Trajectory Data-Driven Network Representation for Traffic State Prediction using Deep Learning

We assume that information K regarding the coordinates and degrees of all intersections within a target area is available as prior knowledge. K is defined as follows:where \({x^K_i}\) and \({y^K_i}\) are the coordinates of intersection i, \({d^K_i}\) is the degree of intersection i, and n is the number of intersections within the target area. The proposed method generates network data only from K and trajectory data:where \({x^T_{j, h}}\) and \({y^T_{j, h}}\) are the coordinates of a dot observed at the j-th point of the trajectory for vehicle h, \({c^T_{j, h}}\) is the timestamp observed at the j-th point of the trajectory for vehicle h, \(m_h\) is the number of dots for vehicle h, and u is the number of vehicles whose trajectories could be observed in the target area.

In this study, intersections with a certain number of vehicles traversing in three or more directions are considered to play an important role as points for route choice, and the set of such intersections is defined as major intersections \(K^M\). We describe how to extract major intersections \(k^M \in K^M\) from the set of all intersections K using directional statistics. As a preprocessing step, for each dot \(t_{j, h} \in T\), an azimuth angle \(a_{j, h}\) to the next dot \(t_{j+1, h}\) is calculated. This process is not performed for the last observed dot of each vehicle. We extract the set \(T_i\) of dots within a distance s for each intersection \(k_i \in K\). \(T_i\) is described as follows:where \(\text {distance}(k_i, t_i)\) represents the distance between point \(k_i\) and point \(t_i\). For each \(k_i\), let \(A_i\) be the set of azimuth angles calculated for all \(t_i\).

\(a_i \in A_i\) can be regarded as sampled from the distribution of azimuth angles in the direction of vehicles traversed within a distance s from intersection \(k_i\). Assuming that the azimuth angles of vehicles traversing from each intersection to the links extending in each direction follow a normal distribution, \(a_i\) follows a mixed normal distribution with the degree \(d^K_i\) of the corresponding intersection as the mixture number. The mathematical expression is as follows:where \(\mu _{i, g}\) is the mean of each normal distribution included in the mixed normal distribution, and \(\pi _{i, g}\) is the weight of each normal distribution. For simplicity, in this study, the variance of each normal distribution is assumed to be a fixed value \(\sigma ^{2}\). If we can estimate \(\pi _{i, g}\), the number of vehicles traveling in each direction can be calculated by multiplying it by the total number of vehicles \(\left| T_i \right| \) that passed near each intersection \(k_i\). In this study, these parameters Expectation-Maximization (EM) algorithm. Using the threshold \(\tau _1\) for major node extraction, an intersection \(k_i\) is considered a major intersection \(k^M\) if there are at least three \(\pi _{i, g}\) values that satisfy:We will explain the process of defining links between major intersections. A threshold \(\tau _2\) is defined for link definition. We trace the trajectories of vehicles that traversed within the target area in a specific order. When a vehicle passes through a range within a distance s from a major intersection and subsequently passes through a range within a distance s from a different major intersection, we store information about these pairs of major intersections, the order of passage, and the timestamp.

This process is repeated for all vehicle trajectories, and for major intersection pairs where the number of vehicle passages exceeds \(\tau _2\), links are defined based on the direction of passage. For all vehicles used in defining the links, we calculate the average speed of the respective link by dividing the total distance between the dots for the given major intersection pair by the total travel time as defined by Edie [9].

In this study, we utilize the proposed network representation to perform traffic state prediction using a deep learning approach and assess its accuracy. Graph Convolutional Network (GCN), which is well-suited for learning from data with graph structures, and Long-Short Term Memory (LSTM), which is effective for capturing time-evolving patterns. We evaluate the accuracy of traffic state prediction using this methodology.

GCN is a method that handles the spatial correlation of inputs by convolving only the features of neighboring nodes for each node. By repeating this convolution operation, the features of nodes as far apart as the number of iterations are convolved. This convolution operation is defined as an approximation of the graph Fourier transform using the graph Laplacian. The output \(\textbf{H}^{(l)}\) of the \(l+1\)th layer is represented as follows:where \(\textbf{H}^{(l)}\) is the output of the lth layer, \(\tilde{\textbf{A}}=\textbf{A}+\textbf{I}\) is a self-connected adjacency matrix, \(\tilde{\textbf{D}}=\textbf{D}+\textbf{I}\) is a self-connected degree matrix, \(\textbf{A}\) is the adjacency matrix, \(\textbf{D}\) is the degree matrix, \(\textbf{W}^{(l)}\) is the weight matrix of the lth layer, and \(\sigma \) is the activation function.

