Spatial-Temporal 3D Residual Correlation Network for Urban Traffic Status Prediction

Abstract

Accurate traffic status prediction is of great importance to improve the security and reliability of the intelligent transportation system. However, urban traffic status prediction is a very challenging task due to the tight symmetry among the Human–Vehicle–Environment (HVE). The recently proposed spatial–temporal 3D convolutional neural network (ST-3DNet) effectively extracts both spatial and temporal characteristics in HVE, but ignores the essential long-term temporal characteristics and the symmetry of historical data. Therefore, a novel spatial–temporal 3D residual correlation network (ST-3DRCN) is proposed for urban traffic status prediction in this paper. The ST-3DRCN firstly introduces the Pearson correlation coefficient method to extract a high correlation between traffic data. Then, a dynamic spatial feature extraction component is constructed by using 3D convolution combined with residual units to capture dynamic spatial features. After that, based on the idea of long short-term memory (LSTM), a novel architectural unit is proposed to extract dynamic temporal features. Finally, the spatial and temporal features are fused to obtain the final prediction results. Experiments have been performed using two datasets from Chengdu, China (TaxiCD) and California, USA (PEMS-BAY). Taking the root mean square error (RMSE) as the evaluation index, the prediction accuracy of ST-3DRCN on TaxiCD dataset is 21.4%, 21.3%, 11.7%, 10.8%, 4.7%, 3.6% and 2.3% higher than LSTM, convolutional neural network (CNN), 3D-CNN, spatial–temporal residual network (ST-ResNet), spatial–temporal graph convolutional network (ST-GCN), dynamic global-local spatial–temporal network (DGLSTNet), and ST-3DNet, respectively.

1. Introduction

Real-time and accurate traffic information (e.g., traffic status, traffic volume and traffic flow) prediction is an important component of the modern intelligent transportation system (ITS) and the advanced passenger information system (ATIS) [1,2]. Knowing reliable traffic information in advance can help travelers make better traffic routes, guide the transportation department to formulate better traffic management strategies, alleviate traffic congestion and reduce carbon emissions [3,4]. Therefore, it is of great significance to improve the performance of the traffic prediction model.

The purpose of the traffic prediction method is to use the historical traffic data to predict the traffic data at the future time. However, urban traffic is complex, showing symmetry in the long-term cycle, but has strong sudden and fluctuation in a short time. Therefore, reliable traffic information prediction is a very challenging task in the real world, affected by the following complex factors:

Dynamic spatial correlation: The spatial characteristics of urban traffic are affected not only by the global or local factors, but also by the historical factors. For example, when the intersection is crowded at 12:00 on Sunday, on the one hand, it is affected by the surge of surrounding vehicles, on the other hand, traffic congestion often occurs at this time.

Long-term temporal correlation: Urban traffic data are not only affected by short-term traffic conditions, but also by long-term traffic cyclical trends. For example, urban traffic conditions at a location may be blocked in the short term, but appear to be smooth in the long term.

Dynamic symmetric correlation: Urban traffic status are symmetric in different days, weeks, months and years. For example, the number of vehicles at 12:00 on Monday and Tuesday shows obvious symmetry and periodicity.

At present, the extraction of complex spatial–temporal features is one of the key research fields of traffic prediction. The research objects of traffic prediction are generally divided into urban road network and expressway. Compared with the latter, urban road network traffic data are affected by many complex factors, and its spatial–temporal feature extraction is more difficult. The structure of traffic data can be divided into non-Euclidean and Euclidean structures. The characteristic of the former is that each node in the road has different adjacent nodes, and the common is the data of expressway. In recent work, the graph convolution network (GCN) and its variants are usually used to perceive the spatial–temporal features of non-Euclidean data [5]. The characteristic of the latter is that each node in the road has the same adjacent node, which is common in urban road network data. The convolution neural network (CNN) and its variants can effectively extract the spatial–temporal features of Euclidean structure data through the globally shared convolution kernel [6]. In this paper, we focus on Euclidean data (i.e., urban road network data). At present, many studies have been carried out on Euclidean traffic data. In recent work [7], the ST-ResNet model effectively extracts the spatial and temporal characteristics of Euclidean structure traffic data through convolution and residual operations, but it ignores the extraction of long-term characteristics of road networks, resulting in the loss of long-term features. ST-3DNet introduces two kinds of temporal properties based on the traditional ST-ResNet, but it still does not get rid of the limitation of using convolution to extract temporal features [8].

