## 2 Methodology
### EnGS-DGR Model
#### 2.2.1 Dynamic Graph Reconfiguration Algorithm  
The data is preprocessed to obtain the same time interval with predefined forecasting interval first, in which the mean interpolation is used to fill in missing values for missing data in the dataset. Thus, the processed data is standardized and used by the DGR algorithm. Instead of the Laplacian Matrix, a low-rank tensor-constrained multi-view subspace representation algorithm is employed to reveal the correlations between the traffic nodes in the road network. Compared with the Laplacian matrix, which can only be applied to the single-feature datasets, this algorithm is more adaptable to the datasets with multi-dimensional features. By defining various features of each traffic node in the road network as different views, the DGR algorithm is used to jointly learn the subspace representations under each feature view in order to mine the high-order correlations within and between the views at the same time. This algorithm is expected to reveal not only the inner associations of views, but also the correlations between the views, in which the low-rank constraint is used to represent the subspace and reduce the size of subspace representation. The specific algorithm flow is shown in Figure 5.  
Figure 4: The framework of EnGS-DGR model. The dataset containing multi-dimensional features is represented by the multi-view subspace. The data from entire nodes in traffic network \(G(V,E)\) can be represented as \(\mathcal{X}=[X^{(1)},X^{(2)},\cdots,X^{(t)},\cdots,X^{(N)}]\), where \(X^{(t)}\in R^{S_{\text{dim}}\times N}\) is a matrix composed of \(t\)th feature, \(S_{\text{dim}}\) is the length of the feature vector (e.g., average travel speed, distance to other nodes), and \(N\) is the number of nodes. Coefficient matrix \(Z\) of the every view can be solved by the following formula:  
\[ \begin{split}\min_{Z^{(b)},\mathcal{K}^{(b)}}&\| \mathcal{Z}\|_{*}+\lambda\|K\|_{2,1},\\ s.t.& X^{(b)}=X^{(b)}Z^{(b)}+K^{(b)},\quad b=1,2, \cdots,B,\\ &\mathcal{Z}=\psi\Big{(}Z^{(1)},Z^{(2)},\cdots,Z^{(B)}\Big{)},\\ K&=\Big{[}K^{(1)};K^{(2)};\cdots;K^{(B)}\Big{]}, \end{split}  \tag{2}\]  
where \(X^{(b)}\) represents the data matrix of the \(v\)th view; \(Z^{(b)}\) is a coefficient matrix of \(X^{(b)}\); \(\psi(\cdot)\) combines different \(Z^{(b)}\) into tensor \(\mathcal{Z}\) with dimension \(N\times N\times B\); \(Z\in R^{l_{1}\times l_{2}\times\cdots\times l_{M}}\) is a \(M\)-order tensor; \(\|.\|_{*}\) represents the tensor under low rank constraint, that is, the tensor nuclear norm; \(K\) is a reconstruction error matrix, which connects each \(K^{(b)}\) together vertically; \(\|K\|_{2,1}\) is the \(l_{2,1}\) norm, and the clustering robustness can be improved by using the \(l_{2,1}\) norm. The objective function is to find the lowest rank subspace expression matrix from many candidate solutions through joint optimization of all perspectives. The low-rank constraint of the multi-rank tensors can be expressed by the tensor nuclear norm:  
\[\|\mathcal{Z}\|_{*}=\sum\limits_{m=1}^{M}\xi_{m}\|Z_{m}\|_{*}, \tag{3}\]  
where \(\xi_{m}\) is a constant and \(\xi_{i}>0\), \(\sum\limits_{m=1}^{M}\xi_{m}=1\), \(Z_{(m)}\) is the matrix of tensor \(\mathcal{Z}\) expanded along \(m\) mode. By replacing \(\|\mathcal{Z}\|_{*}\) of (3) in the objective function, the optimization problem can be transformed as:  
\[\min_{Z^{(b)},\mathcal{K}^{(b)}}\|K\|_{2,1}+\sum\limits_{m=1}^{M}\varpi_{m}\| Z_{m}\|_{*} \tag{4}\]  
where \(\varpi_{m}{=}\frac{\xi_{m}}{\lambda}>0\) represents the constraint strength of the low-rank tensor. By using the Alternating Direction Method of Multipliers (ADMM) algorithm of the extended Augmented Lagrange Method (ALM) algorithm in [31] to solve the objective function (4) optimization problem, tensor \(\mathcal{Z}\) can be obtained.