#  SMA-Hyper: Spatiotemporal Multi-View Fusion Hypergraph Learning for Traffic
Accident Prediction

Xiaowei Gao<EMAIL_ADDRESS>James Haworth<EMAIL_ADDRESS>Ilya
Ilyankou<EMAIL_ADDRESS>Xianghui Zhang
<EMAIL_ADDRESS>Tao Cheng<EMAIL_ADDRESS>Stephen Law
<EMAIL_ADDRESS>Huanfa Chen<EMAIL_ADDRESS>
###### Abstract

Predicting traffic accidents is the key to sustainable city management, which
requires effective address of the dynamic and complex spatiotemporal
characteristics of cities. Current data-driven models often struggle with data
sparsity and typically overlook the integration of diverse urban data sources
and the high-order dependencies within them. Additionally, they frequently
rely on predefined topologies or weights, limiting their adaptability in
spatiotemporal predictions. To address these issues, we introduce the
Spatiotemporal Multiview Adaptive HyperGraph Learning (SMA-Hyper) model, a
dynamic deep learning framework designed for traffic accident prediction.
Building on previous research, this innovative model incorporates dual
adaptive spatiotemporal graph learning mechanisms that enable high-order
cross-regional learning through hypergraphs and dynamic adaptation to evolving
urban data. It also utilises contrastive learning to enhance global and local
data representations in sparse datasets and employs an advance attention
mechanism to fuse multiple views of accident data and urban functional
features, thereby enriching the contextual understanding of risk factors.
Extensive testing on the London traffic accident dataset demonstrates that the
SMA-Hyper model significantly outperforms baseline models across various
temporal horizons and multistep outputs, affirming the effectiveness of its
multiview fusion and adaptive learning strategies. The interpretability of the
results further underscores its potential to improve urban traffic management
and safety by leveraging complex spatiotemporal urban data, offering a
scalable framework adaptable to diverse urban environments.

###### keywords:

Traffic Accident Prediction , Spatiotemporal Hypergraph Learning , Multi-View
Fusion , Adaptive Graph Learning

[inst1]organization=SpaceTimeLab, University College London (UCL),
state=London, country=UK

[inst2]organization=Department of Geography, University College London (UCL) ,
state=London, country=UK

[inst3]organization=The Bartlett Centre for Advanced Spatial Analysis,
University College London (UCL) , state=London, country=UK

##  1 Introduction

Urban traffic management is increasingly challenged by the rapid growth in
vehicle numbers and the expansion of road networks, driven by urban economic
development and changes in transportation systems. This surge in traffic
activity increases the risk of exposure to road accidents, which remain a
major public health concern. According to the latest report by the World
Health Organisation (WHO), road traffic accidents result in approximately 1.19
million deaths annually worldwide, disproportionately affecting vulnerable
road users (WHO,, 2023). Furthermore, data from the Department for Transport
in the UK reveal that despite reduced mobility during the COVID-19 pandemic,
the pattern of road injuries from 2018 to 2022 has shown little variation,
with such injuries costing nearly 1.5% of the annual GDP (DfT,, 2023). These
accidents not only compromise public safety but also affect the sustainability
and efficiency of urban environments and transportation systems, underscoring
the critical need for improved predictive methodologies to prevent such
incidents (UNECE,, 2019).

The increasing complexity of urban traffic management requires the development
of precise models for predicting traffic accidents, crucial for implementing
proactive measures that improve both safety and efficiency. Traditionally,
accident prediction has predominantly employed time series methods such as
Autoregressive Integrated Moving Average (ARIMA) (Ihueze and Onwurah,, 2018),
Gated Recurrent Unit (GRU) (Zhang et al.,, 2020), and Long Short-Term Memory
(LSTM) networks (Ren et al.,, 2018; Yuan et al.,, 2018). Although effective in
capturing temporal dynamics, these approaches often overlook significant
geographical factors, thus restricting their ability to fully comprehend the
intricacies required for accurate predictions. Recent advancements have
shifted focus towards integrating spatial relationships, with Graph Neural
Networks (GNNs) proving particularly effective in urban settings. Urban
environments, with their complex interconnected layouts, are naturally
represented as graphs, where nodes signify geographic locations, and edges
represent spatial relationships between them. This allows Graph Convolutional
Networks (GCNs) (Trirat et al.,, 2023) and spatiotemporal graph neural
networks (ST-GNNs) (Zhou et al., 2020a, ; Karim et al.,, 2022; Rahmani et
al.,, 2023) to model intricate spatial relations essential for understanding
traffic dynamics. ST-GNNs, renowned for their ability to uncover nonlinear
spatiotemporal relationships, significantly improve the understanding of
multiviews contributing to traffic accidents. Their ability to incorporate
heterogeneous urban data dimensions further facilitates big data-driven
modelling solutions (Zhang and Cheng,, 2020).

Despite these technological advances, the common issue in the prediction of
traffic accidents is the sparsity in both spatial and temporal dimensions,
with incidents that occur nonperiodically in a few locations at particular
times. Advanced data enhancement strategies, such as Prior Knowledge-based
Data Enhancement (PKDE) proposed by Zhou et al., 2020b , have proven to be a
promising direction in enriching the data discrimination to better meet the
model requirements for effective local neighbourhood information aggregation.
Furthermore, the adoption of graph attention techniques uses attention scores
to refine node aggregation processes, improving the detection of relationships
among localised similar nodes (Zhou et al., 2020a, ; Yu et al.,, 2021).
Nevertheless, despite the well-addressed sparsity, there are still several
unresolved challenges in traffic accident prediction that necessitate further
research to enhance the effectiveness of predictive models for urban traffic
management:

  * •

Inadequacy of Conventional Pairwise Relations: Traditional graph models in
urban analytics primarily focus on pairwise interactions, limiting analyses to
localised relationships between pairs of nodes. Geographic correlations from
points of interest (POIs), as shown in Figure 1, suggest that relationships
between urban areas go beyond mere proximity, involving complex global
similarities across multiple regions, further indicating that the signals of
nodes should be propagating within a set of similar attributes distribution
nodes. Cities are entangled complex systems whose characteristics intertwine
and overlap. Standard graph models, which prioritize immediate node-to-node
interactions, fail to capture these extended and high-order spatial dynamics
crucial for comprehensive traffic accident analysis.

