# Citywide Cellular Traffic Prediction Based on a Hybrid Spatiotemporal Network
## 4 Experimental Results and Analysis  
### Experimental Process and Parameter Setting  
The experimental dataset was from Telecom Italia, and we used the same pre-processing method as [17] to aggregate data from the 10 min interval in the original dataset to hours. Because the 10 min interval dataset was quite sparse, it was not conducive to extracting spatiotemporal characteristics. The difference was that [17] separately predicted the receive and send dimensions in SMS and Call. We combined the receive and send dimensions and used the total traffic input model for prediction. All data were normalized before inputting in the model, which allowed the model to converge faster and improved the computational efficiency of the fitting process.  
HSTNet uses an optimization algorithm, [PERSON] [22], which can replace the traditional stochastic gradient descent algorithm, which iteratively updates the neural network weights based on the training data. The experiment was carried out in three datasets with a learning rate of 0.01 and a training of 150 epochs. The learning rate decayed as the epoch of training increased. Our model was tested on three datasets: SMS, Call, and Internet. Each dataset contained 1488 (62 days \(\times\) 24 h) slices. Except for the first three days without sufficient historical data, we used 52 days of data (1248 pieces) from 4 November 2013 to 24 December 2013 as the training set and used data from 25 December 2013 to 1 January 2014 (168 pieces) as the test set. In the convolution module, the deformable convolutional layer had 32 filters. The remaining convolutional layers had 16 filters with a kernel size of 1 \(\times\) 1. The normal convolutional layer in the attention module had one filter with a kernel size of 1 \(\times\) 1. The activation function of the convolutional layers was ReLU, except for the last layer, which used the sigmoid activation function. The code of HSTNet was implemented under Python 3.7, Keras 2.1.6, and NumPy 1.15.4. The experimental hardware environment included AMD R5 2600, GTX 1070, and 16 G memory.  
Our experiments compared HSTNet performance with baseline algorithms such as the historical average (HA), ARIMA, LSTM, and STDenseNet. In the experiment process, the deformable convolution, time embedding module, and attention module were embedded in STDenseNet to observe the performance improvement of the model, and HSTNet had all the above improvements added. The generated prediction map was re-adjusted to the normal scale and then evaluated with the true value.  
We used the two indicators of mean absolute error (MAE) and root mean squared error (RMSE) to evaluate the model. MAE is the average of the absolute error, which can better reflect the actual situation of the predicted value error.  
\[MAE=\frac{\sum_{h=1}^{H}\sum_{W=1}^{W}\left|p^{\prime(h,w)}-p^{(h,w)}\right|}{H \times W} \tag{8}\]  
RMSE represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. RMSE is more sensitive to outliers.  
\[RMSE=\sqrt{\frac{\sum_{h=1}^{H}\sum_{W=1}^{W}\left(p^{\prime(h,w)}-p^{(h,w)} \right)^{2}}{H\times W}} \tag{9}\]