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A Dynamic Spatio-Temporal Deep Learning Model for Lane-Level Traffic Prediction

A Dynamic Spatio-Temporal Deep Learning Model for Lane-Level Traffic Prediction Hindawi Journal of Advanced Transportation Volume 2023, Article ID 3208535, 14 pages https://doi.org/10.1155/2023/3208535 Research Article A Dynamic Spatio-Temporal Deep Learning Model for Lane-Level Traffic Prediction 1 1 2 2 2 Bao Li , Quan Yang , Jianjiang Chen , Dongjin Yu , Dongjing Wang , and Feng Wan Zhejiang Testing & Inspection Institute for Mechanical and Electrical Products Quality Co.,Ltd., Hangzhou 310018, China School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China Correspondence should be addressed to Dongjing Wang; dongjing.wang@hdu.edu.cn Received 9 November 2022; Revised 1 February 2023; Accepted 24 February 2023; Published 8 March 2023 Academic Editor: Jing Zhao Copyright © 2023 Bao Li et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Trafc prediction aims to predict the future trafc state by mining features from history trafc information, and it is a crucial component for the intelligent transportation system. However, most existing trafc prediction methods focus on road segment prediction while ignore the fne-grainedlane-level trafc prediction. From observations, we found that diferent lanes on the same road segment have similar but not identical patterns of variation. Lane-level trafc prediction can provide more accurate prediction results for humans or autonomous driving systems to make appropriate and efcient decisions. In trafc prediction, the mining of spatial features is an important step and graph-based methods are efective methods. While most existing graph-based methods construct a static adjacent matrix, these methods are difcult to respond to spatio-temporal changes in time. In this paper, we propose a deep learning model for lane-level trafc prediction. Specifcally, we take advantage of the graph con- volutional network (GCN) with a data-driven adjacent matrix for spatial feature modeling and treat diferent lanes of the same road segment as diferent nodes. Te data-driven adjacent matrix consists of the fundamental distance-based adjacent matrix and the dynamic lane correlation matrix. Te temporal features are extracted with the gated recurrent unit (GRU). Ten, we adaptively fuse spatial and temporal features with the gating mechanism to get the fnal spatio-temporal features for lane-level trafc prediction. Extensive experiments on a real-world dataset validate the efectiveness of our model. machine learning methods such as K-nearest neighbor (KNN) 1. Introduction [8] and support vector regression (SVR) [9] are also used for Intelligent transportation systems (ITS) include driving trafc prediction. But they have higher requirements for fea- behaviour understanding [1], path fnding [2], map tures, which often requires complex feature processing. In matching [3], and trafc prediction [4]. Trafc prediction recent years, deep learning methods have become the main- refers to predict the future state of trafc by analyzing and stream method of trafc prediction due to automatic feature mining trafc information in the mining history [5]. As the modeling and efective data mining capabilities. For example, foundation and important part of ITS, accurate trafc recurrent neural network (RNN)-based methods [10] can ef- prediction can help formulate real-time control strategies, fectively model the temporal features in trafc fows. Con- which is of great importance for scientifc planning of trafc volutional neural network (CNN)-based methods [11] regard management and people’s safe and efcient travel [6]. trafc fows as image and model spatial features or temporal Early eforts in this feld use statistical learning methods for features in European space. Te road network or road sensor trafc prediction, such as diferential average moving autore- network is naturally a graph and has a typically non-Euclidean gression [7], which converts unstable sequences into stationary structure. Recently, researchers have used graph-based sequences by diference for prediction. Trafc state information methods for trafc prediction [12]. CNNs and RNNs can has signifcant nonlinear and uncertain characteristics, and only be used on Euclidean data, while graph-based methods 2 Journal of Advanced Transportation can efectively model the non-Euclidean structure of graphs for more accurate predictions. With a graph as input, graph-based methods have achieved superior performance in trafc pre- diction. Te topology of the graph is represented by an adjacent 1-19 1-20 1-21 1-22 1-23 1-24 1-25 matrix, and graph-based methods are directly afected by the Road section 1, lane 1 adjacent matrix. Time Although related work in the past has proposed many efective algorithms in the feld of trafc prediction, there are still some limitations and challenges. (1) Previous studies ignore the diferences between diferent lanes and mainly focus on road segment prediction. In reality, there is a wide demand for 1-19 1-20 1-21 1-22 1-23 1-24 1-25 lane-level trafc prediction. For example, automated vehicles or Road section 1, lane 2 human-driven vehicles can select appropriate lanes according Time to the prediction results at the lane level. Trafc congestion can thus be avoided or alleviated [13, 14]. Besides, lane-level trafc prediction can provide more refned and accurate trafc in- formation and help humans or machines make more appro- 1-19 1-20 1-21 1-22 1-23 1-24 1-25 priate and efective decisions. Tere are diferent and related Road section 2, lane 1 patterns of trafc states in diferent lanes [15– 17]. As shown in Time Figure 1, there are two lanes in both road section 1 and road section 2, and the trafc information between diferent lanes in the same road section has a similar change pattern, while there still exist some diferences in the change pattern in many details. In the road segment-level trafc prediction, the road 1-19 1-20 1-21 1-22 1-23 1-24 1-25 segment is regarded as a whole, and the prediction results are Road section 2, lane 2 too macroscopic to provide precise information for lane-level Time decisions. (2) Graph-based methods rely heavily on adjacent Figure 1: An example of lane-level trafc fow, where the hori- matrices, while most methods build static adjacent matrices, zontal axis represents the trafc fow, and the vertical axis rep- ignoring that the correlation between diferent nodes on the resents the time the trafc fow recorded. graph may be diferent in diferent situations. For example, there may be similar change patterns for two nodes that are far apart. Besides, the trafc situation of nodes may change in GCN, learns temporal features with GRU, and ob- diferent time periods. It is difcult for the static adjacent tains fused adaptive spatio-temporal features with matrix to respond timely and efectively to spatio-temporal the gating mechanism. changes. (3) Extensive experiments on a real-world dataset vali- To address the aforementioned challenges, we propose date the efectiveness of the model. a deep learning model for lane-level trafc prediction, which Te remainder of this paper is organized as follows: In is mainly composed of data-driven GCN and GRU. GCN is Section 2, we introduced the related work, which includes used to extract spatial features. To adapt GCN for lane-level general methods and deep learning methods. Section 3 trafc prediction, we treat diferent lanes at the same lo- formulates the lane-level trafc prediction task. Section 4 cation as diferent nodes on the graph. Te adjacent matrix introduces the construction of the data-driven adjacent of the graph is calculated in a data-driven manner and matrix and the architecture of our model in detail. Te consists of a traditional distance adjacent matrix and a dy- comprehensive experiment result on a read-world dataset is namic lane correlation matrix. GRU is used to extract demonstrated in Section 5. Finally, we conclude the paper temporal features. Ten, spatio-temporal features are ob- and present future work in Section 6. tained by fusing temporal and spatial features adaptively through the gating mechanism. Finally, lane-level trafc prediction is performed based on the learned spatio- 2. Related Work temporal features. Te main contribution of this paper can be summarized 2.1. General Methods. Traditional trafc prediction methods as follows: can be divided into parametric methods and nonparametric methods [10]. Parametric methods rely on the assumption of (1) A data-driven adjacent matrix is proposed, which data stationarity and provide explicit formulations for consists of a distance-based adjacent matrix and valuable interpretations of trafc characteristics. Classical a dynamic lane correlation matrix. It can respond parametric methods, such as the autoregressive integrated efectively to spatio-temporal changes in a timely moving average model (ARIMA) and its variants [7, 18, 19], manner. have been proven to be efective in many scenarios. For (2) We propose a deep learning model for lane-level example, some studies have found that ARIMA can model trafc prediction, which learns spatial features with highway time series data with high precision [20]. Some Traffic f low Traffic f low Traffic f low Traffic f low Journal of Advanced Transportation 3 ideal for solving trafc prediction problems. Li et al. [39] other parametric methods include exponential [21], multi- variate time series models [22], and Kalman fltering models treated the trafc fow as a difusion process and proposed DCRNN, which uses bidirectional random walks on the [23]. However, the dependency on stationarity makes parametric methods difcult to efectively model the un- graph and GRU to capture spatial and temporal features, certainty and irregular volatility of trafc data. Te structure respectively. Zhao et al. [10] proposed T-GCN, which stacks and parameters of the nonparametric methods are not fxed, GCN and GRU for trafc prediction. Yu et al. [40] proposed and the data requirements are not as strict as those of the STGCN to extract spatio-temporal features with complete parameterized methods. Te nonparametric methods are convolutional structures. Guo et al. [41] established a HGCN more able to deal with complex data such as noisy data and model which operates the convolution operation on both missing data [24]. Typical nonparametric methods include micro- and macrotrafc graphs. Zhu et al. [42] employed support vector regression [8], K-nearest neighbor [9], the GCN in multigraph to analyze correlations from multiple perspectives. Guo et al. [43] proposed a dynamic GCN for Bayesian network [25], the extreme gradient boost [26], and artifcial neural networks (ANN) [24, 27, 28]. Among them, trafc prediction on the basis of Laplace matrix estimation. Cao et al. [44] combined self-attention with GCN for trafc ANN can mine the latent information of trafc data and has nonlinear modeling ability, which is one of the most widely fow prediction. Although there is a lot of excellent work for used nonparametric methods. Although nonparametric trafc prediction, most of them are not suitable for lane-level methods have some