# A Vehicle Velocity Prediction Method with Kinematic Segment Recognition
## 2 Data Preprocessing
### Principal Component Analysis
Principal components can be selected according to the size of the eigenvalue, and the contribution rate represents the retention degree of each principal component to the initial information. The cumulative contribution rate can determine the number of principal components used to express the features of the original data. The calculation formula of the principal component contribution rate is described below. \[W_{j}=\frac{\lambda_{j}}{\sum\limits_{j=1}^{l}\lambda_{j}}\] (17) The formula for calculating the cumulative contribution rate of each principal component is as follows: \[T_{kj}=\frac{V_{kj}}{\sqrt{\lambda_{k}}}\] (18) where \(T_{kj}\) and \(V_{kj}\) are the coefficients of the \(k\)th eigenvector, \(\lambda_{k}\) is the eigenvalue (\(k=1\), \(2\), \(\ldots\), \(g\)) of the \(k\)th principal component, and \(g\) is the number of principal components. The formula for calculating the score of the sample in the ith sample under the first principal component is expressed as: \[f_{ik}=T_{kj}\cdot z_{ij}\quad\left(i=1,2,\ldots,n;\quad j=1,2,\ldots,l\right)\] (19)The principal component score matrix for all samples is obtained as described below:  
\[F= \begin{bmatrix}f_{11}&f_{12}&\cdots&f_{1g}\\ f_{21}&f_{22}&\cdots&f_{2g}\\ \vdots&\vdots&\ddots&\vdots\\ f_{n1}&f_{n2}&\cdots&f_{ng}\end{bmatrix}  \tag{20}\]  
According to the above steps of the principal component analysis, the main data information were obtained as follows. After obtaining the correlation coefficient matrix of the standardized sample, the eigenvalues and their contribution rates can be calculated, which are arranged in descending order according to the size of the eigenvalues, and the cumulative contribution rates are summed line by line starting from the largest eigenvalue. The results are shown in Table 2.  
The eigenvalue is an evaluation index of the information inclusion ability of the principal component. The larger the eigenvalue, the more information the principal component covers and the stronger the evaluation ability of the problem. The eigenvalues of the first three rows in the table were extracted, and the cumulative contribution rate of the three principal components reached 78.3817%, that is, the information of the initial variables could be better described according to these three principal components. Table 3 shows the eigenvector corresponding to the three selected eigenvalues, namely the principal component load. The principal component load matrix reflects the correlation coefficients between the three principal components \(f_{1}\),\(f_{2}\),\(f_{3}\), and 10 feature parameters. The original feature parameters can be transformed according to the feature vector to obtain the scalar value of the sample information described by the principal component. It can be seen from the table that the first principal component mainly reflects the information of five characteristic parameters: average velocity value, maximum velocity value, standard deviation of velocity, maximum acceleration, and average acceleration. The second principal component mainly reflects the information of the acceleration time ratio, one characteristic parameter, while the third principal component mainly reflects the information of deceleration time ratio, maximum deceleration velocity, average deceleration velocity, and total mileage, four characteristic parameters. The three principal components basically cover the information described by the 10 feature parameters, so the three principal components can be used to replace the 10 feature parameters to describe the information of the kinematic segments, and the dimensionality reduction of the feature parameters is completed. Table 4 shows the principal component scores of some of the samples.