ST-3DNet is an effective attempt to extract the dynamic spatial–temporal characteristics of urban road network. However, the ST-3DNet model still has the following shortcomings, such as low symmetry of historical data and low long-term characteristics. To overcome the above shortcomings, we propose a novel spatial–temporal 3D residual correlation network, named ST-3DRCN, to simulate historical data and predict urban traffic status in the near future. The contributions of our study are as follows:

• We introduce the Pearson correlation coefficient method to analyze the symmetry between historical traffic raster data, and the spatial and temporal correlation series are obtained.
• A novel architectural unit termed as the “2D temporal convolution” block is proposed with LSTM to explicitly describe the contributions of the dynamic temporal features.
• We use two real-world traffic datasets (i.e., TaxiCD and PEMS-BAY) to verify the prediction accuracy of the new proposed ST-3DRCN model. The experimental results verify the excellent performance of our model on different prediction tasks compared with the baseline models such as LSTM, CNN, 3D-CNN, ST-ResNet, ST-GCN, DGLSTNet, and ST-3DNet.

2. Related Work

2.1. Traffic Information Prediction

Traffic information prediction provides guarantee and support for the intelligent traffic management system (ITS) [9]. As an important role in ITS, real-time traffic prediction is significant for both traffic management departments and travelers. Based on different prediction cycles, we can divide traffic prediction into long-term and short-term prediction. [10]. Long-term traffic prediction focuses on establishing macro-planning prediction for the development of transportation facilities [11], and short-term traffic prediction focuses on predicting traffic status within the next hour [12]. At present, traffic prediction methods are divided into model-driven methods and data-driven methods.

The common model-driven methods include ARIMA [13,14,15,16], the Kalman filter model [17,18], the grey model [19], etc. Although the model-driven methods have simple algorithm and convenient calculation, it has the problem that it cannot reflect the randomness and nonlinearity if the system model is static.

Data driven methods can be further divided into traditional machine learning methods and deep learning methods. The former category includes support vector machine (SVM) [20,21,22], the Bayesian model [23], and K-nearest neighbour (KNN) [24]. Traditional machine learning methods have good prediction accuracy when dealing with low-dimensional and simple real traffic data, but the prediction accuracy is not high when dealing with high-dimensional data.

With the development of deep learning theory, the traffic flow prediction model using the deep learning method is becoming more and more popular. Because the deep learning method has the ability of high-dimensional data processing and nonlinear data feature mining, it is favored by more and more researchers [25,26]. Among them, the deep belief network (DBN) [27] and the time delay neural network (TDNN) [28] are also used for traffic information prediction. Neural network based on deep learning theory can improve the accuracy of traffic prediction model. However, due to the limitations of neural network back-propagation algorithm, it is easy to fall into local optimization. In order to solve such problems, many combinatorial methods have been proposed [29,30]. However, the traffic data of the urban road network will be affected by the adjacent region and the previous time period. The traditional deep learning methods can only extract part of the information at a time, ignoring the interaction of spatial–temporal features.

2.2. Spatial–Temporal Traffic Information Prediction

The rise of computer vision and image recognition has promoted the development of deep CNN. CNN can capture the spatial characteristics of images through convolution operation [31]; this performance inspired researchers to use convolution operation to extract the spatial features of traffic information. Ma et al. [32] transformed the traffic data into gray image by gray operator and a two-dimensional spatial–temporal matrix was generated to predict traffic speed; their model can effectively capture the spatial characteristics, but ignores the temporal characteristics. The recurrent neural network (RNN) is widely used to process the temporal characteristics. However, RNN is vulnerable to the disappearance of gradient and is difficult to capture the long-term temporal characteristics. LSTM and GRU [33,34], which are two typical improved RNN models, can be used to effectively capture the temporal characteristics of traffic information, but cannot capture the spatial characteristics.

To effectively extract the both spatial and temporal characteristics of non-Euclidean data, Yu et al. [35] proposed a novel deep learning framework, spatio–temporal graph convolutional networks (ST-GCN). Feng et al. [36] proposed the dynamic global-local spatial–temporal network (DGLSTNet) to solve the lack of global and local spatial feature extraction in ST-GCN.

