Combined Dynamic Virtual Spatiotemporal Graph Mapping for Trafﬁc Prediction Yingming Pu Westlake University China

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Combined Dynamic Virtual Spatiotemporal Graph Mapping for Trafﬁc Prediction

Yingming Pu

Westlake University, China

puyingming@westlake.edu.cn

Abstract

The continuous expansion of the urban construc-

tion scale has recently contributed to the demand

for the dynamics of trafﬁc intersections that are

managed, making adaptive modellings become a

hot topic. Existing deep learning methods are pow-

erful to ﬁt complex heterogeneous graphs. How-

ever, they still have drawbacks, which can be

roughly classiﬁed into two categories, 1) spatiotem-

poral async-modelling approaches separately con-

sider temporal and spatial dependencies, resulting

in weak generalization and large instability while

aggregating; 2) spatiotemporal sync-modelling is

hard to capture long-term temporal dependen-

cies because of the local receptive ﬁeld. In or-

der to overcome above challenges, a Combined

Dynamic Virtual spatiotemporal Graph Mapping

(CDVGM) is proposed in this work. The con-

tributions are the following: 1) a dynamic vir-

tual graph Laplacian (DV GL) is designed, which

considers both the spatial signal passing and the

temporal features simultaneously; 2) the Long-

term Temporal Strengthen model (LT 2S) for im-

proving the stability of time series forecasting;

Extensive experiments demonstrate that CDVGM

has excellent performances of fast convergence

speed and low resource consumption and achieves

the current SOTA effect in terms of both accu-

racy and generalization. The code is available at

https://github.com/Dandelionym/CDVGM.

1 Introduction

Trafﬁc ﬂow forecasting is a fundamental intelligent trans-

portation task that requires predicting the trafﬁc ﬂow in all

interactions of a road map [Rao et al., 2022; Tedjopurnomo

et al., 2020; Nagy and Simon, 2018; Medina-Salgado et al.,

2022; Jiang and Luo, 2022; Tang and Zeng, 2022]. Trafﬁc

ﬂow forecasting subsumes a series prediction task, as the ﬂow

of a road network can be thought of as a set of nodes’ tempo-

ral series prediction task. Therefore, it is a more challenging

task than time series prediction by requiring both spatial-level

modelling and temporal-level prediction because of the com-

plex dependencies of spatial dimensions.

Figure 1: General topology-based methods utilize a ﬁxed road map

to represent spatial connection or dynamics aggregated with the road

map as spatial connection(left), which is built on the assumption

that there is no indirect societal level of connection; Our dynamic

virtual spatiotemporal graph (right), has the ability to model low-

high-dimension-oriented dependencies without topological informa-

tion adaptively.

Recently, signiﬁcant progress has been made to address

the topology-based trafﬁc prediction task [Chen et al., 2022;

Wang et al., 2022a]. However, the topological structure of a

graph can be dynamically changing in the real world and the

trafﬁc crash can lead to unavailable crossroads. Latest meth-

ods such as DGCN [Guo et al., 2022], DCRNN [Li et al.,

2017], STFGNN [Li and Zhu, 2021]and S2TAT [Wang et al.,

2022b]have signiﬁcantly improved the ﬁtness of spatiotem-

poral modelling. However, on the one hand, their competitive

result still relies on topological connections that are not adap-

tive enough due to trafﬁc jams or crashes, as shown in Fig 1.

On the other hand, it is generally confused whether it is better

to use the space-time asynchronous method or the space-time

synchronization method because both of them have their ad-

vantages, for example, a synchronous method such as AST-

GCN [Guo et al., 2019a]and DCRNN [Li et al., 2017]of-

ten have the weakness of local receptive ﬁeld, which lead to

the shortage of modelling long-term dependencies and asyn-

chronous methods such as STFGNN [Li and Zhu, 2021]and

S2TAT [Wang et al., 2022b]lack the ability of dependency’s

arXiv:2210.00704v1 [cs.LG] 3 Oct 2022

representation because the spatiotemporal graph structure in-

herently has the complex coupling in both spatial and tempo-

ral dimensions. To our knowledge, existing methods hardly

take into account each of the important conditions mentioned

above simultaneously because of the consideration of com-

putational complexity or inference speed or even modelling

ability.

To overcome these shortages, the Combined Dynamic Vir-

tual spatiotemporal Graph Mapping (CDVGM) is proposed.

In this work, we explore capturing dynamic correlations be-

tween spatial and temporal dimensions without any topolog-

ical additions and the stability of the prediction. The work

draws on cross-entropy theory and uses it as the basis for the

asymmetric study of node correlations in the construction of

dynamic Laplacian. In this work, all trafﬁc nodes are located

in the same quantifying space to compute the differences by

cross-entropy of history ﬂow data. We treat the result as the

expression of correlations of each two nodes in the case of

incorporating temporal features. Therefore, the direction is

also addressed as there are up-streams and down-streams ob-

jectively in the road of the real. Unlike existing methods, CD-

VGM efﬁciently generates adaptive Laplacian through his-

tory ﬂows in a series of states even if the road network is

changing, e.g. some interactions might be unavailable due to

the crash. Finally, we ﬁnd that the graph Laplacian operators

with different order of magnitude scales can better represent

the key nodes in the spatial network and ﬁnd the high-energy

regions existing in the corresponding road network, which is

more conducive to the transmission of induced graph signals.