achievements in the feld of trafc trafc prediction. Besides, most existing works treat the road prediction, these methods are limited in their ability to or sensor network as a static graph. We propose a deep predict lane-level trafc. Besides, both parametric and learning model for lane-level trafc prediction with a dy- nonparametric methods are mainly used to model the namic adjacent matrix driven by data. As for lane-level works, Gu et al. [20] combined LSTM and GRU for lane- temporal features and are weak in modeling the spatial features. level trafc speed prediction. Ke et al. [36] introduced a two- stream multichannel CNN model. Ma et al. [45] proposed a convolutional LSTM network for multilane short-term 2.2. Deep Learning Methods. With the rapid development of trafc forecasting. Lu et al. [46] described a mix deep high-performance data storage and processing technologies, learning model for lane-level trafc speed forecasting. Wang trafc prediction is moving from nonparametric methods to et al. [47] presented a heterogeneous graph convolution deep learning methods [10]. An important step in trafc model for lane-level trafc fow prediction. Existing lane- prediction is to extract spatio-temporal features from trafc level trafc prediction methods mostly use RNN or CNN to data. For the recurrent neural network (RNN) and its model spatial features, which has certain limitations. variants like long short-term memory (LSTM) [29] and gated recurrent unit (GRU) [30] which can efectively utilize 3. Problem Formulation temporal data, RNN-based methods [31] play an important role in mining temporal trafc features. Ma et al. [32] frst In this work, we aim to predict the trafc state of lanes in applied LSTM to solve the prediction of highway trafc a period of time on the basis of the historical trafc state speed and fow. Zhao et al. [10] utilized GRU, which has information recorded on the road sensors. Trafc state is fewer neurons than LSTM, for trafc prediction. Gu et al. a general concept that includes trafc speed, trafc fow, and [20] built a fusion system to capture temporal features. other numerical information related to the road. Specially, RNN-based methods [33, 34] have shown promising results we predict lane-level trafc fow in the experiment section. in trafc prediction feld, while they are not good at mining Defnition: Lane Network G. To describe the non- spatial features in trafc fow. In terms of spatial trafc Euclidean structure of the lane network, we defne it as features, trafc fows in nearby locations are often strongly graph G � (V, E, A). On graph G, V � v , v , . . . , v is the 􏼈 􏼉 1 2 N correlated [35]. For the power of handling image data, CNN set of nodes, where v represents the i-th lane and N is the has been used in trafc prediction by treating the trafc fow number of lanes. Note that we treat diferent lanes on the data as an image. Ke et al. [36] constructed a multichannel same road section as diferent nodes. E is the set of edges. CNN model for multilane trafc speed prediction. Liu et al. Te edge between lane i and lane j only exists if their [37] developed an attention-based CNN structure for trafc distance is less than a certain threshold and there exists speed prediction with the use of trafc fow, speed, and a trafc fow from v to v . To better represent the real i j occupancy. However, CNN and RNN can only be applied to situation, we consider the trafc fow between diferent lanes Euclidean data; they cannot model the topological structure in the same section of the road to be interconnected. of the road network or the road sensor network. Neither N×N A ∈ R is the adjacent matrix. CNN-based methods nor RNN-based methods are perfect 1 2 N N Let X � 􏼈x , x , . . . , x 􏼉 ∈ R represent the trafc fow t t t for spatio-temporal feature extraction. of N lanes on each time stamp t. Suppose the trafc fow data Te road network or the road sensor network is naturally is the graph signal of G, given time t and lane network G, the a graph. Recently, researchers have applied graph neural lane-level trafc fow prediction problem in our work can be networks (GNN), especially graph convolutional networks defned as (GCN) [38], for trafc prediction, and they have superior 􏼂X , . . . , X 􏼃 � f􏼐􏼐X , . . . , X 􏼑, G􏼑, (1) performance compared to previous approaches. For the t+1 t+T t−p+1 t ability to model non-Euclidean graph structures, GNNs are 4 Journal of Advanced Transportation Table 1: Summary of notations. where f represents the learned mapping function, p is the input sequence length, and T is the predicted sequence Symbol Description length. G Lane network Te key symbols used in this paper are summarized in V, E Node set and edge set of in G Table 1. X Trafc information of all lanes at timestamp t x Trafc information of lane i at timestamp t A Data-driven adjacent matrix 4. The Proposed Approach A Distance-based adjacent matrix In view of the lack of work on lane-level trafc prediction, A Trafc information similarity matrix this paper proposes a lane-level trafc prediction model. Te p, T Sequence length for input and predict α A constant that controls the contribution of A architecture of our model is illustrated in Figure 2. Spe- c D Degree matrix cifcally, we frst establish a data-driven adjacent matrix that u, r Update gate and reset gate in GRU can respond to spatio-temporal changes based on the c, h Cell state and hidden state in GRU geographic location and historical trafc information of the W Learnable parameter matrices sensor. Te data-driven adjacent matrix is fed into the graph g Feature fusion gate convolutional network (GCN) to capture spatial features, H Learned spatial features and we model the temporal features with a gated recurrent t H Learned temporal features unit (GRU) model. Ten, we adaptively fuse the spatial and H Fused spatio-temporal features temporal features with the gating mechanism to get com- prehensive spatio-temporal features. Finally, we make multistep lane-level trafc predictions based on the spatio- temporal features. further introduce the dynamic correlation matrix N×N A ∈ R . A is flled with the Pearson correlation co- c c efcient calculated from the observed input data of the lanes. 4.1. Data-Driven Adjacent Matrix. Te graph depicts the ∗ To be specifc, A at time t is calculated with topological relationship structure between nodes through t�t i i j j x − x x − x the adjacent matrix, and the construction of the adjacent 􏽐 ∗ 􏼐 􏼑􏼐 􏼑 t�t −h+1 t t 􏽱�������������������������������� A � , (3) ij matrix directly afects the expressive power of the graph [48]. ∗ 2 ∗ 2 t�t i i t�t j j 􏽐 ∗ 􏼐x − x 􏼑 􏽐 ∗ 􏼐x − x 􏼑 t�t −h+1 t t�t −h+1 t However, most GCN-based trafc prediction works only construct a static adjacent matrix with fxed weights, without where i and j are the index of lane v and lane v , x is the i j t considering that the relationship of diferent nodes may i j value of trafc fow on v observed at time t, x and x are change in various situations. In particular, it is difcult for means of v and v , respectively. Te absolute value of A is i j ij a static adjacent matrix to respond to spatio-temporal closer to 1, the higher the correlation between v and v . i j changes in a timely manner, which makes the model Combining the basic distance-based adjacent matrix A hardly achieve accurate prediction. In our work, we propose and the dynamic correlation matrix A , we propose the data- a data-driven dynamic adjacent matrix, which is composed driven adjacent matrix A, of the basic distance-based adjacent matrix A and the dynamic node correlation matrix A . A � A + αA , (4) d c Te graphs include directed graph and undirected graph. where α is a constant that controls how much A contributes For undirected graphs such as social networks, the adjacent 􏽢 􏽢 to A. On the one hand, A provides geographic relationships matrix is symmetric. In the road sensor network, the trafc that are fundamental and important for spatial feature ex- fows on roads have directions due to the restriction of trafc traction; on the other hand, A can implement timely ad- rules. Graph G is a directed graph, and the adjacent matrix is justments to the adjacent matrix with reference to changes of asymmetric. historical information. For the basic distance-based adjacent matrix A , as most works did [49], we calculate one element A in A with ij d 4.2. Spatial Feature Modeling. Spatial features play an im- ⎧ ⎪ −d ⎪ ij ⎪ ⎛ ⎝ ⎞ ⎠ ⎪ exp , if d ≤ ε, portant role in trafc prediction for trafc fow sequences at ij ⎪ 2 diferent locations with connection to some extent. Before A � (2) ij ⎪ the employment of graph-based methods, research studies usually extract the spatial features with multivariate time 0, if d > ε, ij series models or CNNs [50]. However, limited by the where A represents the infuence degree of lane v on lane structure, multivariate time series models mostly cannot ij i v , d is the distance between v and v , and σ is the standard model the nonlinear relationships between diferent se- j ij i j deviation of d. Te distance between diferent lanes on the quences. Although CNN-based methods can alleviate the same road segment is 0. A has a positive value only if d is situation, the architecture of CNN is bounded to Euclidean ij ij smaller than threshold ε and from v to v exists a trafc fow. space, which is not enough for lane network’s topological i j To compensate for the defects caused by the static structure modeling. Recently, graph-based methods have characteristics of the distance-based adjacent matrix, we attracted wide attention for their ability in modeling non- … Journal of Advanced Transportation 5 Data A A X A + αA c d d c Collection Sensor Trafc Correlation Distance-based Sensor lane1 lane2 lane3 lane4 information matrix adjacent matrix geolocation X X [t–h+1:t] [t–h+1:t] Prediction 1 result X t+1 1 2 Spatial GCN Sensor feature 4 4 Linear 2 2 3 5 transformation lane1 lane2 5 5 Linear Temporal transformation feature … 2 GRU GRU Prediction result X Sensor t+T t–h+1 lane1 lane2 lane3 lane4 Figure 2: Te architecture of our proposed model. to extract the temporal features of the trafc data. Tere are Euclidean structure. Specifcally, we extract the spatial features with GCN. Te GCN model built a flter in the two gates in GRU, which are spatial domain, and the spatial features between diferent u � σ W X + W h + b , t ux t uh t−1 u nodes on a graph are extracted with the usage of flter. As (6) illustrated in Figure 3, the central node models the topo- r � σ W X + W h + b 􏼁, t rx t rh t−1 r logical relationship by aggregating the information of its where u represents the update gate and controls how much neighboring nodes in GCN. Te topological structure of the t history information the current moment has, r represents graph is encoded to acquire spatial features. the reset gate and controls how much history information After the construction of the data-driven adjacent matrix 􏽢 needs to be forgotten. x is the trafc information at time t, A, the GCN model extracts spatial features with and h is the hidden state at time t − 1. t−1 −1/2 −1/2 W , W , W , W , b , b are learnable parameters. With (l) (l−1) (l− 1) ux uh rx rh u r 􏽢 􏽢 H � σ􏼒D AD H W 􏼓, (5) s s the gating