5.3. Results and Analysis
In order to verify the advantages of the proposed model, we show the comparison results of the actual and predicted values of STP-GLN in five types of data. The experimental results are shown in
Figure 9,
Figure 10,
Figure 11. We also selected six time series prediction models to compare with our proposed models, namely HA, LR, GCN, LSTM, STDensenNet [
18], and STGCN [
25], among which HA has only one evaluation index in all communities. The experimental results are shown in
Table 3,
Table 4,
Table 5.
In the selection of cells, we mainly choose two types of cells. The first one is all the cells in the test set, that is, the 264 moments of the true value of 400 cells compared with the predicted value. The second is the test set of the smallest error between the real value and the predicted value of one cell, that is, the 264 moments of the real value of one cell and the predicted value are compared, and the best cell predicted by the different models is not the same. Among which, HA is compared with other models only on the type of all cells. The experimental results are shown in
Table 3,
Table 4,
Table 5.
The GCN and LSTM of the “Model” in
Table 3,
Table 4,
Table 5 are the spatial model and the temporal module of the STP-GLN’s model, respectively. In order to clarify the role of each part of the STP-GLN model, we use three evaluation metrics to compare the correlation and importance of each module with the whole. As can be seen from
Table 3 and
Table 4, the spatial module plays a greater role than the temporal module in the SMS dataset and the Call dataset. From
Table 5, it can be seen that in the Internet dataset, the temporal module plays a greater role than the spatial model. Moreover, as a whole, the prediction effect of STP-GLN is better than that of each module individually, which indicates that our model adopts the method of spatiotemporal parallel structure correctly and adopts two correct deep learning methods to learn spatiotemporal features separately.
Table 3,
Table 4,
Table 5 represent the results of comparing our model and other models using the evaluation metrics in the five categories of data, respectively. The valid data in
Table 3,
Table 4,
Table 5 represent the results of comparing our model with other models. Meanwhile, because of the different order of magnitude of the five types of data, the usage of Internet is much larger than the usage of SMS and the usage of calls, and the usage of SMS is slightly larger than the usage of Call. Therefore, the prediction error in the Internet dataset is much larger than the prediction in the SMS dataset and the Call dataset, and the prediction error in the SMS dataset is larger than the prediction error in the Call dataset. This also explains why the valid numbers in
Table 5 are greater than those in
Table 3 and
Table 4, and the valid numbers in
Table 3 are greater than those in
Table 4. Therefore, the effective numbers of the three tables can only be related to the datasets they use and not to the datasets in the other tables.
Figure 9 shows the comparison of prediction results for SMS dataset over 7 days in one cell. The above figure shows the comparison of prediction results of the receiving SMS (SMS-in) dataset in the test set, and the following figure shows the comparison of prediction results of sending SMS (SMS-out) dataset in the test set.
Figure 10 shows the absolute value of the error between the true and predicted values over a period of 14 h in one cell. The smaller the absolute value of the error in
Figure 10, the better the prediction effect of the model. The above graph shows the prediction error for SMS-in dataset over a period of 14 h, the absolute error is at least 0.1 in this dataset, that is, the difference between the real value and the predicted value is 0.1, indicating that our model can well fit the future trend of the data. The following graph shows the prediction error for SMS-out dataset. The absolute error is at least 0.09, which indicates that the prediction effect is better.
The comparison of the experimental results of HA, LR, GCN, LSTM, STDensenNet [
18], and STGCN [
25] can be seen in
Table 3. On the SMS dataset, our model is better than other models in the evaluation of three evaluation indicators. For example, compared to the state-of-the-art STGCN model in the model, RMSE improved the effect of the SMS-in dataset by 47.2% in one cell and 40.9% in all cells. MAE improved the effect by 52.6% in one cell and 30.5% in all cells. This indicates that the prediction error of our model is less than that of the other models, and R
2 improved the effect by 7.8% in one cell and 22.9% in all cells, which indicates that the quality of our model is higher than that of the other models.
