Spatial-Temporal Graph Convolutional Gated Recurrent Network for Trafﬁc Forecasting Le Zhao Mingcai Chen Yuntao Du Haiyang Yang Chongjun Wang

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Spatial-Temporal Graph Convolutional Gated Recurrent Network for Trafﬁc

Forecasting

Le Zhao, Mingcai Chen, Yuntao Du, Haiyang Yang, Chongjun Wang

State Key Laboratory for Novel Software Technology at Nanjing University

Nanjing University, Nanjing 210023, China

2209557029@qq.com,

{chenmc, duyuntao, hyyang}@smail.nju.edu.cn,

chjwang@nju.edu.cn

Abstract

As an important part of intelligent transportation systems,

trafﬁc forecasting has attracted tremendous attention from

academia and industry. Despite a lot of methods being pro-

posed for trafﬁc forecasting, it is still difﬁcult to model com-

plex spatial-temporal dependency. Temporal dependency in-

cludes short-term dependency and long-term dependency, and

the latter is often overlooked. Spatial dependency can be

divided into two parts: distance-based spatial dependency

and hidden spatial dependency. To model complex spatial-

temporal dependency, we propose a novel framework for traf-

ﬁc forecasting, named Spatial-Temporal Graph Convolutional

Gated Recurrent Network (STGCGRN). We design an atten-

tion module to capture long-term dependency by mining peri-

odic information in trafﬁc data. We propose a Double Graph

Convolution Gated Recurrent Unit (DGCGRU) to capture spa-

tial dependency, which integrates graph convolutional network

and GRU. The graph convolution part models distance-based

spatial dependency with the distance-based predeﬁned adja-

cency matrix and hidden spatial dependency with the self-

adaptive adjacency matrix, respectively. Specially, we employ

the multi-head mechanism to capture multiple hidden depen-

dencies. In addition, the periodic pattern of each prediction

node may be different, which is often ignored, resulting in mu-

tual interference of periodic information among nodes when

modeling spatial dependency. For this, we explore the archi-

tecture of model and improve the performance. Experiments

on four datasets demonstrate the superior performance of our

model.

Introduction

Recently, many cities have been committed to developing

intelligent transportation systems (ITS) . As an important

part of ITS, trafﬁc forecasting has attracted tremendous at-

tention from academia and industry. From the perspective of

trafﬁc managers, trafﬁc forecasting can help reduce conges-

tion and provide early warning for safety accidents. From the

traveler’s perspective, trafﬁc forecasting can help plan travel

routes and improve travel efﬁciency.

Trafﬁc forecasting is a time series forecasting problem,

using the past trafﬁc data to predict the data in the future.

Early works simply deployed the classic time series analy-

sis models, e.g., history average (HA), vector auto regres-

sion (VAR), and auto regressive integrated moving average

(ARIMA)(Ahmed and Cook 1979). These models can only

model the linear dependency in the data, while the trafﬁc

data has complex nonlinear relationship, so the performance

of these linear models is poor in the real scenario. There-

fore, researchers shift to traditional machine learning meth-

ods, such as support vector regression (SVR)(Wu, Ho, and

Lee 2004) and k-nearest neighbors (KNN)(Davis and Ni-

han 1991). However, their performance relies heavily on the

handcrafted features, which need to be designed by domain

experts. Recently, deep learning models have become the

mainstream choice for trafﬁc forecasting due to their auto-

matic feature extraction ability and better empirical perfor-

mance.

In deep learning, the temporal dependency of trafﬁc data

can be modeled with recurrent neural networks (RNNs)(Fu,

Zhang, and Li 2016; Yu et al. 2017) or temporal convolution

modules(Zhang, Zheng, and Qi 2017; Yu, Yin, and Zhu 2018;

Wu et al. 2019). However, such approaches only mines short-

term dependency but ignores long-term dependency. Trafﬁc

data has strong daily and weekly periodicity, which is crucial

for trafﬁc forecasting. We can mine the periodicity in trafﬁc

data to model long-term dependency in trafﬁc data.

