## 4 The Performance of the Optimized SVR Model on Driving Decision-Making
### The Performance of SVR Model  
BP (Back Propagation) neural network (BPNN) is one of the most widely used and successful learning algorithms in current research, and is particularly suitable for solving complex problems with internal mechanisms [27; 28; 29]. In order to verify the performance of SVR model, a typical feed-forward BPNN is established to compare with SVR model on the performance of driving decision-making. The BPNN model is established with five layers (an input layer, three hidden layers, and an output layer). Set the Tan-Sigmoid function as the transfer function of BPNN model. The five principal components \(X=\{x_{1},\ x_{2},\ \dots,\ x_{5}\}\) obtained above are set as its input layer parameters and the corresponding driving decisions \(y_{k}\) is set as the output layer parameter.  
Figure 8: The iterative comparison results of fitted values of two SVR models.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**The Basic Kernel Function**} & \multicolumn{6}{c}{**Optimal Parameters**} \\ \cline{2-7}  & \(a\) & \(b\) & \(d\) & _\(\sigma\)_ & _\(\tau\)_ & _\(\delta\)_ \\ \hline Polynomial kernel function & 12.114 & 3.741 & 0.097 & - & - & - \\ Radial basis function & - & - & - & 60.565 & - & - \\ Sigmoid kernel function & - & - & - & - & 13.255 & 1.651 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The best parameters of each basic kernel function.  
In general, the number range of nodes in the hidden layers depends on the number of nodes in the input and output layer [30]. We use our sample data to check the accuracy performance of BPNNs with different number of nodes in the hidden layers, the final number of nodes in each hidden layer is determined to 7. By the parameter adjustment and the test in MATLAB, the number of iterations is determined to 500, the learning rate is 0.01, and the training goal (mean square error) is 1 \(\times\) 10\({}^{4}\). Then, the same 75% samples are input into BPNN model for training to obtain the BPNN-based DDM (BPNN-DDM). In the training process, the weights and bias are adjusted continuously to suit the desired output corresponding to the reference indexes. After 48 iterations, the network converges to the desired error. Then, the remaining 25% samples are input into the trained BPNN-DDM and SVR-DDM with RBF kernel function, the reasoning results of SVR-DDM with weighted hybrid kernel function, SVR-DDM with RBF kernel function and BPNN-DDM can be seen in the Table 4.  
It can be seen from Table 4 that the SVR-DDM with weighted hybrid kernel function has the best performance in reasoning driving decisions, with the 93.1% accuracy for free driving, 94.7% accuracy for car following, and 89.1% accuracy for lane changing. The reasoning accurate of SVR-DDM with RBF kernel function for three driving decisions is 89.3%, 92.7% and 86.8%, respectively, lower than that of the SVR-DDM with weighted hybrid kernel function, this results are from the optimization of kernel function in SVR Model. When compared with the two SVR-DDMs, the decision reasoning accuracy of BPNN-DDM is lower than SVR-DDM with weighted hybrid kernel function, and has little differences with the SVR-DDM with RBF kernel function. But, the \(E_{\text{R}}\) values show that the reasoning stability of the SVR-DDM with RBF kernel function is better than BPNN-DDM. In addition, the three DDMs have the highest accuracy for car following decision, and the lowest accuracy for lane changing. This result may be due to the small number of samples and the complexity of lane changing itself. In summary, the above results support the superior performance of SVR than BPNN in terms of the reasoning accurate, stability, and time, so the SVR model is more suitable for driving decision-making than BPNN model.