  * •

Overlooked Multi-Perspective Urban Data: Urban environments are rich with
diverse data sources, yet current methodologies in traffic accident prediction
often fail to utilize this multiplicity effectively. As depicted in Figure 1,
various external features such as weather conditions and land use types offer
unique insights that are pivotal for predicting accident risk. Most existing
models rely on simplified single-view graph matrices from accident data
itself, which do not adequately account for the multifaceted nature of urban
data (Zhou et al., 2020b, ; Cui et al.,, 2024). This simplification leads to a
lack of consideration in spatiotemporal latent interactions between different
types of urban data for the models, ultimately resulting in less convincing
predictions.

  * •

Static Models in Dynamic Urban Contexts: Existing modelling approaches tend to
use static affinity matrices for a fixed graph structure based on
representations of geographic proximity and attribute similarity, often guided
by Tobler’s first and third laws of geography. These predefined model graph
structures with strong subjective assumptions make it hard to represent the
evolving nature of urban data as well as a lack of understanding of coupled
spatiotemporal features, like temporal interaction, configuration similarity,
and spatial distance. Furthermore, the rigidity of these models prevents the
effective integration of new data or adjustment to multiview data variations,
which is crucial for maintaining the generalisation of accident predictions in
dynamic urban environments.

(a) Illustration of complex geographic relationships: Regions 1, 2, and 3
share similar POI distributions, yet only Regions 1 and 2 are directly linked
by spatiotemporal correlations.

(b) The distribution of accident risk ratios in different conditions. The
weather conditions include five distinct scenarios, while the greenspace ratio
is divided into ten discrete clusters.

Figure 1: Case studies illustrating traffic accidents: (a) Geographic
relationships among regions with similar POI distributions and their
spatiotemporal correlations. (b) Accident risk ratios under varying weather
conditions and greenspace distributions.

In response to data-driven challenges in urban traffic management, we
introduce the Spatiotemporal Multiview Adaptive HyperGraph Learning (SMA-
Hyper) framework. This novel framework enhances the representation and
interrelation of urban data within graph models by integrating adaptive graph
and hypergraph architectures, tailored to each specific view. By enabling
dynamic representations of graph nodes and structures, SMA-Hyper adeptly
manages the global latent spatiotemporal dependencies stemming from cross-
regional heterogeneous urban data. Further, the SMA-Hyper framework
incorporates an attention mechanism to effectively fuse multilayered urban
data, such as road conditions and points of interest. This step not only
captures the heterogeneity and homogeneity within regional semantic
attributes, but also incorporates complex factors that influence traffic
accidents. Additionally, SMA-Hyper employs a contrastive learning technique
across its graph and hypergraph components to bolster self-supervised learning
capabilities, particularly valuable in scenarios characterised by sparse
accident data. SMA-Hypermaps intricate pairwise and setwise relationships and
assembles a comprehensive information transmission architecture. This
architecture integrates spatiotemporal traffic accident risk patterns with the
latent representations of coupled geographic elements. Key contributions of
the SMA-Hyper framework are summarised as follows.

  * •

SMA-Hyper introduces a novel approach to traffic accident prediction by
integrating an adaptive hypergraph and graph architecture. This integration
enables dynamic data representation and the exploration of complex, higher-
order regional dependencies. It also marks a comprehensive consideration from
traditional models by utilising an attention mechanism for multiview data
fusion and a contrastive learning approach to enhance model learning under
data sparsity.

  * •

Comprehensive comparison testing on diverse temporal resolutions within the
real-world London traffic accident dataset elucidates the framework’s
effectiveness, particularly under extremely sparse non-zero instances (3.07%).
The empirical findings underscore a substantial enhancement in accident risk
prediction accuracy by 50.71% - 58.30% in RMSE and MAE, while maintaining
robust recall scores around 40%, demonstrating the framework’s operational
superiority over existing methods.

  * •

Extensive supplementary testing, including ablation studies and sensitivity
analysis, assesses the impact of each component of SMA-Hyper. These analyses
confirm the value of integrating hypergraph learning for capturing
spatiotemporal dependencies and the effectiveness of the multiview fusion
strategy in improving prediction accuracy. The findings from these studies
provide robust evidence of the framework’s adaptability and efficacy in urban
traffic settings.

The remainder of this paper is organised as follows. Section 2 reviews related
works on deep learning methods for accident prediction and hypergraph learning
in urban computing. Section 3 details the preliminaries, defines the problem,
and describes the proposed Adaptive HyperGraph Learning Adaptive Multiview
(SMA-Hyper) framework. Section 4 discusses the experimental setup and results,
including ablation and sensitivity analyses. Finally, Section 5 concludes the
paper by summarising our findings and suggesting directions for future
research.

##  2 Literature Review

###  2.1 Deep Learning for traffic accident prediction

Early efforts in traffic accident prediction used mainly statistical models or
traditional machine learning techniques, which often struggled with the
complexity and heterogeneity of large datasets and overlooked crucial
spatiotemporal correlations (Ali et al.,, 2024). With the advent of advanced
artificial intelligence technologies, a shift toward deep learning methods has
occurred, leveraging their capacity to unravel complex non-linear
spatiotemporal relationships within traffic accident data.