signals of u and r , the cell state c and output t t t hidden state h can be calculated with (l) where H represents the feature matrix in l-th layer, D is the − 1/2 − 1/2 􏽢 􏽢 􏽢 􏽢 􏽢 c � tanh W X + W r ⊙ h 􏼁 􏼁, degree matrix and D � Σ A . D AD denotes nor- t cx t ch t t−1 ii j ij (7) malize the adjacent matrix A, which can help to keep the h � 1 − u ⊙ h + u ⊙ c , t t t−1 t t distribution of the feature matrix during the information transfer process. W is the learned weight matrix in l-th layer where c can be regarded as the history information stored at (0) and σ represents the activation function. Note that H � X time t, and ⊙ represents element-wise multiplication. and X is the input trafc information matrix. As shown in Figure 4, GRU models the hidden state in time t by taking the current trafc information and the last hidden state h . With this operating mechanism, GRU is t−1 4.3. Temporal Feature Modeling. Trafc data have signifcant capable of retaining the historical information while uti- sequence structure, which means that temporal features are lizing current trafc information, and then it is able to model the key to trafc prediction. Te recurrent neural network temporal features. (RNN) is widely used in the processing of sequence data. However, RNN has the problem of gradient disappearance or gradient explosion with the sequence length growing. To 4.4. Our Model. With GCN and GRU, we obtain spatial and solve this problem, researchers proposed many variants of temporal features, respectively. Our next target aims to fuse RNN such as LSTM and GRU. Tese variants have been the spatial and temporal features into comprehensive spatio- proved to be efective in sequence data modeling. Both temporal features. A convenient operation is to add these LSTM and GRU control the dissemination and update of two kinds of feature directly, which may weaken the information with the gating mechanism. Compared with characteristics of the spatial and temporal features them- LSTM, GRU has smaller training time, fewer parameters, selves. Inspired by the gating mechanism, we introduce and relatively simpler structure. Terefore, we employ GRU a learnable gate g to fuse features. Similarly, to the role of Fusion Gate 6 Journal of Advanced Transportation 4 4 2 2 (a) (b) Figure 3: Spatial feature modeling. h h × + t-1 t h h h 1- t–w+1 t–1 t h h t–w+1 t–1 GRU … GRU GRU × tanh x x x t–w+1 t–1 t Figure 4: Temporal feature modeling. gates in GRU, g controls the degree to which spatial and dynamic changes to get the spatial features with GRU model. temporal features contribute to the fnal spatio-temporal Finally, we fuse these features to make multi-step trafc features. predictions. g � σ􏼐W H + W H + b 􏼑, s s t t g 5. Experiment (8) H � g ⊙ H +(1 − g) ⊙ H , s t In this section, we conduct extensive experiment on a real- world dataset to evaluate the proposed method and several where H represents the extracted spatial features. Suppose baselines answering the following questions: the layer of GCN is L, then H equals to the output feature (L) matrix H in L-th layer. H represents the extracted s t (i) RQ1: How does our method perform compared to temporal features. We stack all units’ output hidden state to baselines in lane-level trafc prediction, and do get the fnal temporal features. W , W , and b are learnable s t g diferent components of our method show real parameters. improvement? Let Y and Y denote the real trafc state and the pre- t t (ii) RQ2: How do various hyperparameters afect the dicted trafc state at time t, respectively. In the training performance of our method? process, the target is to minimize the error between Y and 􏽢 (iii) RQ3: Does our method really work in real Y , and the loss function is defned as situations? � � � � � 􏽢 � loss � Y − Y + λ‖W‖, (9) � � t t where the second term is an L2-regularization term that 5.1. Dataset. We perform experiments on a real-world helps avoid the overftting problem, λ is the regularization dataset. Te dataset is collected from Sutai Expressway parameter, and W represents the weighted parameters. captured by the remote microwaves trafc sensors in Zhe- In summary, we propose a lane-level trafc prediction jiang, China. Afected by the distance between sensors, we model. On the one hand, our model uses GCN to model the selected 30 sensors’ trafc data for experiment. Te fre- topological structure of the lane network to extract spatial quency of trafc information collection for each sensors is features. On the other hand, we mine trafc information’s once every 5 minutes. Te collected data mainly includes Journal of Advanced Transportation 7 lane-level trafc speed and trafc fow. All trafc in- (ii) Root mean squared error (RMSE): 􏽶������������ formation is the average value that passes through the sensor over a sampling time interval. Since some sensors have RMSE � 􏽘 y 􏽢 − y􏼁 , (11) serious data missing in some lanes, the number of valid lanes i i i�1 in 30 sensors is 53. Te record number for each lane is 16,032 and the entire dataset includes 849,696 records in total. To make the prediction result more reliable, we flled in the (iii) Explained variance score (VAR): missing data with the data from the previous moment. Var􏼈y − y 􏽢􏼉 VAR � 1 − , (12) Var(y) 5.2. Baselines. To validate the efectiveness of our model for lane-level trafc prediction, we compare the proposed model where y 􏽢 is the predicted value and y is the real i i with several commonly used baselines: value. Var means to calculate the variance. Specif- ically, for MAE and RMSE, the smaller the value, the (1) MLP, which contains three fully connected layers. better the performance, since they measure the error We concatenate all lanes’ trafc information and between the predicted value and the real value di- fatten it, then we input MLP with the fattened rectly. VAR measures the quality of the prediction information. With the power of nonlinear modeling, result with calculating the correlation coefcient. MLP can model the spatio-temporal features to some Te closer the value of VAR is to 1, the better. extent. (2) LSTM [29], which is a variant of RNN. It achieves efcient modeling of sequence data with gating 5.4. RQ1: Experiment Results. Table 2 shows the perfor- mechanism. It can only capture temporal features for mance of diferent models on the prediction of trafc fow of trafc prediction. 5 minutes, 10 minutes and 15 minutes using the last (3) GRU [30], which is also a variant of RNN and is good 60 minutes trafc fow information, where “ours w/o gate” at modeling sequence data as well. Compared to means that spatial and temporal features are directly added LSTM, it has simpler structure. See section for more in the feature fusion step without using the gating mecha- details. It can only capture temporal features for nism in our model. From the results, we have the following trafc prediction. observations. (4) GCN [38], which can aggregate neighbor in- formation via convolution operations on graph. See 5.4.1. Observations on Our Method. Our model consistently Section for more details. It can only capture the works the best compared to all the baselines, which illus- spatial features for trafc prediction. trates the superiority of our method for lane-level trafc (5) T-GCN [10], which captures spatial features with prediction. (1) Our model performs better than LSTM and GCN and captures temporal features with GRU. GRU. Te main reason is that LSTM and GRU can only Compared to our method, T-GCN constructs a static model the temporal features while they are incapable of adjacent matrix and inputs the learned spatial fea- capturing spatial features. Te results validate the impor- tures for spatio-temporal features modeling. It can tance of spatial feature modeling in trafc prediction tasks. model the spatio-temporal features for trafc (2) Our model obtains better results than GCN. Similarly to prediction. the reason that our model is better than GRU and GCN, GCN models the spatial features only while it ignores the fact 5.3. Implementation and Metrics. We implement our that the trafc data have a signifcant sequence structure. method with Pytorch and optimize it using the Adam op- Tis means that GCN lacks the ability to model temporal timizer. Te history sequence length for prediction is 12 features. Te results verify the importance of temporal which means we use the last 60 minutes’ trafc data for feature modeling. (3) Our model outperforms T-GCN. One trafc prediction. Te batch size is set to 32. Te GCN layer is possible reason is that T-GCN is designed for road-level set to 1. We perform searches for learning rate in [1e − trafc prediction. When faced with complex application 2, 1e − 3, 1e − 4, 1e − 5], and choose the learning to be 1e − 4 scenarios such as lane-level trafc prediction, it is difcult for fnally. In the experiments, the data in all lanes are divided T-GCN to adopt to such changes, which also verifes the into two parts, the frst 80% of the data is used for training rationality of our model’s change for lane-level trafc pre- and the rest 20% for testing. diction. Besides, the dataset only contains 53 lanes’ trafc To compare the performance of our method and other information, which means the constructed graph only has 53 baselines, we evaluated the prediction results with three nodes. T-GCN performs poorly on such a graph while our widely used metrics. model performs well, which further verifes the adaptability of our model to special scenarios. (4) Our model also (i) Mean absolute error (MAE): outperforms MLP. Te major reason is that though MLP can 􏼌 􏼌 model spatio-temporal features to some extent, while it 􏼌 􏼌 􏼌 􏼌 MAE � 􏽘 y 􏽢 − y , 􏼌 􏼌 (10) i i mines the spatio-temporal features roughly and our model i�1 can capture rich and efective spatio-temporal features for 8 Journal of Advanced Transportation Table 2: Te performance of our model and other baselines on trafc fow prediction. Bold scores are the best and underlined scores are the second best. T 5 min 10 min 15 min Model MAE RMSE VAR MAE RMSE VAR MAE RMSE VAR MLP 3.4547 4.3616 0.5305 3.4033 4.4673 0.4902 3.7487 4.7843 0.4248 LSTM 3.2121 4.1408 0.5687 3.3041 4.2225 0.5526 3.3171 4.2376 0.5494 GRU 3.1250 4.1229 0.5659 3.3186 4.2368 0.5527 3.3297 4.2511 0.5479 GCN 4.8086 5.9925 0.0836 4.8028 5.9863 0.0855 4.8052 5.9799 0.0876 T-GCN 4.4467 5.4664 0.2541 4.5756 5.6031 0.2186 4.5271 5.6392 0.1879 Ours w/o gate 2.8311 3.7730 0.6380 2.9249 3.8593 0.6221 3.0161 3.9491 0.6049 Ours 2.8274 3.7697 0.6385 2.9168 3.8522 0.6234 2.9951 3.9268 0.6093 trafc prediction. (5) Our method without the gating 5.5.1. Sensitivity of Input Sequence Length p. As the input mechanism performs worse than the full method. Te results sequence length p depicts the amount of history trafc validate the efectiveness of using the gating mechanism for information used in trafc prediction, which will be con- feature fusion. However, we fnd that the gating mechanism structed as the initial input features of the model. It is brings about a slight improvement. One possible reason is necessary to control the amount of history trafc in- that due to the special characteristic of the dataset, spatial formation for trafc prediction tasks. Specifcally, we run