A New Spatio-Temporal Neural Network Approach for Traffic Accident Forecasting

Figures & data

Figure 1. Periodicities of the traffic accidents series. (a) Number of accidents depending on day of the week. Weekends present less number of accidents. (b) Number of accidents for each month. August seems to be safer. (c) Number of accidents depending on hour of the day. In this case we have the most clear difference

Figure 2. Total number of accidents by neighborhoods of Madrid during 2018

Figure 3. Architecture of the XSTNN model as described in Sect. 4.3

Table 1. Values used for each hyper-parameter. $n_z$ is the dimension of the latent space. The remaining variables were presented in Section 3 or are commonly used parameters

STNN	Learning rate	0.01
$\lambda$	0.01
$n_z$	2
$g(Z)$	Linear
Minibatch size	512
Dropout	0.25
XSTNN	Learning rate	0.01
$\lambda$	0.1
$n_z$	2
$g(Z)$	Linear
Minibatch size	512
Dropout	0.35
XGBoost	Number of rounds	80
Max. depth	15
$\eta$	0.1
$\gamma$	1
Min. child weight	1
Subsample	0.7

Table 2. Performance for $T+1$ to $T+5$ traffic accident regression

Model	MAE	Bias
XSTNN	$\mathbf{0}\mathbf{.0041}\pm \mathbf{0}\mathbf{.0006}$	$-0.0006\pm 0.0004$
STNN	$0.0045\pm 0.0006$	$-0.0004\pm 0.0006$
XGBoost	$0.0052\pm 0.0006$	$0.0004\pm 0.0006$
Linear regression	$0.0050\pm 0.0006$	$0.0002\pm 0.0007$
Mean	$0.0052\pm 0.0007$	$0.0003\pm 0.0007$
Persistence	$0.0055\pm 0.0008$	$0.0006\pm 0.0007$

Figure 4. Forecasting performance (MAE and bias) of the different models by timestep together with the calculated distributions

Figure 5. A practical example of the operation of both networks, XSTNN and STNN, for the same situation. From $17$ p.m. to $21$ p.m. on a Wednesday

Figure 6. A practical example of the operation of both networks, XSTNN and STNN, for a same situation. From $6$ a.m. to $10$ a.m. on a Sunday

Figure 7. Spatial risk in the same scale for the ground truth (left) and the XSTNN (right)