LSTM is a type of recurrent neural network that can capture long-term dependencies and is well-suited for sequential data. It consists of input, forget, and output gates, as well as a memory cell. The equations for LSTM are as follows:where the input at the \(t-1\)th step is \(\varvec{h}^{t-1}\), the weight matrix is \(\textbf{W}_*\), the bias is \(\varvec{b}_*\), and the adamantine product is \(\odot \), \(\varvec{f}^{t}, \varvec{i}^{t}, \varvec{g}^{t}, \varvec{c}^{t}, \varvec{o}^{t}\) are output of the gates and the concatenation of matrices is \([\cdot ,\cdot ]\).

In this study, the output goes through the GCN layer twice at each time step, followed by two LSTM layers, and finally a fully connected layer to obtain the prediction result (Fig. 1). This model is based on the Temporal Graph Convolutional Network (T-GCN) [10], which replaces the Gated Recurrent Unit (GRU) in T-GCN with LSTM. A dropout layer is added before the fully connected layer to mitigate overfitting.

We conducted empirical validation using actual observation data in Kobe area of Japan (mesh code 523502). The traffic observation data used in this study consisted of Electronic Toll Collection System (ETC) 2.0 data, which is vehicle trajectory data collected by the Ministry of Land, Infrastructure, Transport and Tourism of Japan, and detector data from the Hanshin Expressway Company. In addition, we compared the characteristics of the network data constructed in this validation with those of commonly used network data by using OSM data.

The ETC 2.0 data consisted of dot data observed from 00:00, November 1, 2020, to 23:59, November 30, 2020. The detector data focused on one upstream and one downstream detector between interchanges on the Hanshin Expressway. In cases where multiple lanes had detectors, the leftmost lane was selected for analysis. The OSM data within the target area was obtained using the Overpass API. We extracted the road segments that were accessible to automobiles and used them as our target network. The traffic state data were aggregated at 15-minute intervals. For the aggregation, the speed was calculated using the harmonic mean with traffic volume as weights, while traffic volume and occupancy were averaged. After the aggregation, we performed linear interpolation in the temporal direction for each detector and road link. For missing values at the edges, we replaced them with the nearest non-missing value at the edge. In this validation, the prediction target is the occupancy of each detector.

We will explain the parameters used for validation. The parameter \(\tau _1\) for extracting major nodes was set at 50, 100, 200, and 500 (veh/day) in a stepwise manner, and the network generation results and traffic state prediction results were compared for each value. The parameter \(\tau _2\) for link definition was fixed at 50 (veh/day). The distance s used for determining the passage of trajectories near intersections was set to 30 (m). The variance \(\sigma ^2\) of each normal distribution within the mixture normal distribution was fixed at 15. The parameters \(P=4\) and \(\mathcal {T}=10\) mean that the forecast was made on a 4-step time scale based on the last 10 steps of observed data. The training period was from 00:00 on November 1, 2020, to 23:59 on November 23, 2020, and the validation period was from 00:00 on November 24, 2020, to 23:59 on November 30, 2020.

We show the results of the trajectory data-driven network data generated for each value of \(\tau _1\) compared with the original OSM data. Figures 2, 3, 4, 5, and 6 show the visualization of OSM network data and the trajectory data-driven network data. Table 1 shows the number of nodes and links for each dataset.

The results demonstrate the ability to adjust the resolution of the network appropriately by tuning the threshold value, \(\tau _1\). In comparison to the original OSM data, significant reductions in the number of links and nodes have been achieved. By carefully selecting \(\tau _1\) during the major node extraction process, the network can be simplified while retaining the essential connectivity and structural characteristics. This reduction in links and nodes provides computational benefits, as it reduces the complexity and computational cost associated with network-based calculations. The trajectory data-driven network representation offers a more streamlined and efficient network representation compared to the original OSM data, without sacrificing the essential information required for transportation analysis.

We present the results of traffic state prediction using the trajectory data-driven network generated in this validation. Table 2 shows the accuracy of the occupancy projections. Mean Absolute Error (MAE) is the average of the absolute differences between predictions and observed values, making it a measure of the average magnitude of the model’s errors that is not highly sensitive to outliers. Root Mean Squared Error (RMSE) is the square root of the average of squared differences between predictions and observed values, penalizing large errors, thus making it sensitive to outliers. Absolute Percentage Error (MAPE) calculates the average of the absolute percentage differences between predictions and actual observations, offering a scale-independent measure of relative error. Comparing these results, it is evident that adjusting the value of \(\tau _1\) to coarsen the network resolution does not lead to significant changes in accuracy for both MAE, MAPE, and RMSE. This underscores the notion that a higher resolution network representation does not necessarily result in a substantial improvement in prediction accuracy. It suggests the importance of adopting a flexible network representation tailored to the specific context and objectives rather than uniformly pursuing higher resolutions.

Figures 7, 8, 9, and 10 show the prediction accuracy of occupancy for \(\tau _1\)=50,100,200,500. Figures 11, 12, and 13 show the observed and predicted occupancy for each detector for one day on November 24, 2020, when \(\tau _1\)=50, 100, 200, and 500. These results show that the proposed method is promising in terms of accuracy as well as significant reduction in computational speed in traffic condition prediction.