our features are the main component in the fnal spatio-temporal model with the input sequence length p from 12 to 72. Te features. Diferent feature fusion methods have little efect results of the experiment are shown in Figure 5. Te per- on the composition of spatio-temporal features. (6) Our formance of our method decreases when the input sequence model consistently achieves the best performance when the length p increases from 12 to 36, then it increases conversely prediction horizon ranges from 5 minutes to 10 15 minutes. when p keeps growing. Overall, the performance remains Te results indicate that robustness of our method. In ad- relatively stable. From the results we can fnd that further dition to the short-termlane-level trafc prediction, it may considering longer sequences as input does not bring ad- also be used for long-termlane-level trafc prediction tasks. ditional beneft, even a drop has occurred. Tere exist two possible reasons. (1) Longer sequences may introduce more noise and will limit the predictive power of the model. (2) 5.4.2. Other Observations. (1) Te performance of LSTM What we mainly do is short-term trafc prediction and and GRU on all prediction horizons has little diference, short-term trafc state fuctuates more than long-term trafc although GRU has a simpler structure than LSTM. With state. Shorter input sequences may better help to extract limited resources, it is more reasonable to choose GRU dynamic changes in the data. Such results illustrate that the instead of LSTM to capture spatial features. (2) GRU obtains input sequence length for trafc prediction must be chosen better results than GCN. Te main reason is that, limited by properly. Terefore, the input sequence is supposed to the number of lanes in the dataset, the ability of GCN to contain sufcient trafc information when the input se- mine spatial features is restricted, and the spatial features quence length is set to 12. captured by GCN are roughly. Also, Trafc data is presented in the form of a sequence, which is naturally more suitable for temporal feature mining. (3) T-GCN outperforms GCN. 5.5.2. Sensitivity of α. Te data-driven adjacent matrix A is Te reason is that the T-GCN can capture not only the composed of distance-based adjacent matrix A and dy- spatial features but also the temporal features, while GCN namic correlation matrix A . We use parameter α to control can only capture the spatial features. Te results further how much A contributes to A. It is also necessary to fnd out verify that both the spatial features and temporal features the relationship between the performance of our method play an important role in trafc prediction tasks. (4) GRU and the parameter α. Te input sequence length is set to 12. performs better than T-GCN, though it mines temporal As shown in Figure 6, our method performs best when α � only. One possible reason is that the mechanism for T-GCN 0.1. As α increases from 0 to 0.1, the performance improves. to obtain spatio-temporal features is not perfect. When Te main reason is that when α is too small, A has little T-GCN is used for lane-level trafc prediction, the extracted efect on A. With increasing α the infuence of A is gradually spatial features are coarse and inhibit the ability of T-GCN released to compensate for the static defect caused by the instead. distance-based adjacent matrix, and the performance of the model becomes better. Te results verify the necessity and 5.5. RQ2: Parameter Sensitivity Analysis. In this part, we validity of modeling a data-driven adjacent matrix. When α conduct sensitivity analysis of two important hyper- is larger than 0.1, the performance starts to drop. Te parameters in our model. Te two hyperparameters are the possible reason is that larger α makes the model focus more input sequence length p and the parameter α that controls on the dynamic part of the adjacent matrix and starts to the degree to which the dynamic correction matrix A undermine the fundamental role of the static distance-based contributes to the data-driven adjacent matrix A. adjacent matrix. Finally, we set α to be 0.1. Journal of Advanced Transportation 9 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 12 24 36 48 60 sequence length VAR MAE RMSE Figure 5: Te performance of our model as the input sequence length changes. 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.01 0.05 0.1 0.2 0.3 alpha VAR MAE RMSE Figure 6: Te performance of our model as hyperparameter α changes. 5.6. RQ3: Model Interpretation. In this part, we aim to an- a positive role in the prediction of the model. Te reason is swer RQ3 by visualizing the adjacent matrix and model that the trafc information at diferent times changes dy- prediction results. namically, and it is difcult for the static distance-based adjacent matrix to respond to such dynamic changes in a timely and efective manner. With the help of the dynamic 5.6.1. Visualization of Adjacent Matrix. To fgure out how correlation matrix, the data-driven adjacent matrix has the data-driven adjacent matrix afects the prediction results acquired the ability to model dynamically changing trafc of the model, we visualize the distance-based adjacent matrix information. Further, the performance of the model can A and lane correlation matrix A in the morning, after- d c been improved. noon, and evening of a random day, respectively. As shown in Figure 7, the distance-based adjacent matrix and the correlation matrix show diferent relationship patterns be- 5.6.2. Visualization of Prediction Result. To better un- tween lanes in diferent situations. More specifcally, A is derstand our proposed method, we randomly selected 4 static and A presents diferent data distributions at diferent lanes in diferent sections of the road and visualize the times. It can be seen from the answer of RQ3 that the ground truth of the test set and the prediction result. As construction of the dynamic correlation matrix plays shown in Figure 8, the results show the following: 10 Journal of Advanced Transportation 1.0 0.9 0.8 0.7 0.6 (a) (b) 1.0 1.0 0.9 0.8 0.8 0.6 0.7 0.6 0.4 0.5 (c) (d) Figure 7: Visualization of distance-based adjacent matrix A and dynamic correlation matrix A . (a) Visualizes the distance-based adjacent d c matrix. (b) Depicts the correlation matrix of trafc fow collected from 8 am to 9 am. (c) Te correlation matrix of trafc fow collected from 6 pm to 7 pm. (d) Te correlation matrix of trafc fow collected from 10 pm to 11 pm. (a–c) represent the similarity relationship of trafc fow in diferent lanes in the morning, afternoon, and evening of a random day respectively. (1) Similar patterns exist between the ground truths of use of the correlation matrix enables GCN to ag- diferent lanes. Te geographic distance between gregate more information from more neighbors, some lanes may be too large, in which case the which further leads to a smoother prediction result of distance-based adjacent matrix ignores the similar the model. (c) When the ground truth is small, the pattern. As a result, the lanes that are too far apart same gap can cause a larger relative error. cannot cooperate with each other to improve the (3) Our model can capture the trafc trend at the lane fnal prediction quality. Our proposed data-driven level. Tis property can help formulate efective and adjacent matrix efectively alleviates this problem on detailed trafc control strategies in real time and the basis of distance-based adjacent matrix. realize scientifc trafc management planning. (2) Tere is a certain error between the prediction results Besides, Figure 9 displays the ground truth and pre- of the model and the ground truth. Te reasons are diction results for a randomly chosen weekend and a ran- threefold: (a) GCN defnes a smooth flter and models domly chosen weekday. As depicted in Figure 9, our model the spatial features with the flter on the spatial do- can capture trends of trafc fow throughout the day. main. Tis process of aggregating neighbor in- Whether it is weekdays or weekends, peak or low-peak formation results in smooth predictions. (b) Tough times, trafc fow trends are well modeled, allowing for the construction of data-driven adjacent matrix can our model to realize stable and reliable prediction. help to improve model’s performance. However, the Journal of Advanced Transportation 11 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred Figure 8: Visualization of ground truth and prediction results of 4 randomly selected lanes on the test set. Te blue line represents the ground truth and the red line represents the prediction results. Te horizontal axis represents the trafc fow, and the vertical axis represents the time the trafc fow recorded or predicted. Traffic f low Traffic f low Traffic f low Traffic f low 12 Journal of Advanced Transportation 25 25 20 20 15 15 10 10 5 5 0 0 0:00 4:00 8:00 12:00 16:00 20:00 24:00 0:00 4:00 8:00 12:00 16:00 20:00 24:00 (a) (b) 25 25 20 20 15 15 10 10 5 5 0 0 0:00 4:00 8:00 12:00 16:00 20:00 24:00 0:00 4:00 8:00 12:00 16:00 20:00 24:00 (c) (d) Figure 9: Visualization of ground truth and prediction results of all lanes on the test set. (a) Ground truth on a weekend. (b) Prediction results on the same weekend as (a). (c) Ground truth on a weekday. (d) Prediction results on the same weekday as (c). more than two lanes. Besides, we consider to combine with 6. Conclusion some advanced techniques such as attention network to In this paper, we propose a lane-level trafc prediction achieve more accurate and reliable lane-level trafc model for lane-level trafc prediction tasks. Specifcally, we prediction. capture spatial features with GCN. To adapt to the lane-level trafc prediction, we treat diferent lanes of the same road Data Availability segment as diferent nodes on the graph. Furthermore, considering that most existing graph-based methods build Te data used during the study are available from the static adjacent matrix, we construct a data-driven adjacent corresponding author upon request. matrix, which consists of a static distance-based adjacent matrix and a dynamic lane correlation matrix. Additionally, Conflicts of Interest we utilize GRU to capture temporal features. Ten we adaptively fuse spatial features and temporal features Te authors declare that they have no conficts of interest. through the gating mechanism to obtain spatio-temporal features for multi-steplane-level trafc prediction. Experi- Acknowledgments ment on a real-world dataset verifed the efectiveness of our model for lane-level trafc prediction. Tis research was supported by the National Natural Science In the future, we plan to consider more auxiliary fea- Foundation of China under Grant no. 62202131, the Natural tures, such as utilizing speed information in trafc fow Science Foundation of Zhejiang Province under no. prediction. Te current model can also be improved by LQ20F020015, and the Key Science and Technology Project considering more detailed and realistic lane relationships for of Zhejiang Province under no. 2020C01165. Lanes Lanes Lanes Lanes Journal of Advanced Transportation 13 [16] C. F. Daganzo, “A behavioral theory of multi-lane trafc fow. 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A Dynamic Spatio-Temporal Deep Learning Model for Lane-Level Traffic Prediction

