## 3 Problem Statement and Input Data Representation Methods
### Common Forms of Input Representations
#### 3.2.3 Graph-Based Sequence  
After discussing the grid-based sequence data representation, it is worth noting that much traffic data are collected based on complex traffic networks and their spatial dependencies closely rely on the topology of these networks. Therefore, to accurately describe and capture the spatiotemporal big data characteristics existing in traffic networks, we need a data representation method that reflects the network properties at each time step, namely, graph-based sequence data representation, as shown in Figure 4b. In this representation, each sequence element is treated as a graph at each time step, and the relationships or dependencies among elements are represented by time series. The graph-based sequence is \(\mathbf{X}^{g}=\left\{X_{1}^{g},X_{2}^{g},\ldots,X_{t}^{g}\right\}\), where each \(X_{t}^{g}\) is a graph representing the state of the entire traffic network at time \(t\). Each graph \(X_{t}^{g}\) can be further defined as \(X_{t}^{g}=\{V,E,A\}\), where \(V\) is the set of nodes in the graph, with each node representing a specific location in the traffic network. \(E\) is the set of edges in the graph, representing the connections between nodes. \(A\) is the adjacency matrix. This approach is particularly suitable for capturing complex graph-based spatial and temporal data dependencies. It is widely used in multiple tasks in machine learning and data mining, such as sequence classification, clustering, and prediction. In recent years, significant progress in traffic prediction research has been made using graph sequences as input sequences. [PERSON] et al. [59] used graph-based sequence data to characterize road network traffic speed over time. These data encompass recorded journey information for road segments, considering the road network as a unified graph where nodes represent road segments and edges denote connections between these segments. Variable features are integrated into node information through an adjacency matrix, while static features are regarded as edge information. Their study categorized travel times for road segments, creating temporal lists on adjacent nodes sharing the same road segment, thus establishing a speed matrix that records speed variations for all road segments. Finally, the adjacency and speed matrices are combined to form graph-based sequential data. Additionally, [PERSON] et al. [60] used graph-based sequence data to characterize vehicle speeds over a period in urban road networks. Specifically, the road network structure is constructed as a graph based on map data, with special consideration for the accessibility between different road segments. This not only reflects the physical structure of the roads but also accounts for actual traffic flow conditions, like when a road segment is temporarily closed due to maintenance or a traffic accident. Their study computes the traffic speeds of different road segments at various time points using taxi trajectory data, which are then matched with the road network. Graph-based sequence data are formed by continuously constructing these road traffic speed graphs. [PERSON] et al. [61] used graph-based sequence data to predict traffic flow in urban road networks. Specifically, the road network structure is constructed as a graph based on spatial-temporal data, with each node representing a traffic sensor and edges representing the correlations between sensors at different time steps. The study computes traffic flow data at various time points using real-time sensor readings, forming a sequence of graphs where each graph represents the traffic conditions at a specific time step. [PERSON] et al. [62] utilized a data-driven graph construction scheme for traffic prediction. In their approach, nodes represent traffic sensors, and edges represent the correlations between sensor readings at different time points. They dynamically construct graphs by embedding sensor correlations in a latent attention space and generate them at each time step to form a sequence. [PERSON] et al.