Recurrent Neural Networks (RNNs), especially Long Short-Term Memory (LSTM)
networks, have been widely adopted for their efficacy in capturing temporal
dynamics. In contrast, convolutional neural networks (CNNs) have been applied
to spatial analysis. For instance, Ren et al., (2018) pioneered the use of
LSTM to analyse temporal sequences of traffic accidents, but limited their
spatial analysis to basic fully connected layers. Addressing this shortfall,
Yuan et al., (2018) introduced the Heterogeneous Convolutional LSTM (Heter-
ConvLSTM), integrating various urban and external characteristics to better
delineate accident risks, albeit within constrained scenarios like their Iowa
case study. Further developments led to Moosavi et al., (2019) integrating
LSTM with a latent training representation of POI data and historical traffic
event descriptions to capture spatial heterogeneities more effectively. Najjar
et al., (2017) were pioneers in using CNNs to process spatial data derived
from satellite imagery to pinpoint accident locations, though their model
lacked temporal integration.

Despite the progress, traditional CNNs and RNNs have limitations in capturing
extensive spatiotemporal interactions, often restricting their effectiveness
to local information learning without broader contextual understanding (Cui et
al.,, 2024). Graph Neural Networks (GNNs) have subsequently emerged as a
robust solution, adept at encapsulating both localised and expansive
spatiotemporal dependencies through the inherent connectivity of urban
frameworks. This comprehensive approach enhances the understanding of traffic
patterns and facilitates detailed city-wide predictions. For instance, Zhou et
al., 2020a  utilised a Differential Time-varying Graph Neural Network (DTGN),
complemented by a knowledge-based data enhancement strategy, to address zero-
inflated data issues. They, along with Zhou et al., 2020b  and Wang et al.,
(2021), implemented multigranularity risk prediction models that define
regions with varying grid sizes, proposing to simultaneously predict at
different scales. However, this approach has raised feasibility concerns due
to the complexity of managing predictions across multiple spatial resolutions
effectively. Moreover, recent studies like those by Trirat et al., (2023) and
Yu et al., (2021) have opted for single-grid size approaches. Yu et al.,
(2021) employed spatial convolution layers combined with temporal convolution
layers to achieve sophisticated spatiotemporal representations, whereas Trirat
et al., (2023) leveraged a multiview fusion mechanism with attention
mechanisms and a Transformer to learn temporal dependencies. Each approach
highlights distinct advantages and challenges in capturing urban dynamics but
indicates that relying on a single grid size may offer more consistency in
model performance across various urban configurations.

However, all current GNN models are based on predefined matrices and manually
selected grids, which is limited in adapting to the evolving urban environment
and accurately predict traffic accidents in different contexts.

###  2.2 HyperGraph Learning Methods in Urban Prediction

Traditional graph-based models often rely on localised pairwise interactions
between nodes, which can restrict the scope of information propagation and
fail to capture complex multi-node relationships inherent in urban data (Wang
et al.,, 2022). To overcome these limitations, hypergraph learning has been
proposed as a powerful alternative. Hypergraphs extend beyond simple pairwise
interactions by incorporating multiple nodes into a single hyperedge, thereby
facilitating the collaborative extraction of non-Euclidean latent
representations from complex data structures (Antelmi et al.,, 2023; Wu et
al.,, 2024). In the realm of urban computing, hypergraph techniques have shown
substantial success in various applications, including prediction of mobility
flow (Alvarez-Rodriguez et al.,, 2021; Wang and Zhu,, 2024), destination
recommendation (Yan et al.,, 2023), and analysis of social interactions (Hong
et al.,, 2022). Each of these applications benefits from the hypergraph’s
ability to integrate heterogeneous urban elements into a comprehensive, high-
dimensional nonlinear space. This analytical framework improves the
representation of urban dynamics, providing a more complete understanding of
complex interactions within urban systems.

Despite these successes, the application of hypergraph learning to urban event
prediction, such as traffic accidents or crime, remains relatively nascent.
Recent studies have begun to explore this domain; for instance, Xia et al.,
(2021) pioneered the use of global cross-regional hypergraphs to predict the
occurrence of various categories of crime. In their approach, hyperedges act
as intermediate information centres that correlate not only locally connected
but also distant regions, thus improving the relational learning capabilities
of crime data. Building on this, Li et al., (2022) introduced a contrastive
learning module to discern spatiotemporal crime patterns at the local and
global levels while addressing the challenge of sparse crime data by
increasing region self-discrimination. Extending this innovative approach to
the prediction of traffic accidents, Cui et al., (2024) directly applied the
above self-supervised hypergraph learning framework to the prediction of NYC
and London traffic accidents. However, their works overlook the integration of
urban configurations, focussing predominantly on accident data information.

##  3 Methodology

###  3.1 Preliminary

  1. (i)

Pairwise Urban Graph: Under this graph structure, the signals of nodes are
transmitted through edges toward another node. As shown in Figure 2, an
undirected graph $G(\mathcal{V},\mathcal{E})$ represents the spatial
connectivity between urban regions, with the city divided into $N$ subregions.
Here, $\mathcal{V}\in\mathcal{R}^{N}$ denotes the set of vertices, each
corresponding to a subregion, and $\mathcal{E}\in\mathcal{R}^{N\times N}$
represents the set of edges, indicating connections between pairs of
subregions. The adjacency matrix $A\in\mathcal{R}^{N\times N}$ characterises
the spatial relationships between subregions, defined as $A_{i,j}=1$ if
subregions $i$ and $j$ are connected, and $A_{i,j}=0$ otherwise.

  2. (ii)

Setwise Urban Hypergraph: Under this graph structure, the signals of nodes are
propagated within hyperedges toward a cluster of nodes. As shown in Figure 2,
a hypergraph is defined as $\widehat{G}(\widehat{V},\widehat{E},\widehat{W})$,
where $\widehat{V}\in\mathcal{R}^{N}$ represents the nodes (subregions),
$\widehat{E}\in\mathcal{R}^{N\times I}$ denotes the set of hyperedges capable
of linking multiple nodes simultaneously, and $\widehat{W}$ corresponds to the
weights of these hyperedges. A hyperedge captures higher-order spatial
dependencies, allowing advanced representations for the global relationships
through hypergraph information propagations among each region and
corresponding hyperedges.

