# Driver Clustering Based on Individual Curve Path Selection Preference
## 3 Results
### Driver Clustering  
Data of the Human-like Behavior for Automated Vehicles (HLB4 AV) dataset is used [19]. This dataset contains the naturalistic driving data of 30 drivers. The participants drove approximately 40 km on a rural road, with two lanes, without physical separation between the lanes. The driving does not contain urban or highway scenarios. The parameters of LDM were calculated by applying (20) on the drivers' data, individually. Euclidean distance metric (\(\ell_{2}\)) is chosen, as no significant differences have been observed when using other metrics. The number of clusters \(K\) is chosen by testing different values and comparing the silhouette values of the clusters. The values \(K=\{2,3,4\}\) have been tested. The results are shown in Figure 3. In the case of \(K=2\) there are multiple elements in both clusters that are well above the mean silhouette values. In cluster 2, there are a few elements with low silhouette values, though. In the case of \(K=3\) there are no elements with negative silhouette values, the lowest is around \(s=0.08\) in cluster 1 and \(s=0.1\) in cluster 3. In cluster 2, there is only one element, which can be treated as an outlier. For \(K=4\), cluster 2 is an outlier, while cluster 4 contains elements with very low silhouette values. Based on the tests, \(K=3\) clusters are chosen, which complies with similar papers [13; 15; 40], with a note that cluster 2 may be a group of outliers--the number of elements in this group is very low. The cluster centroids for clusters 1 and 3 are calculated based on (26), and are given in (41). \[P^{1} = \begin{bmatrix}-0.10&0.18&-0.05&-0.06&0.28&-0.06\\ -0.52&0.47&-0.06&-0.53&0.57&-0.05\\ 0.12&-0.13&0.03&0.48&-0.43&0.13\\ \end{bmatrix} \] \[P^{3} = \begin{bmatrix}0.44&-0.10&-0.04&0.39&0.04&-0.06\\ -0.06&0.27&-0.05&-0.32&0.53&-0.06\\ 0.11&-0.07&0.09&0.46&-0.44&0.18\\ \end{bmatrix}  \tag{41}\]  
The cluster parameters are used to plan the local path, as introduced in Section 2.5. The vehicle movement is simulated to be ideal (tracking error is zero), and the global path of the vehicle is analyzed. Simulations are run in MATLAB. The reference route is shown in Figure 4. First, there is a straight section, after which an S-curve (first left, then right) part follows. Then, there are a small right and left curves, which are followed again by a straight section. This path is taken from a real measurement; the vehicle speed is set based on the original measured speed. After the simulation, the planned offset to the lane is calculated. The results are shown in Figure 1.  
Figure 3: Results of the clustering with different number of clusters, using Squared Euclidean (\(\ell_{2}\)) distance metric. The resulting clusters are groups of drivers, presumably with similar behavior in their curve path selection. However, we want to also formulate features of each group that define not only numerical similarity between the drivers but also similarity in their behavior of driving. Figure 5 shows the offset-time plot. Cluster 2 contains the data of driver 2 only and produces an outlying behavior. Cluster 3 drivers cut the curve significantly, symmetrically in left and right curves (the peak of the lane offset is similar). In general, these drivers drive closer to the opposite lane. Cluster 1 drivers have much lower curve cut, especially in the left curve. Drivers are slightly different in terms of the curve entry behavior; however, the difference is not significant. In the case of both cluster 1 and 3, there is a small negative offset before the left curve, which means the vehicle is on the outer side of the lane before turning in and cutting the curve. Based on the observations, we propose features of each cluster, and based on the features, driving styles are defined. The results are shown in Table 2. There are two styles that are named empirically: dynamic (cluster 1) and cautious (cluster 2) drivers. One more analysis is conducted by considering the cautious and dynamic groups.