To effectively extract the spatial and temporal characteristics of Euclidean data, a spatial–temporal hybrid model, ConvLSTM [37], has been proposed to improve the prediction accuracy. However, due to the complexity of the hybrid model structure, the training efficiency of the model will decrease with the increasing number of network layers. He et al. [38] introduced the residual element into the depth network structure to improve the training accuracy. Zhang et al. [7] introduced the spatial–temporal residual network (ST-ResNet) into traffic prediction. They divided the city into raster matrix, and used convolution operation with residual units to improve the spatial–temporal dependence. Ren et al. [39] considered the global and local spatial features respectively in the original spatial feature extraction. Guo et al. [40] introduced external factors such as weather and holidays on the basis of ST-3DNet to capture the dynamic characteristics. Zheng [41] improved the model structure of residual network to improve the prediction performance compared with the traditional residual model structure. The above models effectively extract the spatial and temporal characteristics of traffic data. However, they ignore dynamic symmetry correlation analysis and long-term time feature extraction.

The traffic data counted in each time period can be simulated as video frames. Therefore, to overcome the problem that ST-3DNet ignores the dynamic evolution of traffic information temporal characteristics, in this paper, a novel spatial–temporal 3D residual correlation network is proposed to predict future urban traffic status, aiming at automatically learning spatial–temporal information encoded in traffic data.

3. Problem Description

In this section, we will first review the definition of traffic raster data, and then discuss the long-term and short-term characteristics of traffic data.

3.1. Definition of Traffic Raster Data

According to Atluri et al. [42], raster data is one of the most important data structures in the real world. By constantly observing spatial–temporal data and collecting data at a fixed place and time, we can see that the Euclidean structure data with equal position and spacing between intersections in Figure 1 is called raster data. To this end, we firstly divide the area of traffic data into raster areas with a dimension of I × J by latitude and longitude. Secondly, we record the traffic data of each location at a fixed time interval ∆t. The urban traffic data of the network area I × J is represented by X_t ∈ ℝ^I×J, and X_t is named as the traffic raster data; x_t ^i,j represents the urban traffic data stored in the location (i, j) at time t.

3.2. Problem Definition

After conversion in Section 3.1, the traffic prediction problem is transformed into the given historical traffic raster data {X_t|t = 0, …, k} to predict the data X_k+∆t at a certain time interval k + ∆t, where k is the last time node for traffic raster data. There are three difficulties in this problem: firstly, how to evaluate the association between historical data; secondly, how to extract the dynamic spatial-temporal features of urban road network; and finally, how to select the model parameters.

3.3. Long-Term and Short-Term Characteristics of Traffic Data

Traffic data include dynamic spatial characteristics and long-term temporal characteristics. Take the traffic congestion propagation shown in Figure 2 as an example, there are three points, i.e., A, B and C, in which point B is the place where congestion occurs, and points A and C are the places where congestion is transmitted. This phenomenon of congestion transmission reflects the dynamic spatial characteristics of traffic data. At the same time, this congestion phenomenon only occurs in a certain period of time. In a long time, the traffic data at points A, B and C have periodic characteristics, so the traffic data have significant long-term temporal characteristics.

4. Methodology

In this section, we will first present the architecture of the spatial–temporal residual model. Then, the structure of the spatial–temporal 3D residual correlation network will be introduced.

4.1. Basic Architecture of Spatial–Temporal Residual Model

Section 3 shows that traffic data has significant spatial–temporal characteristics. Considering only one of these characteristics will result in poor prediction model accuracy. Based on the selection of convolution kernel dimensions, 2D and 3D spatial–temporal residual models have been proposed. The spatial–temporal residual model extracts traffic characteristics by combining convolution operation and residual units; the structure of typical ST-ResNet is shown in Figure 3.

4.2. Spatial–Temporal 3D Residual Correlation Network

4.2.1. Basic Structure of Spatial–Temporal 3D Residual Correlation Network

As described in Section 1, to extract the dynamic evolution characteristics of traffic information, we propose a spatial–temporal 3D residual correlation network (ST-3DRCN) for urban traffic status prediction. ST-3DRCN consists of a spatial–temporal correlation feature extraction component, and a dynamic spatial and temporal feature extraction component. First, we apply the Pearson correlation coefficient method to extract high symmetric correlation between historical traffic data. Then, a dynamic spatial feature extraction component is constructed by using 3D convolution combined with residual units to extract the dynamic spatial features. After that, the “2D temporal convolution” block is proposed with LSTM to clarify the contributions of the dynamic temporal features. Finally, the dynamic spatial and temporal features are weighted out, and the final predicted value is obtained. The structure of the ST-3DRCN is shown in Figure 4.