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10.1155/2023/3208535
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Hindawi Journal of Advanced Transportation Volume 2023, Article ID 3208535, 14 pages https://doi.org/10.1155/2023/3208535 Research Article A Dynamic Spatio-Temporal Deep Learning Model for Lane-Level Traffic Prediction 1 1 2 2 2 Bao Li , Quan Yang , Jianjiang Chen , Dongjin Yu , Dongjing Wang , and Feng Wan Zhejiang Testing & Inspection Institute for Mechanical and Electrical Products Quality Co.,Ltd., Hangzhou 310018, China School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China Correspondence should be addressed to Dongjing Wang; dongjing.wang@hdu.edu.cn Received 9 November 2022; Revised 1 February 2023; Accepted 24 February 2023; Published 8 March 2023 Academic Editor: Jing Zhao Copyright © 2023 Bao Li et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Trafc prediction aims to predict the future trafc state by mining features from history trafc information, and it is a crucial component for the intelligent transportation system. However, most existing trafc prediction methods focus on road segment prediction while ignore the fne-grainedlane-level trafc prediction. From observations, we found that diferent lanes on the same road segment have similar but not identical patterns of variation. Lane-level trafc prediction can provide more accurate prediction results for humans or autonomous driving systems to make appropriate and efcient decisions. In trafc prediction, the mining of spatial features is an important step and graph-based methods are efective methods. While most existing graph-based methods construct a static adjacent matrix, these methods are difcult to respond to spatio-temporal changes in time. In this paper, we propose a deep learning model for lane-level trafc prediction. Specifcally, we take advantage of the graph con- volutional network (GCN) with a data-driven adjacent matrix for spatial feature modeling and treat diferent lanes of the same road segment as diferent nodes. Te data-driven adjacent matrix consists of the fundamental distance-based adjacent matrix and the dynamic lane correlation matrix. Te temporal features are extracted with the gated recurrent unit (GRU). Ten, we adaptively fuse spatial and temporal features with the gating mechanism to get the fnal spatio-temporal features for lane-level trafc prediction. Extensive experiments on a real-world dataset validate the efectiveness of our model. machine learning methods such as K-nearest neighbor (KNN) 1. Introduction [8] and support vector regression (SVR) [9] are also used for Intelligent transportation systems (ITS) include driving trafc prediction. But they have higher requirements for fea- behaviour understanding [1], path fnding [2], map tures, which often requires complex feature processing. In matching [3], and trafc prediction [4]. Trafc prediction recent years, deep learning methods have become the main- refers to predict the future state of trafc by analyzing and stream method of trafc prediction due to automatic feature mining trafc information in the mining history [5]. As the modeling and efective data mining capabilities. For example, foundation and important part of ITS, accurate trafc recurrent neural network (RNN)-based methods [10] can ef- prediction can help formulate real-time control strategies, fectively model the temporal features in trafc fows. Con- which is of great importance for scientifc planning of trafc volutional neural network (CNN)-based methods [11] regard management and people’s safe and efcient travel [6]. trafc fows as image and model spatial features or temporal Early eforts in this feld use statistical learning methods for features in European space. Te road network or road sensor trafc prediction, such as diferential average moving autore- network is naturally a graph and has a typically non-Euclidean gression [7], which converts unstable sequences into stationary structure. Recently, researchers have used graph-based sequences by diference for prediction. Trafc state information methods for trafc prediction [12]. CNNs and RNNs can has signifcant nonlinear and uncertain characteristics, and only be used on Euclidean data, while graph-based methods 2 Journal of Advanced Transportation can efectively model the non-Euclidean structure of graphs for more accurate predictions. With a graph as input, graph-based methods have achieved superior performance in trafc pre- diction. Te topology of the graph is represented by an adjacent 1-19 1-20 1-21 1-22 1-23 1-24 1-25 matrix, and graph-based methods are directly afected by the Road section 1, lane 1 adjacent matrix. Time Although related work in the past has proposed many efective algorithms in the feld of trafc prediction, there are still some limitations and challenges. (1) Previous studies ignore the diferences between diferent lanes and mainly focus on road segment prediction. In reality, there is a wide demand for 1-19 1-20 1-21 1-22 1-23 1-24 1-25 lane-level trafc prediction. For example, automated vehicles or Road section 1, lane 2 human-driven vehicles can select appropriate lanes according Time to the prediction results at the lane level. Trafc congestion can thus be avoided or alleviated [13, 14]. Besides, lane-level trafc prediction can provide more refned and accurate trafc in- formation and help humans or machines make more appro- 1-19 1-20 1-21 1-22 1-23 1-24 1-25 priate and efective decisions. Tere are diferent and related Road section 2, lane 1 patterns of trafc states in diferent lanes [15– 17]. As shown in Time Figure 1, there are two lanes in both road section 1 and road section 2, and the trafc information between diferent lanes in the same road section has a similar change pattern, while there still exist some diferences in the change pattern in many details. In the road segment-level trafc prediction, the road 1-19 1-20 1-21 1-22 1-23 1-24 1-25 segment is regarded as a whole, and the prediction results are Road section 2, lane 2 too macroscopic to provide precise information for lane-level Time decisions. (2) Graph-based methods rely heavily on adjacent Figure 1: An example of lane-level trafc fow, where the hori- matrices, while most methods build static adjacent matrices, zontal axis represents the trafc fow, and the vertical axis rep- ignoring that the correlation between diferent nodes on the resents the time the trafc fow recorded. graph may be diferent in diferent situations. For example, there may be similar change patterns for two nodes that are far apart. Besides, the trafc situation of nodes may change in GCN, learns temporal features with GRU, and ob- diferent time periods. It is difcult for the static adjacent tains fused adaptive spatio-temporal features with matrix to respond timely and efectively to spatio-temporal the gating mechanism. changes. (3) Extensive experiments on a real-world dataset vali- To address the aforementioned challenges, we propose date the efectiveness of the model. a deep learning model for lane-level trafc prediction, which Te remainder of this paper is organized as follows: In is mainly composed of data-driven GCN and GRU. GCN is Section 2, we introduced the related work, which includes used to extract spatial features. To adapt GCN for lane-level general methods and deep learning methods. Section 3 trafc prediction, we treat diferent lanes at the same lo- formulates the lane-level trafc prediction task. Section 4 cation as diferent nodes on the graph. Te adjacent matrix introduces the construction of the data-driven adjacent of the graph is calculated in a data-driven manner and matrix and the architecture of our model in detail. Te consists of a traditional distance adjacent matrix and a dy- comprehensive experiment result on a read-world dataset is namic lane correlation matrix. GRU is used to extract demonstrated in Section 5. Finally, we conclude the paper temporal features. Ten, spatio-temporal features are ob- and present future work in Section 6. tained by fusing temporal and spatial features adaptively through the gating mechanism. Finally, lane-level trafc prediction is performed based on the learned spatio- 2. Related Work temporal features. Te main contribution of this paper can be summarized 2.1. General Methods. Traditional trafc prediction methods as follows: can be divided into parametric methods and nonparametric methods [10]. Parametric methods rely on the assumption of (1) A data-driven adjacent matrix is proposed, which data stationarity and provide explicit formulations for consists of a distance-based adjacent matrix and valuable interpretations of trafc characteristics. Classical a dynamic lane correlation matrix. It can respond parametric methods, such as the autoregressive integrated efectively to spatio-temporal changes in a timely moving average model (ARIMA) and its variants [7, 18, 19], manner. have been proven to be efective in many scenarios. For (2) We propose a deep learning model for lane-level example, some studies have found that ARIMA can model trafc prediction, which learns spatial features with highway time series data with high precision [20]. Some Traffic f low Traffic f low Traffic f low Traffic f low Journal of Advanced Transportation 3 ideal for solving trafc prediction problems. Li et al. [39] other parametric methods include exponential [21], multi- variate time series models [22], and Kalman fltering models treated the trafc fow as a difusion process and proposed DCRNN, which uses bidirectional random walks on the [23]. However, the dependency on stationarity makes parametric methods difcult to efectively model the un- graph and GRU to capture spatial and temporal features, certainty and irregular volatility of trafc data. Te structure respectively. Zhao et al. [10] proposed T-GCN, which stacks and parameters of the nonparametric methods are not fxed, GCN and GRU for trafc prediction. Yu et al. [40] proposed and the data requirements are not as strict as those of the STGCN to extract spatio-temporal features with complete parameterized methods. Te nonparametric methods are convolutional structures. Guo et al. [41] established a HGCN more able to deal with complex data such as noisy data and model which operates the convolution operation on both missing data [24]. Typical nonparametric methods include micro- and macrotrafc graphs. Zhu et al. [42] employed support vector regression [8], K-nearest neighbor [9], the GCN in multigraph to analyze correlations from multiple perspectives. Guo et al. [43] proposed a dynamic GCN for Bayesian network [25], the extreme gradient boost [26], and artifcial neural networks (ANN) [24, 27, 28]. Among them, trafc prediction on the basis of Laplace matrix estimation. Cao et al. [44] combined self-attention with GCN for trafc ANN can mine the latent information of trafc data and has nonlinear modeling ability, which is one of the most widely fow prediction. Although there is a lot of excellent work for used nonparametric methods. Although nonparametric trafc prediction, most of them are not suitable for lane-level methods have some achievements