(a) Pairwise Graph Structure

(b) Setwise Hypergraph Structure

Figure 2: (a) Pairwise graph mapped by pair-pair region spatial connectivity.
(b) Setwise Hypergraph focusing on high-order relationships with multihop
connections.

  3. (iii)

Adaptive Graph Matrix: We use a learnable adaptive affinity matrix to
represent various non-Euclidean relationships between subregions, offering
topological structures for the propagation of node features. The matrix
$\mathscr{A}^{s}\in\mathcal{R}^{N\times N}$ describes the adaptive graph for
pairwise-based graph construction, while
$\mathscr{H}^{s}\in\mathcal{R}^{N\times I}$ represents the adaptive hypergraph
for setwise-based graph construction. In this context, $I$ denotes the number
of hyperedges.

  4. (iv)

Traffic Accident Risk Score: The accident records are geo-located and time-
stamped data with identification of severity. The risk score of traffic
accidents combines the severity of heterogeneous levels of accidents within a
specific time interval $t$ in individual subregions $n$ as
$y_{n,t}=\sum_{i=1}^{3}f_{n,t}^{i}\times i$, where $f_{n,t}^{i}$ denotes the
frequency of accidents at severity level $i$ in subregion $n$ during time
interval $t$. The weight of severity levels ranges from 1 (slight injuries) to
3 (death), integrating the impacts of varying accident severities to provide a
comprehensive risk profile for the subregion.

  5. (v)

Urban Features: The set of urban features is represented by two views: points
of interest (POI) and road statistical information. The POI distribution
includes the density of different types of POI categories, while road
information encompasses specifics such as road type, average width, and
infrastructure details. These features are represented as
$X^{P}\in\mathcal{R}^{N\times d_{P}}$ (POI) and $X^{R}\in\mathcal{R}^{N\times
d_{R}}$ (Road), respectively, in which $d_{P}$ and $d_{R}$ are the dimension
of the corresponding feature embeddings.

  6. (vi)

External Features: External features refer to the influences other than the
urban geographical environment that affect accidents. These factors mainly
include meteorology and calendar information. Meteorology features include
temperature, snow depth, and visibility, while calendar information covers
holidays, peak travel times, and days of the week. These features are
represented as $X^{M}\in\mathcal{R}^{N\times T\times{d_{M}}}$ (Meteorology)
and $X^{C}\in\mathcal{R}^{N\times T\times{d_{C}}}$ (Calendar), where $d_{M}$
and $d_{C}$ indicate the dimension of feature embedding, respectively.

###  3.2 Problem Definition

Given the adaptive graph and also the adaptive hypergraph
$\mathbf{G}\in(G,\widehat{G})$ of the city, the input is the historical
accident risk series $\mathbf{X_{t}}$ for $t=1,2,\ldots,T$, the output is to
predict the accident risk score, resulting from $y_{n,t}$, for each subregion
in the next time intervals $\tau$. Formally, the problem can be formulated as
finding a function $P_{\Theta}(\cdot)$ such that:

$[\mathbf{X_{t}};\mathbf{G}]\xrightarrow{P_{\Theta}(\cdot)}[Y_{t+1},\ldots,Y_{t+\tau}]$
(1)

where $P_{\Theta}(\cdot):\mathbb{R}^{N\times
T}\rightarrow\mathbb{R}^{N\times\tau}$ is the target function mapping from
spatiotemporal features of the past $T$ steps to the predicted accident risk
in the next $\tau$ steps. $\Theta$ represents the learnable parameters and
$Y_{t}\in\mathbb{R}^{N}$ is the accident risk score metrics for all nodes in
the time step $t$.

###  3.3 Tackling Sparse Accident Data

A significant challenge in the prediction of fine-grained traffic accidents is
zero inflation. To address this, we use the PKDE method to augment zero-value
data, which was proposed by Zhou et al., 2020b ; Zhou et al., 2020a . This
approach adjusts zero-value elements based on statistical accident information
across different subregions, incorporating prior knowledge by assigning
negative lower risk scores to nonaccident instances and positive higher scores
to accident instances to improve the model’s ability to discriminate accident
risk levels. Specifically, we replace the risk of zero value for the subregion
$i$ in each time interval with the negative statistical intensity of the
accident $\pi_{i}$: $\pi_{i}=b_{1}\log_{2}\epsilon_{i}+b_{2}$. Here,
$\epsilon_{i}$ represents the statistical accident indicator that quantifies
the accident risk of subregion $i$. The coefficients $b_{1}$ and $b_{2}$
ensure that the range of $\pi_{i}$ reflects the situation of actual risk
levels.

The zero value elements are therefore adjusted based on the proportion of the
total risk level of the subregion and assigned to the range $[-1,0]$ through
the logarithmic and linear transformations described above. Nonzero values are
normalised to the interval $[0,1]$, thereby preserving the rank of actual
accident risks. It enhances the distinction between positive and negative
samples by making the accident intensity value negative and distinct.

###  3.4 Spatiotemporal Multiview Adaptive HyperGraph Learning Framework

In this section, we describe the details of the proposed SMA-Hyper model, an
adaptive framework for predicting traffic accidents, as illustrated in Figure
3, it is primarily composed of four main modules:

1) Multiview adaptive graph and hypergraph construction: Graphs and
hypergraphs are constructed based on spatial relationships, urban features,
and accident sequences, capturing low-order and high-order relationships
between subregions, respectively. 2) Multiview spatiotemporal feature encoder:
In the multiview context, the propagation of accident characteristics between
pairwise edges and setwise hyperedges captures the complex spatiotemporal
correlations of accident occurrences. 3) Temporal decoder: Integrating
external characteristics, the spatiotemporal embedding vectors of each
subregion are decoded through gated convolutions to generate predictions for
future accident sequences. 4) Local-global contrastive learning: The
contrastive learning between multiview graphs and hypergraphs offers
additional self-supervisory signals to the model, mitigating the negative
impact of data sparsity on model learning.

