# Logistics Transportation Vehicle Supply Forecasting Based on Improved Informer Modeling
## 3 Problem Description and Model Design
### Improved Informer Modeling
#### 3.3.1 Multidimensional Feature Engineering Construction for Supply Data  
Feature engineering is mainly used to extract and select the features closely related to the model prediction task, including the steps of feature selection and encoding, etc. Suitable features can reduce redundancy and noise, enhance data complexity, and improve the model's generalization ability and prediction effect. This paper mainly analyzes demand, freight rate, and spatiotemporal evolution patterns in the prediction task where supply is the output label. For the input supply volume data, this paper mines the time information, adding the weekend, quarter, mid-year day, and month global timestamps to construct the feature engineering, and takes the labels for coding. For example, the quarter timestamp takes the value range of [1; 4], where the first quarter covers January to March, the second quarter covers April to June, the third quarter includes July to September, and the fourth quarter is from October to December. The feature construction and coding are shown in Table 1.  
According to Table 1, to construct the data for the seven-dimensional characteristics of supply engineering, supply is closely related to demand, freight rates, time-space evolutionary patterns, and other factors. To further determine the quantitative correlation between these influencing factors and supply, this chapter introduces the Pearson correlation coefficient and carries out a Pearson correlation analysis of the influencing factors one by one, time step by time step, as shown below:\[r=\frac{\sum\limits_{i=1}^{n}{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}}{\sqrt{ \sum\limits_{i=1}^{n}{(X_{i}-\overline{X})^{2}\sum\limits_{i=1}^{n}{(Y_{i}- \overline{Y})^{2}}}}} \tag{8}\]  
\(X_{i}\) and \(Y_{i}\) are the values of the influencing factors and indicators taken at the \(i\)th time step, \(\overline{X}\) and \(\overline{Y}\) are the mean values of the influencing factors and indicators, respectively, and \(n\) is the sample size. The Pearson correlation coefficient value domain is [\(-1\), \(1\)], where a value close to \(1\) indicates a positive correlation; the classification of the correlation coefficient varies in different industries and fields, and the interpretation of the correlation coefficient criterion is not universal. This paper uses the literature in the field of time series prediction [46] to obtain the classification of the correlation coefficient, as shown in Table 2.  
\(\left|r_{xy}\right|\) As the later stages require the consideration of sequential spatiotemporal information, the positional and temporal information of input sequences are encoded into vector form. Positional encoding involves generating corresponding position vectors using sine and cosine functions, which are then added to the embedding layer for processing. Let the length of the input sequence be \(L\), with the position represented by \(p\), the embedding vector dimension as _dmodel_, and the embedding dimension as \(i\); then, the position encoding vector \(E\) is shown in the following equation. The specific position encoding steps are shown in Figure 2.  
\[\left\{ \begin{array}{l}E_{(p,2i)}=\sin(p/(2L)^{2i/d_{\text{model}}})\\ E_{(p,2i+1)}=\cos(p/(2L)^{2i/d_{\text{model}}})\end{array} \right. \tag{9}\]  
Similarly, time coding converts dates to timestamp coding; the unit time step in this paper is days (d) and the timestamp generated after encoding is a three-dimensional variable that includes mid-week days, mid-month days, and mid-year days. In addition, since the supply and characteristics are different types of data with differences in size and unit, this paper uses the Z-Score normalization method to process them separately, and the calculation formula is shown below.