4.2.2. Spatial–Temporal Correlation Feature Extraction Component

This paper mainly uses historical traffic raster data to predict the traffic raster data of a future node at a certain time. The historical traffic raster data of different time nodes have some symmetric correlation, as shown in Figure 5.

In order to calculate the symmetric correlation between traffic raster data, the Pearson correlation coefficient method is used to analyze the correlation between data [43]. The Pearson correlation coefficient formula is:

$${\rho }_{x,y}=[{\displaystyle \sum _{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}]/({\sigma }_x{\sigma }_y)$$

(1)

where x_i and y_i (i = 1, …, n) are the target traffic raster data and the traffic raster data to be compared, respectively; and σ_x and σ_y are the sample population standard deviation of the target traffic raster data and the traffic raster data to be compared, respectively. We divide the original traffic raster data into spatial and temporal series based on the Pearson correlation coefficient method.

4.2.3. Dynamic Spatial Feature Extraction Component

We use 3D convolution and residual units to construct a dynamic spatial feature extraction component, as shown in Figure 6. Take the traffic raster data dimension I × I for example. Selecting M × M traffic raster data from spatial sequence to construct 3D traffic raster data with M × I × I dimension, convolution kernel dimension is set to w × h × j, step is set to s, and no pooling is done. The dynamic spatial feature extraction component 3D convolution operation is defined as:

$${\mathit{X}}_{\mathrm{S}}^l=f_{\mathrm{AF}}({\mathit{W}}_{\mathrm{S}}^l\ast {\mathit{X}}_{\mathrm{S}}^{l-1}+{\mathit{b}}_{\mathrm{S}}^l),l=1,\dots ,L_{\mathrm{S}}$$

(2)

where X_s^l−1 and X_s^l are the input and output of the l-th layer of the dynamic spatial feature extraction component 3D convolution operation, respectively, W_s^l is the 3D convolution kernel, b_s^l is the bias term of the l-th 3D convolution layer, L_S is the number of layers that the dynamic spatial feature extraction component 3D convolution operation needs to convolute, and f_AF is the activation function.

To avoid the problem of model precision degradation due to the large number of convolution layers, we introduce residual units to improve the sensitivity, as shown in Figure 6. The output X_s^l of the dynamic spatial feature extraction component 3D convolution operation is input to the residual unit. The residual operation of the dynamic spatial feature extraction component is defined as:

$${\mathit{Z}}_{\mathrm{R}}^l={\mathit{Z}}_{\mathrm{R}}^{l-1}+F_{\mathrm{R}}({\mathit{Z}}_{\mathrm{R}}^{l-1};{\theta }_{\mathrm{R}}^l),l=1,\dots ,L_{\mathrm{R}}$$

(3)

where Z_R^l−1 and Z_R^l are the input and output of the l-th residual unit, respectively, θ_R^l is the set of learnable parameters in the l-th residual unit, F_R is the residual mapping of the dynamic spatial feature extraction component, and L_R is the number of residual layers required for dynamic spatial feature. After the output of the dynamic spatial feature extraction component is processed by residual operation, the dynamic spatial feature output X_S is obtained.

4.2.4. Dynamic Temporal Feature Extraction Component

In addition to extracting the dynamic spatial feature from urban traffic data, we also need to extract the dynamic temporal feature. In this component, As shown in Figure 7, we designed a new architecture unit of the “2D time convolution” block to extract dynamic temporal features. The 2D temporal convolution operation is similar to the 3D convolution operation formula. The difference is that the 2D temporal convolution operation converts the dimension of M traffic raster data in the time series from (M, I, I) to (M, I × I), and the convolution kernel with design dimension (M, 1) is transformed to extract dynamic temporal characteristics with dimension (1, I × I).

To ensure that long-term temporal features are extracted from the dynamic temporal evolution of the traffic raster data, we input the traffic raster data after extracting the dynamic temporal into the LSTM network to maintain the long-term time characteristics. The overall formula for dynamic temporal feature extraction components is defined as:

$$\mathit{x}{(t)}^{(1,I\ast I)}=f_{\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{u}}({\mathit{W}}_{2\mathrm{DT}}^{(M,1)}\mathit{x}{(t-1)}^{(M,I\ast I)}+{\mathit{b}}_{2\mathrm{DT}}^{(1,I\ast I)})$$

