# Path Planning Strategy for Vehicle Navigation Based on User Habits
## 2 Materials and Methods
### Mining and Clustering of Users' Driving Habits
#### 2.1.2 Acquisition of Individualized Driving Styles
Step 1: A three-dimensional cluster coordinate system is established based on driving speed, consumption rate for fuel and facilities, total root mean square acceleration, and integrated environmental quality. The time, economic, and comfort information contained in each log vector element are expressed in the cluster coordinate system. Step 2: According to the selection principle of clustering centers, the initial time, economic, and comfort clustering centers are ensured when constraint conditions are satisfied. In this way, the three cluster centers are moderately separated. Step 3: The Hausdorff distance \(d_{\text{HD}}(f,o)\) of the log road vector element \(f\) to the time, economy, and comfort cluster centers \(O\) is calculated in Formula (5), where \(F\) is the finite set of vector elements, and \(O\) is the set of time, economy, and comfort clustering centers. \begin{table}
\begin{tabular}{c c} \hline
**Total Vibration \(a_{v}\)/m-s\({}^{-2}\)** & **Time Feature Weight \(\omega_{1}\)** \\ \hline \(<\)0.315 & Without malaise \\
0.315-0.63 & Slightly uncomfortable \\
0.5–1 & Quite uncomfortable \\
0.8–1.6 & Uncomfortable \\
51.25-2.5 & Extremely uncomfortable \\ \(>\)2 & Terrible \\ \hline \end{tabular}
\end{table} 
Table 1: Corresponding relation between acceleration and comfort level. \[\left\{ \begin{array}{l}d_{\rm HD}(f,o)=\min\limits_{f\in F}\min\limits_{o\in{\rm O }}d(f,o)\\ h({\rm O},F)=\max\limits_{o\in{\rm O}}\min\limits_{f\in F}d(o,f)\end{array} \right. \tag{5}\]  
Step 4: The membership degree of each vector element \(f\) to the three cluster centers is calculated in Formula (6). \[R_{o\gets f}=\frac{{\rm card}F/d_{\rm HD}^{2}(f,o)}{\sum\limits_{o\in{\rm O }}\sum\limits_{f\in F}\bigl{(}1/d_{\rm HD}^{2}(f,o)\bigr{)}} \tag{6}\]  
Step 5: The vector elements of the time, economy, and comfort cluster centers are updated according to the membership degree, as shown in Formula (7). \[o^{\prime}=\frac{\sum\limits_{f\in F}f\bullet R_{o\gets f}^{2}}{\sum \limits_{f\in F}R_{o\gets f}^{2}} \tag{7}\]  
Step 6: If the conditions shown in Formula (8) are satisfied, the iteration stops. Otherwise, the process returns to Step 2, where \(O^{\prime}\) and \(O\) represent the cluster center variables of the current time and the previous moment, respectively. \[\max\limits_{o\in{\rm O}}\bigl{\{}\,\|o^{\prime}-o\|\bigr{\}}\,<\varepsilon \tag{8}\]  
Step 7: Normalization is conducted according to Formula (9), where \(j={\rm t},{\rm m},{\rm c}\) represent the arbitrary sample time, economy, and comfort dimensions, respectively. \({\rm s}_{i,j},{\rm s}_{\min j},\) and \({\rm s}_{\max:j}\) represent the performance value, and the minimum and maximum performance values of sample \(i\) underdimension \(j\), respectively. \(s_{i,j}^{*}\) is the new performance value of sample \(i\) under dimension \(j\), after the normalization process. \[{\rm s}_{i,j}^{*}=\frac{{\rm s}_{i,j}-{\rm s}_{\min j}}{{\rm s}_{\max j}-{\rm s }_{\min j}} \tag{9}\]  
The clustering results of the log road vector element features relative to the time (red), economic (green), and comfort (blue) cluster centers are shown in Figure 3.  
* Sample screening and class-weighted combination  
In the LFCM clustering, the validity of the statistics of the number of vectors in each cluster center directly affects the accuracy of driving style judgement. The effectiveness of each cluster center sample is as follows. Figure 3: The result of LFCM. Step 1: The small effective ball radius \(r_{0}\) is selected randomly (Figure 4a) to initialize the valid range of the sample. The corresponding plane projection of the valid ball is shown in Figure 4b. Step 2: Taking the sample local density [33] and the Euclidean distance of the high-density point samples as the standard, the effective radius is adjusted positively according to Formula (10). The effective radius of clustering is finally determined as \(r\).