in the feld of trafc trafc prediction. Besides, most existing works treat the road prediction, these methods are limited in their ability to or sensor network as a static graph. We propose a deep predict lane-level trafc. Besides, both parametric and learning model for lane-level trafc prediction with a dy- nonparametric methods are mainly used to model the namic adjacent matrix driven by data. As for lane-level works, Gu et al. [20] combined LSTM and GRU for lane- temporal features and are weak in modeling the spatial features. level trafc speed prediction. Ke et al. [36] introduced a two- stream multichannel CNN model. Ma et al. [45] proposed a convolutional LSTM network for multilane short-term 2.2. Deep Learning Methods. With the rapid development of trafc forecasting. Lu et al. [46] described a mix deep high-performance data storage and processing technologies, learning model for lane-level trafc speed forecasting. Wang trafc prediction is moving from nonparametric methods to et al. [47] presented a heterogeneous graph convolution deep learning methods [10]. An important step in trafc model for lane-level trafc fow prediction. Existing lane- prediction is to extract spatio-temporal features from trafc level trafc prediction methods mostly use RNN or CNN to data. For the recurrent neural network (RNN) and its model spatial features, which has certain limitations. variants like long short-term memory (LSTM) [29] and gated recurrent unit (GRU) [30] which can efectively utilize 3. Problem Formulation temporal data, RNN-based methods [31] play an important role in mining temporal trafc features. Ma et al. [32] frst In this work, we aim to predict the trafc state of lanes in applied LSTM to solve the prediction of highway trafc a period of time on the basis of the historical trafc state speed and fow. Zhao et al. [10] utilized GRU, which has information recorded on the road sensors. Trafc state is fewer neurons than LSTM, for trafc prediction. Gu et al. a general concept that includes trafc speed, trafc fow, and [20] built a fusion system to capture temporal features. other numerical information related to the road. Specially, RNN-based methods [33, 34] have shown promising results we predict lane-level trafc fow in the experiment section. in trafc prediction feld, while they are not good at mining Defnition: Lane Network G. To describe the non- spatial features in trafc fow. In terms of spatial trafc Euclidean structure of the lane network, we defne it as features, trafc fows in nearby locations are often strongly graph G � (V, E, A). On graph G, V � v , v , . . . , v is the 􏼈 􏼉 1 2 N correlated [35]. For the power of handling image data, CNN set of nodes, where v represents the i-th lane and N is the has been used in trafc prediction by treating the trafc fow number of lanes. Note that we treat diferent lanes on the data as an image. Ke et al. [36] constructed a multichannel same road section as diferent nodes. E is the set of edges. CNN model for multilane trafc speed prediction. Liu et al. Te edge between lane i and lane j only exists if their [37] developed an attention-based CNN structure for trafc distance is less than a certain threshold and there exists speed prediction with the use of trafc fow, speed, and a trafc fow from v to v . To better represent the real i j occupancy. However, CNN and RNN can only be applied to situation, we consider the trafc fow between diferent lanes Euclidean data; they cannot model the topological structure in the same section of the road to be interconnected. of the road network or the road sensor network. Neither N×N A ∈ R is the adjacent matrix. CNN-based methods nor RNN-based methods are perfect 1 2 N N Let X � 􏼈x , x , . . . , x 􏼉 ∈ R represent the trafc fow t t t for spatio-temporal feature extraction. of N lanes on each time stamp t. Suppose the trafc fow data Te road network or the road sensor network is naturally is the graph signal of G, given time t and lane network G, the a graph. Recently, researchers have applied graph neural lane-level trafc fow prediction problem in our work can be networks (GNN), especially graph convolutional networks defned as (GCN) [38], for trafc prediction, and they have superior 􏼂X , . . . , X 􏼃 � f􏼐􏼐X , . . . , X 􏼑, G􏼑, (1) performance compared to previous approaches. For the t+1 t+T t−p+1 t ability to model non-Euclidean graph structures, GNNs are 4 Journal of Advanced Transportation Table 1: Summary of notations. where f represents the learned mapping function, p is the input sequence length, and T is the predicted sequence Symbol Description length. G Lane network Te key symbols used in this paper are summarized in V, E Node set and edge set of in G Table 1. X Trafc information of all lanes at timestamp t x Trafc information of lane i at timestamp t A Data-driven adjacent matrix 4. The Proposed Approach A Distance-based adjacent matrix In view of the lack of work on lane-level trafc prediction, A Trafc information similarity matrix this paper proposes a lane-level trafc prediction model. Te p, T Sequence length for input and predict α A constant that controls the contribution of A architecture of our model is illustrated in Figure 2. Spe- c D Degree matrix cifcally, we frst establish a data-driven adjacent matrix that u, r Update gate and reset gate in GRU can respond to spatio-temporal changes based on the c, h Cell state and hidden state in GRU geographic location and historical trafc information of the W Learnable parameter matrices sensor. Te data-driven adjacent matrix is fed into the graph g Feature fusion gate convolutional network (GCN) to capture spatial features, H Learned spatial features and we model the temporal features with a gated recurrent t H Learned temporal features unit (GRU) model. Ten, we adaptively fuse the spatial and H Fused spatio-temporal features temporal features with the gating mechanism to get com- prehensive spatio-temporal features. Finally, we make multistep lane-level trafc predictions based on the spatio- temporal features. further introduce the dynamic correlation matrix N×N A ∈ R . A is flled with the Pearson correlation co- c c efcient calculated from the observed input data of the lanes. 4.1. Data-Driven Adjacent Matrix. Te graph depicts the ∗ To be specifc, A at time t is calculated with topological relationship structure between nodes through t�t i i j j x − x x − x the adjacent matrix, and the construction of the adjacent 􏽐 ∗ 􏼐 􏼑􏼐 􏼑 t�t −h+1 t t 􏽱�������������������������������� A � , (3) ij matrix directly afects the expressive power of the graph [48]. ∗ 2 ∗ 2 t�t i i t�t j j 􏽐 ∗ 􏼐x − x 􏼑 􏽐 ∗ 􏼐x − x 􏼑 t�t −h+1 t t�t −h+1 t However, most GCN-based trafc prediction works only construct a static adjacent matrix with fxed weights, without where i and j are the index of lane v and lane v , x is the i j t considering that the relationship of diferent nodes may i j value of trafc fow on v observed at time t, x and x are change in various situations. In particular, it is difcult for means of v and v , respectively. Te absolute value of A is i j ij a static adjacent matrix to respond to spatio-temporal closer to 1, the higher the correlation between v and v . i j changes in a timely manner, which makes the model Combining the basic distance-based adjacent matrix A hardly achieve accurate prediction. In our work, we propose and the dynamic correlation matrix A , we propose the data- a data-driven dynamic adjacent matrix, which is composed driven adjacent matrix A, of the basic distance-based adjacent matrix A and the dynamic node correlation matrix A . A � A + αA , (4) d c Te graphs include directed graph and undirected graph. where α is a constant that controls how much A contributes For undirected graphs such as social networks, the adjacent 􏽢 􏽢 to A. On the one hand, A provides geographic relationships matrix is symmetric. In the road sensor network, the trafc that are fundamental and important for spatial feature ex- fows on roads have directions due to the restriction of trafc traction; on the other hand, A can implement timely ad- rules. Graph G is a directed graph, and the adjacent matrix is justments to the adjacent matrix with reference to changes of asymmetric. historical information. For the basic distance-based adjacent matrix A , as most works did [49], we calculate one element A in A with ij d 4.2. Spatial Feature Modeling. Spatial features play an im- ⎧ ⎪ −d ⎪ ij ⎪ ⎛ ⎝ ⎞ ⎠ ⎪ exp , if d ≤ ε, portant role in trafc prediction for trafc fow sequences at ij ⎪ 2 diferent locations with connection to some extent. Before A � (2) ij ⎪ the employment of graph-based methods, research studies usually extract the spatial features with multivariate time 0, if d > ε, ij series models or CNNs [50]. However, limited by the where A represents the infuence degree of lane v on lane structure, multivariate time series models mostly cannot ij i v , d is the distance between v and v , and σ is the standard model the nonlinear relationships between diferent se- j ij i j deviation of d. Te distance between diferent lanes on the quences. Although CNN-based methods can alleviate the same road segment is 0. A has a positive value only if d is situation, the architecture of CNN is bounded to Euclidean ij ij smaller than threshold ε and from v to v exists a trafc fow. space, which is not enough for lane network’s topological i j To compensate for the defects caused by the static structure modeling. Recently, graph-based methods have characteristics of the distance-based adjacent matrix, we attracted wide attention for their ability in modeling non- … Journal of Advanced Transportation 5 Data A A X A + αA c d d c Collection Sensor Trafc Correlation Distance-based Sensor lane1 lane2 lane3 lane4 information matrix adjacent matrix geolocation X X [t–h+1:t] [t–h+1:t] Prediction 1 result X t+1 1 2 Spatial GCN Sensor feature 4 4 Linear 2 2 3 5 transformation lane1 lane2 5 5 Linear Temporal transformation feature … 2 GRU GRU Prediction result X Sensor t+T t–h+1 lane1 lane2 lane3 lane4 Figure 2: Te architecture of our proposed model. to extract the temporal features of the trafc data. Tere are Euclidean structure. Specifcally, we extract the spatial features with GCN. Te GCN model built a flter in the two gates in GRU, which are spatial domain, and the spatial features between diferent u � σ W X + W h + b , t ux t uh t−1 u nodes on a graph are extracted with the usage of flter. As (6) illustrated in Figure 3, the central node models the topo- r � σ W X + W h + b 􏼁, t rx t rh t−1 r logical relationship by aggregating the information of its where u represents the update gate and controls how much neighboring nodes in GCN. Te topological structure of the t history information the current moment has, r represents graph is encoded to acquire spatial features. the reset gate and controls how much history information After the construction of the data-driven adjacent matrix 􏽢 needs to be forgotten. x is the trafc information at time t, A, the GCN model extracts spatial features with and h is the hidden state at time t − 1. t−1 −1/2 −1/2 W , W , W , W , b , b are learnable parameters. With (l) (l−1) (l− 1) ux uh rx rh u r 􏽢 􏽢 H � σ􏼒D AD H W 􏼓, (5) s s the gating signals