(4)

$$\mathit{g}(t)=\tanh ({\mathit{W}}_{\mathrm{g}\mathrm{x}}\mathit{x}(t)+{\mathit{W}}_{\mathrm{g}\mathrm{h}}\mathit{h}(t-1)+{\mathit{b}}_{\mathrm{g}})$$

(5)

$$\mathit{i}(t)=\mathrm{\sigma }({\mathit{W}}_{\mathrm{ix}}\mathit{x}(t)+{\mathit{W}}_{\mathrm{ih}}\mathit{h}(t-1)+{\mathit{b}}_{\mathrm{i}})$$

(6)

$$\mathit{f}(t)=\mathrm{\sigma }({\mathit{W}}_{\mathrm{fx}}\mathit{x}(t)+{\mathit{W}}_{\mathrm{fh}}\mathit{h}(t-1)+{\mathit{b}}_{\mathrm{f}})$$

(7)

$$\mathit{o}(t)=\mathrm{\sigma }({\mathit{W}}_{\mathrm{ox}}\mathit{x}(t)+{\mathit{W}}_{\mathrm{oh}}\mathit{h}(t-1)+{\mathit{b}}_{\mathrm{o}})$$

(8)

$$\mathit{s}(t)=\mathit{g}(t)\ast \mathit{i}(t)+\mathit{s}(t-1)\ast \mathit{f}(t)$$

(9)

$$\mathit{h}(t)=\tanh (\mathit{s}(t))\ast \mathit{o}(t)$$

(10)

where x(t − 1) and x(t) are the input and output of the 2D temporal convolution operation, respectively. h(t) and h(t − 1) are the unit outputs of the LSTM at the current and last moment, respectively. s(t) and s(t − 1) are the cell states of the LSTM at the current and last moment, respectively. g(t) is the cell state used to describe the current input to LSTM. f(t) is the forgetting gate, i(t) is the input gate, and o(t) is the output gate. W and b are the weight and offset terms of each unit, respectively. σ is the activation function, and f_ReLu is ReLu function. Finally, we get the output X_T of the dynamic time feature extraction component.

4.2.5. Fusion

We adopt a parameter matrix fusion method to perform weighted fusion of the dynamic spatial feature output X_S, and dynamic temporal feature output X_T. The weight value is dynamically adjusted according to training. The formula is:

$${\mathit{X}}_{\mathrm{Fusion}}=f_{\mathrm{AF}}({\mathit{W}}_{\mathrm{S}}\ast {\mathit{X}}_{\mathrm{S}}+{\mathit{W}}_{\mathrm{T}}\ast {\mathit{X}}_{\mathrm{T}})$$

(11)

4.2.6. Loss Function

The index mean square error (MSE) is used as the loss function to evaluate the errors of real value and predicted value in model training.

$$L_{\mathrm{MSE}}=\frac{{\displaystyle \sum _{i=1}^n|{\mathit{X}}_{\mathrm{Tr}}-{\mathit{X}}_{\mathrm{Pr}}{|}^2}}{n}$$

(12)

where X_Tr and X_Pr are the real value and predicted value respectively, and n is the total number of samples.

5. Experiments

In this section, two traffic datasets will be applied in our experiment to evaluate the performance of ST-3DRCN. The experimental parameters will be set as follows.

5.1. Datasets

We select two typical data to validate the predictive performance of different models, TaxiCD (Urban road data) and PEMS-BAY (Expressway data).

(a)

TaxiCD: The experimental data comes from GPS data of taxis in Chengdu, China from 3 August 2014 to 20 August 2014. The data is of a real road from 6 am to 12 pm every day. Data details are shown in

Table 1. Statistics of the traffic condition dataset.

Dataset	TaxiCD	PEMS-BAY
Location	In Chengdu, China	In California, USA
Time span	3 August 2014 to 20 August 2014	1 January 2017 to 31 May 2017
Time interval	5 min	5 min
Raster size	(36, 36)	(36, 36)
Number of available time intervals	3888	43,200
Maximum Longitude and Latitude	(104.20591, 30.791764)	(−121.805543, 37.416413)
Minimum Longitude and Latitude	(103.944323, 30.583564)	(−122.078275, 37.249226)
Area	576 square kilometers	354 square kilometers

. We convert taxi data into traffic raster data with 36 × 36 dimensions based on the information in Table 1. In this article, a number of taxis are used in the raster to represent urban traffic status. TaxiCD is a typical Euclidean structure data set, which is mainly used to compare the prediction performance of models processing Euclidean data.