Besides, the stability of the mid-range forecasting problem

also got relief by the way of LT 2Smodule, which takes the

trend as the key of the prediction task and improves the whole

accuracy even in complex couplings of spatiotemporal depen-

dencies.

1) The ﬁrst topological-structure-free framework with dy-

namic dependencies modelling is proposed, which com-

bined both synchronous and asynchronous advantages

within fast convergence speed and excellent prediction

accuracy.

2) The Laplacian is carefully designed by a dynamic vir-

tual graph for graph signal passing, which considers the

temporal correlations and spatial connections simultane-

ously in a time-series-based way by similarity theory.

3) A Long-Term Temporal Strengthen (LT 2S) module is

proposed to enhance the perception of long-range de-

pendencies with ﬂexibility. It gives a simple but effec-

tive way to the series prediction task.

4) Extensive experiments on four benchmarks demonstrate

that the proposed framework outperforms many recent

state-of-the-art methods, implying that CDVGM has the

best predictive ability and application value so far.

2 Related works

2.1 Trafﬁc Prediction

Trafﬁc forecasting has many application values in smart city

construction. Trafﬁc data is often viewed as a spatiotemporal

graph. Due to the limited modelling ability of the early sta-

tistical methods [Junior et al., 2014], they only consider the

temporal dimension for modelling, ignoring the geographic

effect of the spatial dimension, which leads to the funda-

mental defects of such methods. Subsequently, STGCN [Yu

et al., 2017a]and DCRNN [Li et al., 2017]model the spa-

tial dimension through a deep learning method with GLU or

RNN for temporal prediction asynchronously while methods

such as STSGCN [Song et al., 2020]and STFGNN [Li and

Zhu, 2021]use a local graph to represent spatiotemporal cor-

relation synchronously. S2TAT [Wang et al., 2022b]uses a

time-oriented graph convolution network to improve the abil-

ity of spatiotemporal perception. Owing to the challenges

of spatiotemporal modelling, attention mechanism is adopted

such as ASTGCN [Guo et al., 2019a]and DGCN [Guo et al.,

2022]etc. Except this, STGODE [Fang et al., 2021]uses

spatial-based adjacency matrices and semantic-based adja-

cency matrices to reﬂect spatial dependencies, and perceive

high-dimensional spatiotemporal correlations through ordi-

nary differential equations. ST-3DNet [Guo et al., 2019b]

ﬁrst utilizes a 3D-convolution operator for spatiotemporal

graph modelling and ST-ResNet [Zhang et al., 2017]consid-

ers the fact of temporal characteristics of crowd movement to

ﬁt the real-world situation better.

In a word, existing methods normally either consider the

complex coupling as a separate modelling problem wrongly

within the IID assumption or ignore the direct or indirect en-

tanglement that exists between potential spatiotemporal de-

pendencies, which leads to the drawbacks of low general-

izability. Unlike prior works, our novelty is that propos-

ing a topological-free virtual graph designed by combining

spatiotemporal dimensions and equipped with a temporal

strengthen strategy asynchronously to boost performance for

the prediction task.

2.2 Graph convolutional neural network

The graph convolutional neural network realizes the opera-

tion of convolution of non-Euclidean graph data, and GNN

has had a signiﬁcant impact in the ﬁelds of social relation-

ship mining and chemical biology. It can be roughly divided

into two categories, one is a spectral graph neural network

based on spectral graph theory, and the other is a graph net-

work based on the spatial method. Among them, ChebyNet

[Defferrard et al., 2016]uses Chebyshev polynomials to ap-

proximate the Laplacian operator of spectral graph decompo-

sition, which greatly reduces the computational complexity

and is a typical representative of spectral graph neural net-

works. Then graph convolution neural network (GCN) [Kipf

and Welling, 2016]simpliﬁes ChebyNet with a ﬁrst-order

polynomial, which removes the hyperparameter of K-level

adjacent and becomes the cornerstone of spatial graph neu-

ral network. Space-based GCN generalizes convolution in

Euclidean space to work on graph data. For example, Graph-

SAGE [Hamilton et al., 2017]transmits the neighbour node’s

signal through an adjacency matrix before aggregating fea-

tures, and Graph Attention Network (GAT) [Velickovic et al.,

2017]weight node signals by attention mechanism. Simpli-

ﬁed Graph Convolution Network (SGC) [Wu et al., 2019]re-

moves the non-linear activations in hidden layers for local av-

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CombinedDynamicVirtualSpatiotemporalGraphMappingforTrafcPredictionYingmingPuWestlakeUniversity,Chinapuyingming@westlake.edu.cnAbstractThecontinuousexpansionoftheurbanconstruc-tionscalehasrecentlycontributedtothedemandforthedynamicsoftrafcintersectionsthataremanaged,makingadaptivemodellingsbecomeah...

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Combined Dynamic Virtual Spatiotemporal Graph Mapping for Trafﬁc Prediction Yingming Pu Westlake University China

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