Figure 11 shows the comparison of the prediction results for Call dataset over 7 days in one cell. The above figure shows the comparison of prediction results of the incoming Call (Call-in) dataset in the test set, and the following figure shows the comparison of prediction results of outgoing Call (Call-out) dataset in the test set.
Figure 12 shows the absolute value of the error between the true and predicted values over a period of 14 h in one cell. The above graph shows the prediction error for Call-in dataset over a period of 14 h, and the following graph shows the prediction error for Call-out dataset. In the two subgraphs in
Figure 12, the smallest absolute error is 0.01, which indicates that our model shows an accurate prediction in the Call dataset.
Table 4 compares the experimental results of HA, LR, GCN, LSTM, STDensenNet [
18], and STGCN [
25]. On the Call dataset, our model outperforms the other models in all three evaluation metrics measures. For example, compared to the state-of-the-art model STGCN, RMSE improved the effect of the Call-in dataset by 57.0% in one cell and 36.1% in all cells. MAE improved the effect by 53.4% in one cell and 31.2% in all cells. This indicates that the prediction error of our model is less than that of the other models, and R
2 improved the effect by 4.7% in one cell and 9.3% in all cells, which indicates that the quality of our model is higher than the other models.
Figure 13 shows the comparison of prediction results for Internet dataset over 7 days in one cell. The figure shows the comparison of the prediction results of the Internet dataset in the test set.
Figure 14 shows the absolute value of the error between the true and predicted values over a period of 14 h in one cell for internet dataset. The true value is measured in hundreds or thousands in this dataset, and our prediction error is controlled to within 30, which has little impact on the overall data.
Table 5 shows a comparison of the experimental results of HA, LR, GCN, LSTM, STDensenNet [
18], and STGCN [
25]. On the Internet dataset, our model outperforms the other models in all three evaluation metrics measures. For example, compared to the state-of-the-art model STGCN, RMSE improved the effect by 81.7% in one cell and 4.1% in all cells. MAE improved the effect by 82.7% in one cell and 12.7% in all cells. This indicates that the prediction error of our model is less than that of the other models, and R
2 improved the effect by 2.2% in one cell and 7.6% in all cells, which indicates that the quality of our model is higher than that of the other models.
Figure 9,
Figure 10,
Figure 11 show the comparison of the prediction results of five types of data in one cell. These figures show the comparison of prediction results of short message service in the test set. The change trend of five types of data in
Figure 9,
Figure 10,
Figure 11 is similar to that of the short message service under the spatial-temporal characteristics analysis in
Section 3. The change trend of the predicted value is the same as that of the real value. Our model can well capture the peak value of the short message service. In general, the dynamic change curves of the two are basically consistent.
To verify the stability, novelty, and transferability of our model, we compared it with the STGCN model on the CIKM21-MPGAT dataset [
37] in
Table 6. From the comparison results, it can be seen that the prediction accuracy of our model is better than that of the STGCN model on the CIKM21-MPGAT dataset, which indicates that our model is not only accurate on the Milan dataset, but also has a good effect on other datasets, with good stability and novelty, and is transferable.
The results show that the proposed model has better prediction effect than the comparison model in the five types of data. The proposed model performs better in a single cell and in all the evaluation indicators of cells than the comparison model. We can also see that the forecasting results of traditional time series analysis methods are not ideal, which proves that the ability of these methods to process complex spatiotemporal data is limited. In contrast, deep learning-based methods generally obtain better forecasting results than traditional time series analysis methods. Among the single deep learning methods, the LSTM method and GCN method selected in this paper are the temporal module and the spatial module in the STP-GLN model, and the results show that the prediction method, using a deep-learning algorithm that only analyzes the temporal characteristics or the spatial characteristics, is better than the traditional method, but the prediction effect is less accurate than that of the model STP-GLN which also considers the spatiotemporal characteristics. It is shown that considering the spatiotemporal correlation of cellular networks is useful for data prediction in practice. In the deep learning method, the STDensNet model, the STGCN model, and the proposed model STP-GLN all take into account the spatiotemporal correlation, and it can be seen from the comparison results that the prediction effect of our model is better than the two comparison models.