(b)

PEMS-BAY: PEMS-BAY data from the California Department of Transportation recorded five-month data from 325 sensors (1 January 2017~31 May 2017) at five-minute intervals. PEMS-BAY is a typical non-Euclidean data used to evaluate the predictive performance of models suitable for non-Euclidean data.

Figure 8 shows the rasterization of the map of Chengdu. Point A represents a raster involved in road links, and point B represents a roadless raster.

5.2. Hyperparameter

Our model is developed by using Pytorch-GPU and parameter iteration in model training through the Adam optimization algorithm. The training step is set at 0.0001, the number of batches is set at 20, and the maximum number of iterations is set at 800. The other parameters of our model are shown in

Table 2. Structure of the ST-3DRCN.

Parameter	ST-3DRCN
Input dimension	[Batch_size, 36, 36]
Dimension of 2D Conv kernel	1 × 3
Step size of 2D Conv kernel	1
Dimension of 3D Conv kernel	3 × 1 × 1
Step size of 3D Conv kernel	1
Dimension of LSTM input layer	1 × 1296
Dimension of LSTM out layer	1 × 1296
Number of Residual units	8

.

5.3. Traffic Status Transformation and Standardization

In order to better show the traffic status, we will protocol the traffic raster data. According to the number of automobiles counted by the traffic raster data, we divide into six traffic states, one for smooth traffic and six for heavy congestion. After the traffic status data is generated, we need to standardize the traffic raster data to reduce the influence of different dimensions between the data, and the calculation formula is as follows:

$${\mathit{X}}_{\mathrm{nor}}^n=({\mathit{X}}_{\mathrm{real}}^n-{\overline{\mathit{X}}}_{\mathrm{real}})/{\sigma }_x$$

(13)

where ${\mathit{X}}_{\mathrm{real}}^n$ is the n-th data in the traffic raster data, ${\overline{\mathit{X}}}_{\mathrm{real}}$ is the average value of all traffic raster data, and ${\sigma }_x$ is the standard deviation of the overall traffic raster data.

5.4. Spatial–Temporal Correlation Feature Extraction

To ensure a strong symmetric correlation between the input data, the Section 4.2.2 method is used to extract the spatial–temporal correlation characteristics of the raster data. Taking x_0,17 data of TaxiCD as an example, the spatial–temporal correlation is shown in Figure 9. Figure 9a,b show the spatial–temporal correlation of traffic data in a day. The accuracy of the model can be improved by using time nodes that are highly associated with them.

5.5. Baseline Models

To better reflect the prediction accuracy of the proposed model, we use the following five baseline models as comparisons to verify the prediction effect.

• LSTM: Long short-term memory network, as an improved RNN, effectively reduces the gradient disappearance and gradient explosion during RNN training. LSTM is often used to extract the temporal characteristics of traffic information.
• CNN: Convolution neural network or 2D-CNN uses a 2D convolution kernel to extract spatial features of two-dimensional data.
• 3D-CNN: Unlike 2D-CNN, 3D-CNN uses a 3D convolution kernel to extract spatial features of 3D data. Compared with 2D-CNN, it is easier to find the dynamic characteristics.
• ST-ResNet: The spatial–temporal residual network is a deep neural network used to extract spatial–temporal features.
• ST-3DNet: Deep spatial–temporal 3D convolutional neural network uses 3D convolution combined with residual units to extract spatial and temporal features of traffic information.
• ST-GCN: Spatial–temporal graph convolutional network, ST-GCN considers time series as one of the factors on the basis of traditional GCN.
• DGLSTNet: Dynamic global-local spatial–temporal network, which consists of multiple spatial–temporal modules and focuses on local and global information of traffic data on the basis of ST-GCN.

5.6. Evaluating Indicator

In order to scientifically evaluate the prediction effects of different models, we use root mean square error (RMSE) and mean absolute error (MAE) to compare the prediction results of the models. The two formulas are as follows:

$$E_{\mathrm{RMSE}}=\sqrt{\frac{1}{m}{\displaystyle \sum _{i=1}^m{(y_i-{\overline{y}}_i)}^2}}$$

(14)

$$E_{\mathrm{MAE}}=\frac{1}{m}{\displaystyle \sum _{i=1}^m|y_i-{\overline{y}}_i|}$$

(15)

where y_i is the true value of traffic data, ${\overline{y}}_i$ is the traffic data predicted by the model, and m is the number of samples.

