# Research on Driving Style Recognition of Autonomous Vehicles Based on ACO-BP
## 3 Methodology
### Principal Component Analysis (PCA)  
Principal component analysis (PCA) is a commonly used data dimensionality reduction technique that can transform high-dimensional data into lower-dimensional data while preserving the essential information from the original data [32]. The main idea behind PCA is to project the original data onto a new coordinate system in such a way that the projected data has the maximum variance. These new coordinate axes are called principal components, and they are linear combinations of the original data. By retaining a few of the most important principal components, data can be reduced in dimensionality while retaining important information. At present, in the field of autonomous driving, two commonly used methods for data dimensionality reduction are principal component analysis (PCA) and factor analysis [33; 34]. In comparison to factor analysis, PCA possesses three advantages in terms of  
Figure 4: Acceleration smoothing effects. (**a**) Global view of the acceleration smoothing effect; (**b**) acceleration smoothing effect in 10 s before and after lane changing. Figure 3: Vehicle speed smoothing effects. (**a**) Global view of the speed smoothing effect; (**b**) smoothing effect of vehicle speed in 10 s before and after lane changing. dimensionality reduction. Firstly, PCA is an unsupervised algorithm that does not require the prior specification of latent variables or latent models, whereas factor analysis usually necessitates the specification of the number of latent factors and the model structure. Secondly, PCA selects principal components by maximizing data variance, thereby retaining the maximum information contained in the data. This aids in preserving the primary information within the data. Lastly, PCA offers interpretability of the data. The principal component vectors can explain the variance within the data, helping us understand the data structure and relationships. Therefore, PCA exhibits advantages in efficient unsupervised dimensionality reduction and data interpretability, particularly when dealing with large-scale data. Selecting appropriate feature parameters is a prerequisite in order to better study the driving styles of different drivers using PCA dimensionality reduction. According to related research, speed, acceleration, following distance, following time distance, and other parameters have a more obvious influence on driving style. For example, the average value can characterize the vehicle's driving over a period of time, while the standard deviation can reflect the degree of dispersion of the speed and acceleration, that is, the speed stability of the vehicle's acceleration or deceleration behavior. Hence, six driving style-related characteristic parameters are chosen, utilizing the data presented in Table 2.  
Before solving the principal components, the raw data need to be standardized in order to make the units and scales the same among different variables and to eliminate the effect of magnitude [35]. The standardized data are used as input for principal component analysis. After performing linear mapping on the data, the principal components are assessed and ranked based on their respective contribution rates. The selection of the principal components is then carried out by considering the cumulative contribution rate. The equations for variance contribution ratio and cumulative contribution ratio are shown below:  
\[\alpha_{k}=\frac{\lambda_{k}}{\sum_{i=1}^{n}\lambda_{i}} \tag{15}\]  
In Equation (15), \(\alpha_{k}\) is the variance contribution of principal component \(k\), and \(\lambda\) is the eigenvalue. \[G(k)=\frac{\sum_{i=1}^{k}\lambda_{k}}{\sum_{i=1}^{n}\lambda_{i}} \tag{16}\]  
In Equation (16), \(G(k)\) is the cumulative contribution. The variance contribution rates for each principal component are shown in Figure 5, and in the selection of principal components, the top \(k\) principal components with a cumulative contribution greater than 85% are generally selected.