## 3 Materials and Methods
### Methods  
#### 3.2.1 Decomposition Integration System  
In complex systems, time series often show the characteristics of multi-dimensional data. These complex features make time series prediction difficult. A single model can no longer meet the requirements of complex system analysis and prediction. In recent years, hybrid models have attracted more attention. In this paper, we used different time series analysis for three different components, and finally integrated the results. In decomposition and integration system, multi-scale decomposition was used to process time series data, so as to reduce the modeling difficulty of complex system and improve the analysis and prediction performance of the model. Specifically, the decomposition integration method decomposed the complex system into subsystems that are easy to analyze, which can significantly reduce the difficulty of prediction and improve the analysis and prediction performance of the model. The decomposition integration system in this paper included three steps: empirical mode decomposition, preliminary integration based on K-nearest neighbor (KNN) and prediction result integration.  
Hilbert-Huang transform (HHT) is an empirical data analysis method. This method is adaptive. HHT consists of two parts, empirical mode decomposition (EMD) and Hilbert spectrum analysis (HSA) [30]. This technique is feasible for analyzing nonlinear and non-stationary data [31]. To fully describe EMD, we first define the IMF. IMF in EMD algorithm should meet two conditions [32]:  
1. The number of extreme points (including local maximum points and local minimum points) is equal to the number of zero crossings or the difference is 1.
2. At any point, the average value of the envelope of local maximum and local minimum is 0. Different from the modal components in other decomposition methods, IMF is a generalized harmonic function rather than a simple fixed function, and its amplitude and frequency change with time.  
EMD algorithm assumes that time series data generally contain multiple volatility components, and different volatility functions can be solved through the column part of the screening process and expressed by the IMF function [32]. EMD decomposition is based on the following assumptions: there is at least one maximum and minimum in the decomposed data. The local characteristic time scale is determined by the time interval between levels. If the data has no extreme points but contains inflection points, the extreme values can be obtained by one-order or multi-order differentiation.  
Traffic data set can be expressed as \(S=[S_{1},S_{2},...S_{N}]\), where \(N\) is the number of base stations in the region. In this paper, \(N=22\). For any \(S_{n}\) contained in \(S\), we perform  
Figure 3: Coverage of base stations in the area.  
EMD empirical mode decomposition. The HHT based EMD process for traffic data is as follows:  
1. Identify all maximum and minimum values existing in \(S_{n}\), which form upper envelope \(M_{U}\) and lower envelope \(M_{L}\);
2. The average value of envelopes can be expressed as \(m_{1}\), which is obtained by Formula (1): \[m_{1}(t)=(M_{U}+M_{L})/2\] (1)
3. The initial component \(h_{1}\) can be obtained by Formula (2): \[h_{1}(t)=S_{n}(t)-m_{1}(t)\] (2)
4. Calculate the envelope average value \(m_{11}\) of \(h_{1}\);
5. \(h_{11}\) can be obtained according to \(m_{11}\), as shown in the Formula (3): \[h_{11}(t)=h_{1}(t)-m_{11}(t)\] (3)
6. After repeating the extraction process for \(K\) times, \(h_{1k}\) becomes an IMF, which can be expressed as: \[h_{1k}(t)=h_{1(k-1)}(t)-m_{1k}(t)\] (4) which can be also expressed as: \[c_{1}(t)=h_{1k}(t)\] (5)
7. Separate \(C_{1}\) from \(S\), and the remaining data can be expressed as: \[r_{1}(t)=S_{n}(t)-c_{1}(t)\] (6)
8. By repeating the same operations from step 1 to step 6, a plurality of decomposed components \(c_{1}(t),c_{2}(t)...r_{1}(t),r_{2}(t)...\) can be obtained.