The spatial dependency can be captured by convolutional

neural network (CNN)(Fang et al. 2019; Lin et al. 2019; Yao

et al. 2019a) or graph convolutional networks (GCN)(Wu

et al. 2019; Wang et al. 2020; Bai et al. 2020). CNN can be

applied to grid-based maps to capture spatial dependency. In

this case, the data needs to be divided into

H×W

equal size

grids, where

and

represent the height and width of the

grid-based map respectively. However, CNN cannot handle

non-Euclidean data, which is a more common form when

describing road topology in real scenarios, with the predicted

positions as nodes and the roads as edges. GCN can process

non-Euclidean data, calculating the weight of the edge by

the distance between the nodes, obtaining a distance-based

predeﬁned adjacency matrix, and then feeding it into GCN

to capture distance-based spatial dependency(Li et al. 2018;

Yu, Yin, and Zhu 2018). Besides, the self-adaptive adjacency

matrices can be used to model hidden spatial dependency(Wu

et al. 2019; Wang et al. 2020; Bai et al. 2020). However, there

may be multiple hidden spatial dependencies, which have not

been considered in existing works. In addition, the periodic

patterns of each prediction node may be different, which

need to be taken into account when modeling the spatial

arXiv:2210.02737v1 [cs.LG] 6 Oct 2022

dependency to prevent the periodic information of different

nodes from interfering with each other.

To solve the above problems, we propose Spatial-Temporal

Graph Convolutional Gated Recurrent Network (STGCGRN)

to improve the accuracy of trafﬁc forecasting. Our contribu-

tions are as follows:

•

We propose a new framework to better exploit temporal

and spatial dependency: We capture long-term temporal

dependency by explicitly introducing daily and weekly

periodic data, which are fed into the attention module

with a sliding window. The DGCGRU layer is designed

to extract the distance-based spatial dependency and mul-

tiple hidden spatial dependencies, which are captured by

the predeﬁned distance-based adjacency matrix and the

multi-head self-adaptive adjacency matrix, respectively.

•

We explore the model structure and ﬁnd that mining the

periodic information of a single node, and then performing

spatial dependency modeling can reduce the interference

of periodic information among different nodes.

•

We conduct experiments on four datasets. The results

show that our model outperforms the baseline methods.

We also conduct ablation experiments to evaluate the im-

pact of each component of our model on the performance.

Related Work

Graph Convolutional Neural Network

Graph convolutional neural network is a special form of CNN

generalized to non-Euclidean data, which can be applied

to different tasks and domains, such as node classiﬁcation

(Kipf and Welling 2017), graph classiﬁcation (Ying et al.

2018), link prediction (Zhang and Chen 2018), node cluster-

ing (Wang et al. 2017), spatial-temporal graph forecasting,

etc. Bruna et al.(Bruna et al. 2014) is the ﬁrst work to gen-

eralize the convolution operation to non-Euclidean data, and

proposes a spatial method and a spectral method.

Spatial-based approaches aggregate neighborhood feature

informations in the spatial domain to extract a node’s high-

level representation. DCNNs(Atwood and Towsley 2016) ex-

tend convolutional neural networks (CNNs) to general graph-

structured data by introducing a ‘diffusion-convolution’ op-

eration. Message Passing Neural Network (MPNN)(Gilmer

et al. 2017) describes a general framework for supervised

learning on graphs, applying graph convolution to super-

vised learning of molecules. GraphSage(Hamilton, Ying, and

Leskovec 2017) proposes a general inductive framework to

efﬁciently generate node embeddings for previously unseen

data, sampling and aggregating features from the node’s local

neighborhood.

Spectral-based approaches implement the convolution op-

eration in the spectral domain with graph Fourier transforms.

ChebyNet(Defferrard, Bresson, and Vandergheynst 2016)

achieves fast localized spectral ﬁltering by introducing C

order Chebyshev polynomials parametrization. GCN(Kipf

and Welling 2017) further reduces computational complexity

of ChebNet by limiting C=2.