Figure 3: Overview of the Spatiotemporal Multiview Adaptive HyperGraph
Learning (SMA-Hyper) Framework. Section (a) depicts the graph construction
process, integrating historical accident data with urban features into the
graph and hypergraph structures. Section (b) presents the encoder phase,
incorporating contrastive learning to enhance feature representation and
differentiation. Section (c) illustrates the multi-view fusion decoder, which
synthesizes various urban data streams like POIs and road information,
culminating in the predictive output for traffic accident risks

Detailed information and calculation processes are outlined below.

####  3.4.1 Multiview AdaptiveGraph and Hypergraph Learning

Multiview Graph Embedding Traditional ST-GNN models often rely on predefined
topologies based on spatial connections or interaction weights. This approach
lacks comprehensive geographic relationships and depends on a single
criterion, which limits its ability to generalize across scenarios involving
both static and dynamic urban features (Wang et al.,, 2024; Xiong et al.,,
2023). Additionally, defining these criteria requires specific spatial
knowledge, which is not always available or easily generalizable, especially
when multiple types of views are considered. Inspired by Tobler’s first law
and the third law of geography, which suggest that closer spatial distances
lead to similar target labels and that long-distance spatial interactions can
occur with similar urban configurations, we propose adaptive conventional
graph structure definitions to incorporate evolving configurations from
multiple views rather than relying on a single criterion.

To be specific, for static urban features including POI and the complexity of
the road network, we employ fully connected layers to achieve characteristic
mapping and denote them as $U^{s},s\in\\{P,R\\}$. Meanwhile, the similarity of
historical accident sequences can also provide effective information for
uncovering correlations between different sub-regions. Due to the dynamic
nature of the sequences, we utilise a combination of stacked convolutional
layers and fully connected layers to generate its embedding(Zhang et al.,,
2022), and denote it as $U^{T}$.

After embedding, the non-Euclidean spatiotemporal correlations between sub-
regions are mapped through multiple views: accident spatial view, accident
temporal view, POI view and road view, with each view is constructed by the
pairwise graph $\mathscr{A}^{s}$ and the setwise hypergraph $\mathscr{H}^{s}$,
where $s$ denotes different views.

Pairwise Graph Construction Accident spatial view reflects the impact of
spatial proximity on accident prediction. According to Tobler’s First Law of
Geography, two adjacent regions tend to exhibit a closer spatiotemporal
correlation. Therefore, we utilize the adjacency matrix $A$ as the topology
for this view and denote it as $\mathscr{A}^{S}$.

For the construction of the remaining three views based on adaptive manner,
the extracted features mentioned above are used to establish connections
between sub-regions based on the geography’s third law (Zhu et al.,, 2018).
For instance, two sub-regions with similar POI distribution or historical
accident sequences may share similar accident patterns. Hence, the product of
features is applied to measure the similarity, after which the activation
function $Tanh(\cdot)$ and $Relu(\cdot)$ are used to scale the values to
[-1,1] and eliminate unwarranted negative values:

$\mathscr{A}^{s}=Relu(Tanh(U^{s}U^{s\top})),$ (2)

where $s$ here represents the accident temporal view, POI view and road view,
respectively.

For each sub-region, aggregating information from thousands of other sub-
regions may introduce a significant amount of noise, thereby reducing
predictive performance. Therefore, we set a threshold $k$ for the maximum
number of edges related to each sub-region to control the sparsity of graph.
Specifically, we first sort the values in each row of matrix $\mathscr{A}^{s}$
and retain only the top $k$ values:

$indices_{i}=topk(\mathscr{A}^{s}[i,:]),i=1,2,...,N$ (3)
$\mathscr{A}^{s}[i,:]=\mathscr{A}^{s}[i,indices_{i}],i=1,2,...,N$ (4)

Therefore, we can obtain the pairwise adaptive graphs under the four views,
which are represented as follows: $\mathscr{A}^{S}$ (accident spatial view),
$\mathscr{A}^{T}$ (accident temporal view), $\mathscr{A}^{P}$ (POI view),
$\mathscr{A}^{R}$ (road view).

Setwise Hypergraph Construction The same functional distributions may exert
similar effects on the accident patterns across multiple sub-regions.
Traditional graphs can only model pairwise relationships between two entities,
which results in their limitations, and it is extremely difficult to integrate
distant information through stacked multi-layer signal transmission.
Therefore, we employ hypergraphs to model the high-order relationships among
cross-regional nodes from multi-views, which may exhibit similar accident
patterns, POI distributions, or road characteristics. Consequently, we adopt
an adaptive hypergraph construction approach to automatically mine learnable
high-order similarities.

Different from the adaptive pairwise graph, the adaptive setwise hypergraph is
represented by an incidence matrix $\mathscr{H}^{s}\in\mathcal{R}^{N\times
I}$, where $I$ denotes the number of hyperedges. Each hyperedge is capable of
simultaneously connecting multiple sub-regions, thereby capturing global
higher-order dependencies. We derive $\mathscr{H}^{s}$ by multiplying a
feature matrix $K^{s}\in\mathcal{R}^{d_{s}\times I}$, where $d_{s}$ is the
embedding dimensions of embedding set $s$. Furthermore, we utilize
$Tanh(\cdot)$ and $Relu(\cdot)$ to confine the values of the correlation
matrix within a reasonable range. Similarly, we control the sparsity of
hyperedges through the parameter $k$:

$\mathscr{H}^{s}=Relu(Tanh(U^{s}K^{s})),$ (5)
$indices_{i}=topk(\mathscr{H}^{s}[i,:]),i=1,2,...,N$ (6)
$\mathscr{H}^{s}[i,:]=\mathscr{H}^{s}[i,indices_{i}],i=1,2,...,N$ (7)

where $s$ here also represents the accident temporal view, POI view and road
view, respectively.