of u and r , the cell state c and output t t t hidden state h can be calculated with (l) where H represents the feature matrix in l-th layer, D is the − 1/2 − 1/2 􏽢 􏽢 􏽢 􏽢 􏽢 c � tanh W X + W r ⊙ h 􏼁 􏼁, degree matrix and D � Σ A . D AD denotes nor- t cx t ch t t−1 ii j ij (7) malize the adjacent matrix A, which can help to keep the h � 1 − u ⊙ h + u ⊙ c , t t t−1 t t distribution of the feature matrix during the information transfer process. W is the learned weight matrix in l-th layer where c can be regarded as the history information stored at (0) and σ represents the activation function. Note that H � X time t, and ⊙ represents element-wise multiplication. and X is the input trafc information matrix. As shown in Figure 4, GRU models the hidden state in time t by taking the current trafc information and the last hidden state h . With this operating mechanism, GRU is t−1 4.3. Temporal Feature Modeling. Trafc data have signifcant capable of retaining the historical information while uti- sequence structure, which means that temporal features are lizing current trafc information, and then it is able to model the key to trafc prediction. Te recurrent neural network temporal features. (RNN) is widely used in the processing of sequence data. However, RNN has the problem of gradient disappearance or gradient explosion with the sequence length growing. To 4.4. Our Model. With GCN and GRU, we obtain spatial and solve this problem, researchers proposed many variants of temporal features, respectively. Our next target aims to fuse RNN such as LSTM and GRU. Tese variants have been the spatial and temporal features into comprehensive spatio- proved to be efective in sequence data modeling. Both temporal features. A convenient operation is to add these LSTM and GRU control the dissemination and update of two kinds of feature directly, which may weaken the information with the gating mechanism. Compared with characteristics of the spatial and temporal features them- LSTM, GRU has smaller training time, fewer parameters, selves. Inspired by the gating mechanism, we introduce and relatively simpler structure. Terefore, we employ GRU a learnable gate g to fuse features. Similarly, to the role of Fusion Gate 6 Journal of Advanced Transportation 4 4 2 2 (a) (b) Figure 3: Spatial feature modeling. h h × + t-1 t h h h 1- t–w+1 t–1 t h h t–w+1 t–1 GRU … GRU GRU × tanh x x x t–w+1 t–1 t Figure 4: Temporal feature modeling. gates in GRU, g controls the degree to which spatial and dynamic changes to get the spatial features with GRU model. temporal features contribute to the fnal spatio-temporal Finally, we fuse these features to make multi-step trafc features. predictions. g � σ􏼐W H + W H + b 􏼑, s s t t g 5. Experiment (8) H � g ⊙ H +(1 − g) ⊙ H , s t In this section, we conduct extensive experiment on a real- world dataset to evaluate the proposed method and several where H represents the extracted spatial features. Suppose baselines answering the following questions: the layer of GCN is L, then H equals to the output feature (L) matrix H in L-th layer. H represents the extracted s t (i) RQ1: How does our method perform compared to temporal features. We stack all units’ output hidden state to baselines in lane-level trafc prediction, and do get the fnal temporal features. W , W , and b are learnable s t g diferent components of our method show real parameters. improvement? Let Y and Y denote the real trafc state and the pre- t t (ii) RQ2: How do various hyperparameters afect the dicted trafc state at time t, respectively. In the training performance of our method? process, the target is to minimize the error between Y and 􏽢 (iii) RQ3: Does our method really work in real Y , and the loss function is defned as situations? � � � � � 􏽢 � loss � Y − Y + λ‖W‖, (9) � � t t where the second term is an L2-regularization term that 5.1. Dataset. We perform experiments on a real-world helps avoid the overftting problem, λ is the regularization dataset. Te dataset is collected from Sutai Expressway parameter, and W represents the weighted parameters. captured by the remote microwaves trafc sensors in Zhe- In summary, we propose a lane-level trafc prediction jiang, China. Afected by the distance between sensors, we model. On the one hand, our model uses GCN to model the selected 30 sensors’ trafc data for experiment. Te fre- topological structure of the lane network to extract spatial quency of trafc information collection for each sensors is features. On the other hand, we mine trafc information’s once every 5 minutes. Te collected data mainly includes Journal of Advanced Transportation 7 lane-level trafc speed and trafc fow. All trafc in- (ii) Root mean squared error (RMSE): 􏽶������������ formation is the average value that passes through the sensor over a sampling time interval. Since some sensors have RMSE � 􏽘 y 􏽢 − y􏼁 , (11) serious data missing in some lanes, the number of valid lanes i i i�1 in 30 sensors is 53. Te record number for each lane is 16,032 and the entire dataset includes 849,696 records in total. To make the prediction result more reliable, we flled in the (iii) Explained variance score (VAR): missing data with the data from the previous moment. Var􏼈y − y 􏽢􏼉 VAR � 1 − , (12) Var(y) 5.2. Baselines. To validate the efectiveness of our model for lane-level trafc prediction, we compare the proposed model where y 􏽢 is the predicted value and y is the real i i with several commonly used baselines: value. Var means to calculate the variance. Specif- ically, for MAE and RMSE, the smaller the value, the (1) MLP, which contains three fully connected layers. better the performance, since they measure the error We concatenate all lanes’ trafc information and between the predicted value and the real value di- fatten it, then we input MLP with the fattened rectly. VAR measures the quality of the prediction information. With the power of nonlinear modeling, result with calculating the correlation coefcient. MLP can model the spatio-temporal features to some Te closer the value of VAR is to 1, the better. extent. (2) LSTM [29], which is a variant of RNN. It achieves efcient modeling of sequence data with gating 5.4. RQ1: Experiment Results. Table 2 shows the perfor- mechanism. It can only capture temporal features for mance of diferent models on the prediction of trafc fow of trafc prediction. 5 minutes, 10 minutes and 15 minutes using the last (3) GRU [30], which is also a variant of RNN and is good 60 minutes trafc fow information, where “ours w/o gate” at modeling sequence data as well. Compared to means that spatial and temporal features are directly added LSTM, it has simpler structure. See section for more in the feature fusion step without using the gating mecha- details. It can only capture temporal features for nism in our model. From the results, we have the following trafc prediction. observations. (4) GCN [38], which can aggregate neighbor in- formation via convolution operations on graph. See 5.4.1. Observations on Our Method. Our model consistently Section for more details. It can only capture the works the best compared to all the baselines, which illus- spatial features for trafc prediction. trates the superiority of our method for lane-level trafc (5) T-GCN [10], which captures spatial features with prediction. (1) Our model performs better than LSTM and GCN and captures temporal features with GRU. GRU. Te main reason is that LSTM and GRU can only Compared to our method, T-GCN constructs a static model the temporal features while they are incapable of adjacent matrix and inputs the learned spatial fea- capturing spatial features. Te results validate the impor- tures for spatio-temporal features modeling. It can tance of spatial feature modeling in trafc prediction tasks. model the spatio-temporal features for trafc (2) Our model obtains better results than GCN. Similarly to prediction. the reason that our model is better than GRU and GCN, GCN models the spatial features only while it ignores the fact 5.3. Implementation and Metrics. We implement our that the trafc data have a signifcant sequence structure. method with Pytorch and optimize it using the Adam op- Tis means that GCN lacks the ability to model temporal timizer. Te history sequence length for prediction is 12 features. Te results verify the importance of temporal which means we use the last 60 minutes’ trafc data for feature modeling. (3) Our model outperforms T-GCN. One trafc prediction. Te batch size is set to 32. Te GCN layer is possible reason is that T-GCN is designed for road-level set to 1. We perform searches for learning rate in [1e − trafc prediction. When faced with complex application 2, 1e − 3, 1e − 4, 1e − 5], and choose the learning to be 1e − 4 scenarios such as lane-level trafc prediction, it is difcult for fnally. In the experiments, the data in all lanes are divided T-GCN to adopt to such changes, which also verifes the into two parts, the frst 80% of the data is used for training rationality of our model’s change for lane-level trafc pre- and the rest 20% for testing. diction. Besides, the dataset only contains 53 lanes’ trafc To compare the performance of our method and other information, which means the constructed graph only has 53 baselines, we evaluated the prediction results with three nodes. T-GCN performs poorly on such a graph while our widely used metrics. model performs well, which further verifes the adaptability of our model to special scenarios. (4) Our model also (i) Mean absolute error (MAE): outperforms MLP. Te major reason is that though MLP can 􏼌 􏼌 model spatio-temporal features to some extent, while it 􏼌 􏼌 􏼌 􏼌 MAE � 􏽘 y 􏽢 − y , 􏼌 􏼌 (10) i i mines the spatio-temporal features roughly and our model i�1 can capture rich and efective spatio-temporal features for 8 Journal of Advanced Transportation Table 2: Te performance of our model and other baselines on trafc fow prediction. Bold scores are the best and underlined scores are the second best. T 5 min 10 min 15 min Model MAE RMSE VAR MAE RMSE VAR MAE RMSE VAR MLP 3.4547 4.3616 0.5305 3.4033 4.4673 0.4902 3.7487 4.7843 0.4248 LSTM 3.2121 4.1408 0.5687 3.3041 4.2225 0.5526 3.3171 4.2376 0.5494 GRU 3.1250 4.1229 0.5659 3.3186 4.2368 0.5527 3.3297 4.2511 0.5479 GCN 4.8086 5.9925 0.0836 4.8028 5.9863 0.0855 4.8052 5.9799 0.0876 T-GCN 4.4467 5.4664 0.2541 4.5756 5.6031 0.2186 4.5271 5.6392 0.1879 Ours w/o gate 2.8311 3.7730 0.6380 2.9249 3.8593 0.6221 3.0161 3.9491 0.6049 Ours 2.8274 3.7697 0.6385 2.9168 3.8522 0.6234 2.9951 3.9268 0.6093 trafc prediction. (5) Our method without the gating 5.5.1. Sensitivity of Input Sequence Length p. As the input mechanism performs worse than the full method. Te results sequence length p depicts the amount of history trafc validate the efectiveness of using the gating mechanism for information used in trafc prediction, which will be con- feature fusion. However, we fnd that the gating mechanism structed as the initial input features of the model. It is brings about a slight improvement. One possible reason is necessary to control the amount of history trafc in- that due to the special characteristic of the dataset, spatial formation for trafc prediction tasks. Specifcally, we run our features