Performance of the NN to Predict Traffic

The trained NN was used to predict the whole traffic of the next two weeks. In Figure 9.3 we show the actual and the predicted traffic against the time samples. (Note that we selected sequentially 1 sample every 4 samples for drawing to make the Figure somewhat clear.) We also show in Figure 9.4 the actual and the predicted traffic for the third and fourth days in the predicted third week. For this prediction we got MSE = 0.0046. From these Figures, we can see that the NN managed to predict the whole next two weeks with very good precision. To visualize the performance of the NN, we depict in Figure 9.5 the difference between the actual and the predicted traffic for this experiment. Furthermore, a histogram for the percentage distribution of the samples from -1 to 1 with a step of 0.1 is shown in Figure 9.6. From these Figures we can see that about 78% of the samples are predicted with a precision between $\pm$ 0.05. About 8% of the samples are predicted with a precision between 0.05 and 0.15, where the actual traffic is higher than the prediction. On the other hand, about 10% of the samples are predicted with a precision between 0.05 and 0.15, where the actual traffic is lower than the prediction. From Figure 9.5, we can see that a few samples are predicted with a precision between 0.2 and 0.4. This is due to the phenomena known as the ``spikes''. A spiky sample occurs when the difference between the future and current sample is large and there is no information in the past samples that could indicate the possible occurrence of the spike. This is a well known phenomena in the traffic process. By definition, spikes are non-predictable (at least, with the same precision as the rest of the process). Furthermore, we recommend that the spikes should be removed from the training database. The idea is to avoid introducing spurious information during the learning process. Fortunately, their occurrence in real traffic is not frequent as seen from In addition, if the spikes are not taken into account for the calculation of the MSE, the performance improves significantly. For example, by removing 124 spiky samples out of the 4200 samples of the predicted weeks, and considering simply that a sample is spiky if it differs by greater than 0.3 from the past sample, the MSE improved from 0.0046 to 0.00163. Figure 9.7 shows the difference between the actual and the predicted traffic after removing these spikes. It is clear that the performance is much better than in the case of Figure 9.5.

Figure 9.3: The actual traffic against the predicted one for the whole complete next two weeks.

Figure 9.4: The Normalized actual against that predicted for the third and fourth days from the third week.

Figure 9.5: The difference between the actual and the predicted traffic for the complete next two weeks.

Figure 9.6: The histogram of the distribution of difference between actual and prediction with a step of 0.1.

Figure 9.7: The difference between the actual and the predicted traffic for the complete next two weeks once the spiky samples are removed.