It is noteworthy that in accident spatial view, we employ a learnable matrix
$U_{n}^{S}$ to represent the positional embeddings of subregions, with the
expectation that the constructed adaptive hypergraph will uncover higher-order
positional relationships.

$\mathscr{H}^{S}=Relu(Tanh(U^{S}K^{S})),$ (8)

Therefore, we can obtain the corresponding setwise adaptive hypergraphs under
the four views, which are represented as follows: $\mathscr{H}^{S}$ (accident
spatial view), $\mathscr{H}^{T}$ (accident temporal view), $\mathscr{H}^{P}$
(POI view), $\mathscr{H}^{R}$ (road view).

####  3.4.2 Multi-View Spatio-temporal Features Encoder

The extraction of complex spatiotemporal features based on learned multi-view
graphs and hypergraghs presents the next challenge. Graph Convolutional
Network (GCN) is a technique widely employed in the field of spatiotemporal
data mining, which facilitates the learning of spatial dependencies by
aggregating signals from adjacent nodes. In contrast, Heterogeneous Graph
Convolutional Network (HGCN) operates based on high-order relationships within
hypergraphs, contributing to the generation of a more robust spatial
representation. In this context, we propose the multi-view spatio-temporal
features encoder illustrated in Figure 3 (b), which encompasses both graph-
based and hypergraph-based encoders. Each encoder module is composed of a
”sandwich” structure comprising gated temporal convolution blocks and spatial
convolution blocks. Lastly, the spatial features extracted by spatial
convolution blocks are integrated through an attention based fusion block.

Accident Embedding Firstly, an embedding layer is applied to the input $X$ to
generate the initial representation of the historical accident sequence.
Specifically, each element in $X$ is multiplied by a randomly initialized
vector $e$ to obtain its representation: $E_{n,t}=X_{n,t}\cdot e$.

Gated Temporal Convolution Block The prediction of accident risks is
inherently a time series forecasting problem. hence, we extract temporal
features of accident sequences through a dedicated temporal learning block,
names GTC (Gated Temporal Convolution) block. Specifically, the temporal
learning block consists of two stacked temporal convolution modules, each of
which models the contextual information of the sequence via a gating mechanism
to enhance the expressiveness. The equation for each temporal convolution
module is as follows:

$gt(E_{in})=sigmoid(W_{1}E_{in}+b_{1})$ (9) $E_{out}=(1-gT(E_{in}))\cdot
E_{in}+gt(E_{in})\cdot(W_{2}E_{in}+b_{2})$ (10)

where $E_{out}$ represents the output of the time learning block in layer $l$.
$gt(\cdot)$ denotes the gating unit, which facilitates the fusion of residual
connections and learned features. Lastly, $W_{1},W_{2}$ and $b_{1},b_{2}$ are
the learnable parameters of the convolutional layers.

Graph Convolution Block Extensive research in the past has demonstrated that
Graph Convolutional Network (GCN) possesses remarkable capabilities in
learning and aggregating spatial relationships. Based on the constructed
multi-view topology, stacked graph convolutional blocks are capable of
capturing spatial relationships ranging from one-hop to multi-hops. The
spatial convolution block is defined as follows:

$E_{out}^{s}=ReLU(\mathscr{A}^{s}E_{in}W_{3}),$ (11)

where $\mathscr{A}^{s}$ is the normalized adjacency matrix in view $s$, and
$E_{out}^{s}$ is the hidden representation obtained therefrom. $W_{3}$
represents the weights of the corresponding convolutional kernels. It is worth
noting that graph convolution block generates corresponding representations
under the topology of 4 views respectively. Consequently, we can derive multi-
view representations: $E^{s},s\in\\{S,T,P,R\\}$.

Hypergraph Convolution Block In previous works, the higher-order relationships
between sub-regions have been overlooked. Hypergraph convolution can uncover
the high-order spatial relationships between sub-regions, thereby achieving
more advanced representations. Unlike graph convolution, hypergraph
convolution calculates based on the incidence matrix and can be expressed as:

$\widehat{E}_{out}^{s}=ReLU({D_{R}^{s}}^{-1/2}\mathscr{H}^{s\top}{D_{E}^{s}}^{-1/2}ReLU({D_{E}^{s}}^{-1/2}\mathscr{H}^{s}{D_{R}^{s}}^{-1/2}E_{in}^{s}W_{4}))$
(12)

where ${D_{R}^{s}}$ and ${D_{E}^{s}}$ denote diagonal degree matrices of
$\mathscr{H}^{s},s\in\\{S,T,P,R\\}$. $W^{H}$ denotes the weights of the
hypergraph convolution. Similarly, based on the incidence matrix
$\mathscr{H}^{s}$ constructed under 4 views mentioned above, we can obtain the
corresponding hypergraph representations $\widehat{E}^{s},s\in\\{S,T,P,R\\}$.

Attention-based Multi-View Features Fusion Block: For different accident
sequence patterns, it is necessary to pay closer attention to specific views,
where the multi-head attention mechanism can assist in capturing the complex
relationships among them. For adaptive pairwise graphs and adaptive setwise
hypergraphs, we utilize the Transformer module to fuse the spatial-temporal
representations of 4 views, respectively:

$E_{out}=Transformer(E_{in}^{S},E_{in}^{T},E_{in}^{P},E_{in}^{R}),$ (13)

$\widehat{E}_{out}=Transformer(\widehat{E}_{in}^{S},\widehat{E}_{in}^{T},\widehat{E}_{in}^{P},\widehat{E}_{in}^{R}),$
(14)

where $E_{out}$ and $\widehat{E}_{out}$ denote the multi-view fused spatial-
temporal representions based on graphs and hypergraphs, respectively.