6. Results

The experiments will be carried out according to the steps outlined in the above sections. In order to verify the superiority of the proposed ST-3DRCN model, the results from the proposed model will be compared with LSTM, CNN, 3D-CNN, ST-ResNet, ST-GCN, DGLSTNet and ST-3DNet. The Euclidean and non-Euclidean traffic data will be analyzed respectively. The possible network topologies to be employed in ST-3DRCN and its influence on the results will also be investigated.

6.1. The Global-Local Predictions Based on the ST-3DRCN

After the initialization of our model, we use the training set to train, and use the test set of TaxiCD to verify the prediction effects. The ST-3DRCN prediction results of local positions are shown in Figure 10. The prediction results of the training set and the test set are before and after node 431, respectively.

Meanwhile, we also verify the prediction performance of the model to the global status; Figure 11 shows a comparison between the true value and the predicted value of the global traffic status at a certain time. The color depth in the graph represents the number of vehicles. The deeper the color, the larger the number of vehicles.

6.2. Comparison with Five Classical Baseline Models

6.2.1. Settings of Baseline Models

In order to verify the prediction performance of ST-3DNet on Euclidean urban road network data, we evaluate our proposed model by comparing the results of five classical baseline models. Some parameters of all models are set uniformly to verify the prediction effect between models fairly. The specific parameter settings are shown in

Table 3. Parameter setting of five classical baseline models.

Parameter	LSTM	CNN	3D-CNN	ST-ResNet	ST-3DNet
Input dimension	(1, 1296)	(36, 36)	(2, 36, 36)	(36, 36)	(2, 36, 36)
Output dimension	(1, 1296)	(36, 36)	(36, 36)	(36, 36)	(36, 36)
Training times	800	800	800	800	800
Batchsize	20	20	20	20	20
Training step	0.0001	0.0001	0.0001	0.0001	0.0001
Time interval	5 min	5 min	5 min	5 min	5 min

.

6.2.2. Comparison Results with Five Classical Baseline Models

We used TaxiCD to train and test six models.

Table 4. Comparison of average accuracy.

Model	TaxiCD
	RMSE	MAE
LSTM	0.6307	0.3217
CNN	0.6297	0.3167
3D-CNN	0.5617	0.2804
ST-ResNet	0.5560	0.2792
ST-3DNet	0.5074	0.2430
ST-3DRCN	0.4958	0.2317

shows the accuracy comparison between our model and the baseline model with RMSE and Mae as evaluation indicators. Based on LSTM, CNN, 3D-CNN, ST-ResNet and ST-3DNet, the prediction accuracy of the proposed model is improved by 21.4%, 21.3%, 11.7%, 10.8% and 2.3%, respectively, with RMSE as the evaluation index.

In the city traffic management, we need to understand the traffic status of a section or a point, so we need to compare the prediction effect of different models on a point in the raster data. Figure 12 shows the effect of different models on traffic status prediction at the same point.

In order to verify the prediction effect of all models on global traffic conditions, we also need to predict all areas of urban road network. Figure 13 shows the prediction effects of different models on the global region. To compare the similarity between predicted and real data from different models, we use the Pearson correlation coefficient method to list the similarity of each group of data, as shown in Figure 14.

We choose different time intervals to verify the multi-step prediction ability of the model. The multi-step prediction ability determines the effect of the model on the extraction of long-term features of traffic data. Referring to the work of [8], the selection of time span is random. For the convenience of statistics, the time interval ranges from 5 min to 60 min. Figure 15a and Figure 16b show the short-term (0–30 min) prediction accuracy of different models, respectively. Figure 16a,b show the long-term (30–60 min) of different models, respectively.

Training time is also one of the indicators of the evaluation model. The shorter the training time of a model is, the stronger the application ability of the model in actual production is. The number of iterations for all models is set to 800, and the loss iteration is shown in Figure 17. It can be seen from the figure that ST-3DRCN has a faster convergence speed.

6.3. Comparison with Two Typical Models Dealing with Non-Euclidean Data

In order to verify the prediction performance of our proposed model for non-Euclidean data, we use two typical models, ST-GCN and DGLSTNet, as baseline models to compare the prediction performance. We used data of TaxiCD and PEMS-BAY to train and test all models. The structures of TaxiCD and PEMS-BAY are shown in Figure 18. Based on the two structures, we can get the adjacency matrix.

The prediction results of models are shown in the

Table 5. Comparison with the model considering global-local features (5 min).