are the main component in the fnal spatio-temporal model with the input sequence length p from 12 to 72. Te features. Diferent feature fusion methods have little efect results of the experiment are shown in Figure 5. Te per- on the composition of spatio-temporal features. (6) Our formance of our method decreases when the input sequence model consistently achieves the best performance when the length p increases from 12 to 36, then it increases conversely prediction horizon ranges from 5 minutes to 10 15 minutes. when p keeps growing. Overall, the performance remains Te results indicate that robustness of our method. In ad- relatively stable. From the results we can fnd that further dition to the short-termlane-level trafc prediction, it may considering longer sequences as input does not bring ad- also be used for long-termlane-level trafc prediction tasks. ditional beneft, even a drop has occurred. Tere exist two possible reasons. (1) Longer sequences may introduce more noise and will limit the predictive power of the model. (2) 5.4.2. Other Observations. (1) Te performance of LSTM What we mainly do is short-term trafc prediction and and GRU on all prediction horizons has little diference, short-term trafc state fuctuates more than long-term trafc although GRU has a simpler structure than LSTM. With state. Shorter input sequences may better help to extract limited resources, it is more reasonable to choose GRU dynamic changes in the data. Such results illustrate that the instead of LSTM to capture spatial features. (2) GRU obtains input sequence length for trafc prediction must be chosen better results than GCN. Te main reason is that, limited by properly. Terefore, the input sequence is supposed to the number of lanes in the dataset, the ability of GCN to contain sufcient trafc information when the input se- mine spatial features is restricted, and the spatial features quence length is set to 12. captured by GCN are roughly. Also, Trafc data is presented in the form of a sequence, which is naturally more suitable for temporal feature mining. (3) T-GCN outperforms GCN. 5.5.2. Sensitivity of α. Te data-driven adjacent matrix A is Te reason is that the T-GCN can capture not only the composed of distance-based adjacent matrix A and dy- spatial features but also the temporal features, while GCN namic correlation matrix A . We use parameter α to control can only capture the spatial features. Te results further how much A contributes to A. It is also necessary to fnd out verify that both the spatial features and temporal features the relationship between the performance of our method play an important role in trafc prediction tasks. (4) GRU and the parameter α. Te input sequence length is set to 12. performs better than T-GCN, though it mines temporal As shown in Figure 6, our method performs best when α � only. One possible reason is that the mechanism for T-GCN 0.1. As α increases from 0 to 0.1, the performance improves. to obtain spatio-temporal features is not perfect. When Te main reason is that when α is too small, A has little T-GCN is used for lane-level trafc prediction, the extracted efect on A. With increasing α the infuence of A is gradually spatial features are coarse and inhibit the ability of T-GCN released to compensate for the static defect caused by the instead. distance-based adjacent matrix, and the performance of the model becomes better. Te results verify the necessity and 5.5. RQ2: Parameter Sensitivity Analysis. In this part, we validity of modeling a data-driven adjacent matrix. When α conduct sensitivity analysis of two important hyper- is larger than 0.1, the performance starts to drop. Te parameters in our model. Te two hyperparameters are the possible reason is that larger α makes the model focus more input sequence length p and the parameter α that controls on the dynamic part of the adjacent matrix and starts to the degree to which the dynamic correction matrix A undermine the fundamental role of the static distance-based contributes to the data-driven adjacent matrix A. adjacent matrix. Finally, we set α to be 0.1. Journal of Advanced Transportation 9 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 12 24 36 48 60 sequence length VAR MAE RMSE Figure 5: Te performance of our model as the input sequence length changes. 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.01 0.05 0.1 0.2 0.3 alpha VAR MAE RMSE Figure 6: Te performance of our model as hyperparameter α changes. 5.6. RQ3: Model Interpretation. In this part, we aim to an- a positive role in the prediction of the model. Te reason is swer RQ3 by visualizing the adjacent matrix and model that the trafc information at diferent times changes dy- prediction results. namically, and it is difcult for the static distance-based adjacent matrix to respond to such dynamic changes in a timely and efective manner. With the help of the dynamic 5.6.1. Visualization of Adjacent Matrix. To fgure out how correlation matrix, the data-driven adjacent matrix has the data-driven adjacent matrix afects the prediction results acquired the ability to model dynamically changing trafc of the model, we visualize the distance-based adjacent matrix information. Further, the performance of the model can A and lane correlation matrix A in the morning, after- d c been improved. noon, and evening of a random day, respectively. As shown in Figure 7, the distance-based adjacent matrix and the correlation matrix show diferent relationship patterns be- 5.6.2. Visualization of Prediction Result. To better un- tween lanes in diferent situations. More specifcally, A is derstand our proposed method, we randomly selected 4 static and A presents diferent data distributions at diferent lanes in diferent sections of the road and visualize the times. It can be seen from the answer of RQ3 that the ground truth of the test set and the prediction result. As construction of the dynamic correlation matrix plays shown in Figure 8, the results show the following: 10 Journal of Advanced Transportation 1.0 0.9 0.8 0.7 0.6 (a) (b) 1.0 1.0 0.9 0.8 0.8 0.6 0.7 0.6 0.4 0.5 (c) (d) Figure 7: Visualization of distance-based adjacent matrix A and dynamic correlation matrix A . (a) Visualizes the distance-based adjacent d c matrix. (b) Depicts the correlation matrix of trafc fow collected from 8 am to 9 am. (c) Te correlation matrix of trafc fow collected from 6 pm to 7 pm. (d) Te correlation matrix of trafc fow collected from 10 pm to 11 pm. (a–c) represent the similarity relationship of trafc fow in diferent lanes in the morning, afternoon, and evening of a random day respectively. (1) Similar patterns exist between the ground truths of use of the correlation matrix enables GCN to ag- diferent lanes. Te geographic distance between gregate more information from more neighbors, some lanes may be too large, in which case the which further leads to a smoother prediction result of distance-based adjacent matrix ignores the similar the model. (c) When the ground truth is small, the pattern. As a result, the lanes that are too far apart same gap can cause a larger relative error. cannot cooperate with each other to improve the (3) Our model can capture the trafc trend at the lane fnal prediction quality. Our proposed data-driven level. Tis property can help formulate efective and adjacent matrix efectively alleviates this problem on detailed trafc control strategies in real time and the basis of distance-based adjacent matrix. realize scientifc trafc management planning. (2) Tere is a certain error between the prediction results Besides, Figure 9 displays the ground truth and pre- of the model and the ground truth. Te reasons are diction results for a randomly chosen weekend and a ran- threefold: (a) GCN defnes a smooth flter and models domly chosen weekday. As depicted in Figure 9, our model the spatial features with the flter on the spatial do- can capture trends of trafc fow throughout the day. main. Tis process of aggregating neighbor in- Whether it is weekdays or weekends, peak or low-peak formation results in smooth predictions. (b) Tough times, trafc fow trends are well modeled, allowing for the construction of data-driven adjacent matrix can our model to realize stable and reliable prediction. help to improve model’s performance. However, the Journal of Advanced Transportation 11 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Time truth pred Figure 8: Visualization of ground truth and prediction results of 4 randomly selected lanes on the test set. Te blue line represents the ground truth and the red line represents the prediction results. Te horizontal axis represents the trafc fow, and the vertical axis represents the time the trafc fow recorded or predicted. Traffic f low Traffic f low Traffic f low Traffic f low 12 Journal of Advanced Transportation 25 25 20 20 15 15 10 10 5 5 0 0 0:00 4:00 8:00 12:00 16:00 20:00 24:00 0:00 4:00 8:00 12:00 16:00 20:00 24:00 (a) (b) 25 25 20 20 15 15 10 10 5 5 0 0 0:00 4:00 8:00 12:00 16:00 20:00 24:00 0:00 4:00 8:00 12:00 16:00 20:00 24:00 (c) (d) Figure 9: Visualization of ground truth and prediction results of all lanes on the test set. (a) Ground truth on a weekend. (b) Prediction results on the same weekend as (a). (c) Ground truth on a weekday. (d) Prediction results on the same weekday as (c). more than two lanes. Besides, we consider to combine with 6. Conclusion some advanced techniques such as attention network to In this paper, we propose a lane-level trafc prediction achieve more accurate and reliable lane-level trafc model for lane-level trafc prediction tasks. Specifcally, we prediction. capture spatial features with GCN. To adapt to the lane-level trafc prediction, we treat diferent lanes of the same road Data Availability segment as diferent nodes on the graph. Furthermore, considering that most existing graph-based methods build Te data used during the study are available from the static adjacent matrix, we construct a data-driven adjacent corresponding author upon request. matrix, which consists of a static distance-based adjacent matrix and a dynamic lane correlation matrix. Additionally, Conflicts of Interest we utilize GRU to capture temporal features. Ten we adaptively fuse spatial features and temporal features Te authors declare that they have no conficts of interest. through the gating mechanism to obtain spatio-temporal features for multi-steplane-level trafc prediction. Experi- Acknowledgments ment on a real-world dataset verifed the efectiveness of our model for lane-level trafc prediction. Tis research was supported by the National Natural Science In the future, we plan to consider more auxiliary fea- Foundation of China under Grant no. 62202131, the Natural tures, such as utilizing speed information in trafc fow Science Foundation of Zhejiang Province under no. prediction. Te current model can also be improved by LQ20F020015, and the Key Science and Technology Project considering more detailed and realistic lane relationships for of Zhejiang Province under no. 2020C01165. Lanes Lanes Lanes Lanes Journal of Advanced Transportation 13 [16] C. F. Daganzo, “A behavioral theory of multi-lane trafc fow. 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