Attention-based Multi-Layer Features Fusion Block: The accident features are
processed sequentially through the gated temporal convolution block, the
multi-view graph and hypergraph convolution block, and another gated temporal
convolution block, resulting in the outputs of each layer. The outputs of
different layers encapsulate spatio-temporal features of varying levels. The
higher-level outputs aggregate multi-step spatiotemporal information through
the propagation and convergence of stacked signals. Traditional methods based
on average pooling assign the same weight to each layer, which may limit the
expressiveness of the fused representations. Therefore, in the face of multi-
layer spatial-temporal features $E^{l},l=1,2,...,L$ and
$\widehat{E}^{l},l=1,2,...,L$, we employ an attention module to capture the
relationships among the different layers:

$E^{encoder}=Transformer(E_{t}^{1},E_{t}^{2},...,E_{t}^{L}),$ (15)

$\widehat{E}^{encoder}=Transformer(\widehat{E}_{t}^{1},\widehat{E}_{t}^{2},...,\widehat{E}_{t}^{L}),$
(16)

Here,we can get the graph-based and hypergraph-based encoder outputs:
$E^{encoder}$ and $\widehat{E}^{encoder}$.

####  3.4.3  Temporal Decoder Incorporating External Features

Dynamic external features encompass weather and calendar information. Extremes
in weather conditions, such as rain and snow, may result in a further increase
in accident risk. Similarly, during specific time periods within a week,
heavier traffic congestion may also increase the risk of accidents . Hence,
when decoding, dynamic external features should be incorporated as part of the
input and fused with encoder outputs, and we can obtain the decoder outputs as
follows:

$E^{decoder}=GTC([E^{encoder},W^{M}X^{M},W^{C}X^{C}]),$ (17)

where $GTC(\cdot)$ indicates the gated temporal convolution block. $[\cdot]$
refers to the concatenation option, in which $X^{M},X^{C}$ are matrices of
external features, and $W^{M},W^{C}$ are learnable parameters of external
features embedding. Following this, we can obtain the decoder outputs
$E^{decoder}$ and $\widehat{E}^{decoder}$, respectively, based on the outputs
of the graph encoder and hypergraph encoder .

Finally, incorporating urban features including POI and road statistical
information is crucial for prediction as well. For instance, certain specific
POIs such as supermarkets and hospitals, due to their surroundings with higher
traffic density, may lead to a higher level of accident risk. Therefore, the
last prediction layer can be modeled as:

$Y=FC(ReLU(FC([E^{decoder},W^{P}X^{P},W^{R}X^{R}])))$ (18)

In this formula, we recalculate the embeddings for urban features, as the
purpose here is to assess the impact of urban features on accident risk
prediction. In contrast, embeddings $U^{P}$ and $U^{R}$ are designed to
uncover the similarities in the distribution of urban features across
different regions. Ultimately, the output $Y$ of the prediction layer is taken
as the predictive outcome of the model.

####  3.4.4 Local-Global Contrastive Learning

The local spatio-temporal encoder based on pairwise graph is capable of
aggregating local information from multiple hops through multi-layer graph
convolutions, while the global spatio-temporal encoder based on setwise
hypergraph can facilitate higher-order cross-region information learning. To
facilitate the alignment and integration of the information of local and
global encoders, we employ cross-view contrastive learning. It promotes the
collaborative supervision between the local and global encoders through self-
supervised learning, thereby providing additional supervisory signals and
mitigating the impact of data sparsity. Moreover, the resultant more robust
spatio-temporal embeddings can reduce the influence of input noise.

Specifically, in our cross-view contrastive learning module, embeddings based
on pairwise graphs and embeddings based on setwise hypergraphs from the same
view and the same sub-region are treated as positive samples, while those from
different views or sub-regions are considered negative samples. Consequently,
the loss function can be formulated as follows:

$\mathcal{L}^{(C)}=\sum_{s}\sum_{l=1}^{L}\sum_{n=1}^{N}\log\frac{\exp(\cos(E_{n}^{l,s},\widehat{E}_{n}^{l,s}))}{\sum_{n^{\prime}}\exp(\cos(E_{n}^{l,s},\widehat{E}_{n^{\prime}}^{l,s}))}$
(19)

In which $s\in\\{S,T,P,R\\}$ represents spatial accident view, temporal
accident view, POI view and Road view, respectively, and $L$ is a
hyperparameter that denotes the number of stacked layers of multi-View spatio-
temporal features encoder.

####  3.4.5 Model Optimisation

In the model optimisation process, we employ the Mean Squared Error (MSE)
function to gauge the accuracy of the prediction results. Incorporating the
aforementioned contrastive learning loss, the ultimate joint loss function
obtained is as follows:

$\mathcal{L}=\sum(Y-\widehat{Y})^{2}+\lambda_{1}\mathcal{L}^{(C)}+\lambda_{2}\|\boldsymbol{\Theta}\|_{2}^{2}$
(20)

where $Y_{t}$ and $\widehat{Y}_{t}$ represent the actual and predicted
accident risk scores, respectively. $\boldsymbol{\Theta}$ denotes the
learnable parameters, and a regularisation loss based on the $L_{2}$ norm is
applied to prevent overfitting. Lastly, $\lambda_{1}$ and $\lambda_{2}$ are
hyperparameters, representing the weights for contrastive learning loss and
the regularisation loss, respectively.