Model	TaxiCD	PEMS-BAY
	RMSE (Average)	RMSE (Average)
ST-GCN	0.5203	2.2451
DGLSTNet	0.5147	2.1956
ST-3DRCN	0.4958	2.2132

. On the TaxiCD dataset, the prediction performance of ST-3DRCN is the best; on the PEMS-BAY dataset, DGLSTNet has the best prediction performance. For Euclidean and non-Euclidean traffic data, ST-3DRCN and DGLSTNet have the best prediction accuracy, respectively. Taking RMSE as the evaluation index, the prediction accuracy of ST-3DRCN on the TaxiCD dataset is 4.7% and 3.6% higher than that of ST-GCN and DGLSTNet, respectively.

6.4. Network Configuration of the ST-3DRCN

In order to study the impact of different network structures on the model, taking RMSE as the evaluation index and TaxiCD as the data set, we established two groups of control experiments. Figure 19a shows the prediction accuracy of the proposed model when the convolution layer is 1 and the filter size changes from 2 × 2 to 6 × 6. Considering that the larger the size of convolution kernel, the greater the computational cost of the model, we set the size of filter size to 3 × 3. Figure 19b shows the accuracy of the proposed model when the filter size is 3 × 3 and the number of convolution layers increases from 1 to 7. Experiments show that the optimal parameters of the model on TaxiCD dataset are: the filter size set to 3 × 3 and the number of convolution layers set to 5.

6.5. Discussion

From the numerical results in Section 6.1, Section 6.2, Section 6.3 and Section 6.4, we see that our proposed ST-3DRCN model shows a significant improvement on the prediction accuracy. Meanwhile, the effectiveness of the proposed method is further proved by comparison with other classical models. These models include LSTM, CNN, 3D-CNN, ST-ResNet, ST-3DNet, ST-GCN, and DGLSTNet.

In particular, ST-3DRCN shows excellent performance in extracting dynamic spatial–temporal features from traffic data. The results of the experiment show that LSTM is a time series-based prediction model, which has a strong ability to capture the temporal characteristics of traffic data, but a poor ability to capture the spatial characteristics. CNN, as a traditional prediction model for mining spatial characteristics, is difficult to capture the temporal characteristics. 3D-CNN enhances the capture of dynamic traffic characteristics based on CNN. ST-ResNet and ST-3DNet do not filter the time series when dealing with traffic data of urban road network. They are easy to capture time series with low correlation and ignore the long-term time characteristics when capturing small changes.

ST-GCN and DGLSTNet have excellent prediction performance in non-Euclidean traffic data, but ignore the dynamic spatial correlation and long-term time characteristics of traffic data, resulting in the above two models not performing as well as ST-3DRCN in Euclidean traffic data processing.

At the same time, it should be pointed out that choosing the appropriate network parameters is very important to improve the prediction performance of ST-3DRCN.

In summary, through the experimental comparison of the above sections, it is found that the ST-3D RCN model proposed in this paper has better prediction performance in an urban environment. Compared with other baseline models, ST-3DRCN not only extracts dynamic spatial features effectively, but also has the ability to extract long-term temporal features. As shown in Figure 20, taking the root mean square error (RMSE) as the evaluation index, the prediction accuracy of ST-3DRCN on TaxiCD dataset is 21.4%, 21.3%, 11.7%, 10.8%, 4.7%, 3.6% and 2.3% higher than LSTM, CNN, 3D-CNN, ST-ResNet, ST-GCN, DGLSTNet and ST-3DNet, respectively. Therefore, the ST-3D RCN model proposed in this paper is more suitable for urban road network traffic data prediction.

7. Conclusions

In this paper, we propose a novel spatial–temporal 3D residual correlation network (ST-3DRCN) for predicting urban traffic status. ST-3DRCN introduces the Pearson correlation coefficient method to obtain the spatial and temporal symmetric correlation series. A dynamic spatial feature extraction component is constructed by using 3D convolution and residual units, and the component is used to extract the dynamic spatial features. A novel “2D temporal convolution” block is proposed to extract the dynamic temporal features. We used TaxiCD and PEMS-BAY data sets to verify the prediction accuracy of the proposed ST-3DRCN model. The experimental results show that the prediction accuracy of the proposed model is improved by 10.8% on average, compared with the baseline models such as LSTM, CNN, 3D-CNN, ST-ResNet, ST-GCN, DGLSTNet and ST-3DNet. Our next work will focus on the problem of reduced prediction accuracy due to model structure solidification.