# Driver Clustering Based on Individual Curve Path Selection Preference
## 1 Introduction  
The development of Advanced Driver Assistance Systems (ADASs) reached a maturity level where, besides technological challenges, the behavior of these systems is getting more and more focus. While automated driving functions can handle various driving tasks, their behavior is highly different from that of human drivers. One of the most controversial functions is the lane centering system (LCS). People often claim that LCS is annoying, and therefore, they switch it off. In many cases, car buyers refuse to purchase the newer generation of LCS. This hinders the widespread use of higher-level automated driving systems. Also, LCS is not only a comfort function, but it also aids drivers in emergency situations. The dislike of this system is therefore directly related to driving safety problems. By realizing the situation, car manufacturers decided to invest research effort in making lane centering systems more human-like, which eventually results in better acceptance of these systems. In order to achieve human-likeness, it is a common approach to observe people's naturalistic driving and build models that can reproduce their behavior. It is observed thatdrivers do not always drive in the center of the lane [1; 2]. Therefore, driver models in the field of path planning aim to plan the position offset of the vehicle to the centerline. The latest solutions in the field, such as the Generalized Regression Neural Network (GRNN) model [3], the Long-Short-Term-Memory (LSTM) model [4], or the Preview Horizon Trajectory Planning Model (PHTPM) [5], all use certain neural network structures. Even though these models are exceptionally accurate, they are difficult to use for driver clustering, as they have no model parameters. Further trajectory planning analysis work was conducted to distinguish drivers based on their risk-taking willingness [6]. Even though such papers give remarkable insight into driving behavior mechanisms, the modeling of the analyzed behavior is not straightforward. Other driver models from the vehicle control fields, such as the Pure-Pursuit algorithm [7], Model Predictive Control (MPC) models [8; 9; 10], or the compensatory driver model [11], describe the drivers' control, and not their planning behavior, which is a much more limited view of the complete driving procedure. There are parametric driver models such as the Linear Driver Model (LDM) that give a simple but robust description of the drivers' path planning behavior [12], and their parameters make it possible to directly quantify one's path planning policy. After the selected driver model is trained, it can be used to reproduce the path selection of the driver. However, learning the behavior of all drivers individually would result in a theoretically infinite number of behavioral variations. This makes practical utilization difficult. Therefore, drivers are classified into behavioral groups. These are reference groups that must be created first. For that, unsupervised learning (i.e., clustering) is applied to the learned parameters of reference drivers. Then, the resulting driver groups are compared with judge their behavior. Such concepts are used in the literature. Driving styles are identified via clustering drivers based on their driving dynamics [13; 14], their curve speed selection [15] or time-to-collision [13]. These papers use the k-means algorithm, on an average 25-30 test drivers, that are clustered to 3-4 groups (e.g., dynamic, normal and comfortable). However, these solutions use directly the measured driving quantities, and they do not use any higher-level driver models. Assuming the driving groups are created, the parameters of a new driver can be learned, and he can be classified into one of the groups. Practically, this happens in real time while the driver is driving. Therefore, the algorithm of parameter learning must be computationally efficient enough in order to implement it on an embedded control unit. In case of parametric models, parameter identification solutions, such as Kalman filters are often used [16; 17].