data**} & \multicolumn{4}{c}{**Proposed Method**} \\ \hline
**Aotizhonhxin** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline
**Univariate LSTM** & 28.1138 & 63.4783 & 0.45535 & 18.083 & 44.4132 & 0.7165 & 30.6951 & 63.0365 & 0.3073 \\
**Univariate 1D** & 10.8385 & 19.8228 & 0.9468 & 11.2217 & 20.54922 & 0.9393 & 10.7215 & 19.4150 & 0.9342 \\
**Univariate GRU** & 20.9584 & 51.2164 & 0.6454 & 19.6057 & 47.97042 & 0.6692 & 16.9252 & 39.5841 & 0.7268 \\
**Multivariate LSTM** & 10.4696 & 13.6125 & 0.7509 & 13.7667 & 19.78918 & 0.8095 & 7.44549 & 9.8883 & 0.8159 \\ \hline
**Gucheng** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline
**Univariate LSTM** & 24.574 & 61.329 & 0.5888 & 20.867 & 53.297 & 0.619 & 17.653 & 41.912 & 0.6882 \\
**Univariate 1D** & 12.586 & 23.795 & 0.9381 & 11.699 & 22.004 & 0.9351 & 10.56 & 19.832 & 0.9302 \\
**Univariate GRU** & 25.761 & 63.746 & 0.5557 & 25.227 & 61.884 & 0.4863 & 19.555 & 46.121 & 0.6224 \\
**Multivariate LSTM** & 19.12256 & 23.00376 & 0.148226 & 18.0171 & 26.6355 & 0.8444 & 11.1987 & 13.9660 & 0.6480 \\ \hline
**Tiantan** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline
**Univariate LSTM** & 32.311 & 68.194 & 0.3872 & 57.104 & 65.6630 & \(-0.382\) & 21.272 & 47.265 & 0.6202 \\
**Univariate 1D** & 11.431 & 19.983 & 0.9474 & 11.674 & 20.352 & 0.9373 & 11.211 & 19.567 & 0.9349 \\
**Univariate GRU** & 31.733 & 67.657 & 0.3969 & 28.747 & 63.273 & 0.3939 & 19.312 & 43.369 & 0.6802 \\
**Multivariate LSTM** & 13.10567 & 17.301 & 0.8305 & 18.0027 & 28.239 & 0.8054 & 10.6244 & 13.884 & 0.5845 \\ \hline
**Ghazibad** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline
**Univariate LSTM** & 30.1511 & 62.4346 & 0.4963 & 43.7731 & 94.1758 & 0.4100 & 37.0318 & 74.6937 & 0.4000 \\
**Univariate 1D** & 17.5631 & 34.6024 & 0.8453 & 21.4284 & 43.8764 & 0.87194 & 24.7072 & 43.5987 & 0.7955 \\
**Univariate GRU** & 46.8667 & 87.3550 & 0.0140 & 31.1143 & 72.6943 & 0.6484 & 68.5177 & 112.294 & \(-0.3561\) \\
**Multivariate LSTM** & 32.3471 & 46.6165 & 0.6351 & 14.7406 & 21.0891 & 0.2630 & 13.002 & 16.5374 & \(-0.0237\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of results of experimentation performed on the dataset of four cities. Figure 4: Graphs showing MAE values for all experimentations. It is clear that the proposed method obtains the best result with the smallest RMSE value among all the methods. For the Gucheng location, the results show that the RMSE values for the raw data with the missing values removal, with IIET imputed data, and with the proposed data preprocessing method are 23.7949, 22.0042, and19.8316, respectively; the case is the same for the MAE values which are 12.5858, 11.6991, and 10.5600, respectively, which shows that prediction error decreases as we preprocess the data initially with imputation and later by removing anomalies. Moreover, the R\({}^{2}\) value is 0.9302, which is the highest among all the methods, showing that 1D CNN is better in comparison to all regression models in terms of the RMSE value. Table 4 shows the results for the dataset from Ghaziabad, India. The best results are obtained from the multivariate LSTM model. With the proposed method, the RMSE values for the raw data with the missing values removal, with IIET imputed data, and with the proposed data preprocessing method are 46.6165, 21.0891, and 16.5373, respectively. The case is the same with the MAE values which are 32.3471, 14.7405, and 13.0029, respectively.