Trafﬁc Forecasting

As an important component of ITS, trafﬁc forecasting has

received wide attention for decades. Most of the early traf-

ﬁc forecasting works are based on some classic time se-

ries analysis models. ARIMA (Ahmed and Cook 1979) is

used to predict the short-term freeway trafﬁc data. Subse-

quently, many variants of ARIMA are applied to this task,

such as KARIMA (Van Der Voort, Dougherty, and Watson

1996), subset ARIMA (Lee and b. Fambro 1999), ARIMAX

(Williams 2001), etc. Trafﬁc data contains complex spatial-

temporal dependency. However, the aforementioned works

only consider the linear relationship in the temporal dimen-

sion, which is obviously insufﬁcient. Researchers apply tra-

ditional machine learning algorithms to trafﬁc forecasting,

including SVR (Wu, Ho, and Lee 2004), KNN (Davis and

Nihan 1991), and so on. These methods need handcrafted

features, which require expert experience in related ﬁelds

Due to the advantages of deep learning in solving nonlin-

ear problems and automatically extracting features, scholars

pay more attention to deep learning. RNN (Fu, Zhang, and Li

2016; Yu et al. 2017) and CNN (Zhang, Zheng, and Qi 2017;

Yu, Yin, and Zhu 2018; Wu et al. 2019) are adopted to capture

temporal dependency. For example, Graph Wavenet (Wu et al.

2019) uses dilated casual convolutions to model the tempo-

ral dependency to increase the receptive ﬁeld. To model the

spatial dependency, Some works (Fang et al. 2019; Lin et al.

2019; Yao et al. 2019a) divide the trafﬁc data into grid-based

map, and extract spatial information by CNN. However, due

to natural limitations, CNN can not handle non-Euclidean

data. For this reason, researchers apply GCN to the ﬁeld

of trafﬁc forecasting. DCRNN (Li et al. 2018) captures the

spatial dependency using bidirectional random walks on the

graph. STGCN (Yu, Yin, and Zhu 2018) employs a gener-

alization of Chebnet to capture the spatial dependency of

trafﬁc data. These methods only utilize the predeﬁned graph

structures, which is not sufﬁcient. Some works (Wu et al.

2019; Wang et al. 2020; Bai et al. 2020) calculate similari-

ties among learnable node embeddings to capture the hidden

spatial dependency in the data. DGCRN (Li et al. 2021a)

ﬁlters the node embeddings and then uses them to generate

dynamic graph at each time step. However, these works do

not adequately model spatial dependency and ignore periodic

information.

Preliminaries

•

Deﬁnition 1: Trafﬁc Network. The trafﬁc network is an

undirected graph

G= (V, E, A)

, where

is a set consists

nodes,

is a set of edges and

A∈RN×N

is the

adjacency matrix representing the nodes distance-based

proximity.

•

Deﬁnition 2: Trafﬁc Signal Matrix. Trafﬁc signal matrix

can be denoted as a tensor

Xt∈RN×C

, where

is the

number of trafﬁc features of each node (e.g., the speed,

volume), tdenotes the time step.

The problem of trafﬁc forecasting can be described as:

given the trafﬁc network

G= (V, E, A)

and

steps traf-

ﬁc signal matrix

X(t−P):t= (Xt−P, Xt−P+1, ..., Xt−1)∈

RP×N×C

, learning a function

which maps

X(t−P):t

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Spatial-TemporalGraphConvolutionalGatedRecurrentNetworkforTrafcForecastingLeZhao,MingcaiChen,YuntaoDu,HaiyangYang,ChongjunWangStateKeyLaboratoryforNovelSoftwareTechnologyatNanjingUniversityNanjingUniversity,Nanjing210023,China2209557029@qq.com,{chenmc,duyuntao,hyyang}@smail.nju.edu.cn,chjwang@nju.e...

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