##  4 Experiments

###  4.1 Dataset

The proposed SMA-Hyper model was evaluated using London traffic accident data
from the STATS19
dataset111https://www.data.gov.uk/dataset/cb7ae6f0-4be6-4935-9277-47e5ce24a11f/road-
safety-data, officially published by the Department of Transport, UK. This
dataset is collected from police reports, so incidents without injuries are
not included. The dataset provides detailed information about the vehicles and
casualties involved, as well as the geographical location and time of each
incident. The data were pre-processed and formatted using the R package
‘stats19’ by Lovelace et al., (2017).

For this study, we used a total of 23,096 accidents in London from 1 January
to 31 December 2021. The breakdown of accident severity is as follows: slight
accidents account for 19,624 incidents (84.97%), serious accidents for 3,399
incidents (14.72%), and fatal accidents for 73 incidents (0.31%).

For the spatial unit, we used Middle Super Output Areas (MSOAs), which are
official census units with an average area of 19 square kilometers. Unlike
manually divided grids, MSOAs offer several advantages for deep learning
embeddings: (1) Consistency with Demographic Data: MSOAs are designed to be
consistent with demographic data, providing a robust framework for integrating
socio-economic variables into the model. This improves the model’s ability to
learn complex exposure patterns related to traffic accidents. (2) Population
homogeneity: MSOAs contain populations that are relatively homogeneous in
terms of socio-economic characteristics. This helps reduce variability within
each unit, making the model’s learning process more effective. (3)
Administrative Relevance: Using MSOAs aligns the model with administrative
boundaries, which is beneficial for policy-making and urban planning. Local
authorities can directly use predictions made by the model for targeted
interventions. (4) Geographic accuracy: MSOAs provide more accurate
geographical representations compared to grid-based divisions. They account
for natural and built environment features, which are crucial for accurately
capturing the spatial dynamics of traffic accidents.

Therefore, we spatially joined the traffic accident data points to a total of
1,002 MSOAs, with temporal prediction resolutions of 24 hours and 12 hours,
respectively. Figure 4(a) shows the spatial density of traffic accidents in
each MSOA for 2021. It demonstrates the spatial inequality in accident risk
across all regions, and the non-grid spatial shapes provide a density
measurement based on socio-demographic and size exposure effects. Figure 4(b)
illustrates the daily count of traffic accidents in London throughout 2021,
along with a 7-day moving average to smooth the trend and highlight patterns
over time.

For multiview urban configuration, we used POI data and road network data from
Ordnance Survey through the Digimap
platform222https://digimap.edina.ac.uk/help/our-maps-and-data/os_overview/.
Meteorological data was obtained from the MIDAS
platform333https://archive.ceda.ac.uk/, providing hourly weather information.
Calendar information was automatically generated using the Python package
‘holidays’444https://pypi.org/project/holidays/.

(a) The density map of traffic accidents for MSOAs. It is calculated by
dividing the number of non-zero elements (accidents happened) by the size and
people count of each MSOA.

(b) Daily cycling accident counts and 7-day moving average from January 1,
2021, to December 31, 2021. The grey line shows daily accident counts, and the
orange line represents the 7-day moving average. Shaded regions indicate
different periods: training (light yellow, January 1 - August 1), validation
(white, August 1 - October 1), and testing (light green, October 1 - December
31). This segmentation aids in model training and evaluation.

Figure 4: Spatial and Temporal Comparison of traffic accident data
visualizations of London, 2021.

###  4.2 Baselines

For a comprehensive comparison, we choose four major types of model with in
total 9 models as the baselines and SOTA models. The details are listed below.

  * •

Traditional Models

    * –

ARIMA (Box et al.,, 1976): The Autoregressive Integrated Moving Average
(ARIMA) is a classical model used for time series prediction. It predicts
future accidents based on the average of historical accident risk as well as
autoregressive patterns.

    * –

SVR (Drucker et al.,, 1996): Support Vector Regression (SVR) is a variant of
Support Vector Machine (SVM) designed for regression tasks. It predicts future
sequences by training an optimal regression curve and allows accident data
points to deviate from the regression curve to enhance generalisation
capabilities.

  * •

Spatial/Temporal Deep Learning Models

    * –

Hetero-Convlstm (Yuan et al.,, 2018): The Convolutional Long Short-Term Memory
(Hetero-ConvLSTM) network is the first model to address the spatial
heterogeneity challenge in the large amount of accident data, while handling
long-term dependencies.

    * –

GRU (Cho et al.,, 2014): The Gated Recurrent Unit (GRU) is a variant of RNNs
with fewer parameters and a simpler structure compared to the traditional
LSTM. It uses two gates, the update gate and the reset gate, to manage the
flow of information.

    * –

GCN (Kipf and Welling,, 2016): The Graph Convolutional Network (GCN) is a
classical spatial learning model capable of aggregating feature information
from surrounding locations layer by layer.

  * •

Spatiotemporal Graph Models

    * –

STGCN (Yu et al.,, 2017): The Spatiotemporal Graph Convolutional Network
(STGCN) leverages spatial convolutions to aggregate feature information from
adjacent geographical locations and gated convolutions to enhance temporal
feature extraction, making it popular for spatiotemporal data mining.

    * –

DSTGCN (Yu et al.,, 2021): The Deep Spatio-Temporal Graph Convolutional
Network (DSTGCN) integrates spatial learning layers and spatiotemporal
learning layers to learn from static and dynamic data. Consider both the
accident sequence and the influence of external factors, representing the
state of the art in this category.

  * •

Spatiotemporal HyperGraph Models

    * –

HyGCN (Wang and Zhu,, 2024): The Hybrid Graph Convolutional Network (HyGCN)
represents state-of-the-art work in hypergraphs-based urban computing. It
captures higher-order relationships, achieving a spatial fusion of pairwise
lower-order and higher-order relationship features in urban mobility flow
predictions.

    * –

SST-DHL (Cui et al.,, 2024): The Sparse Spatio-Temporal Dynamic Hypergraph
Learning (SST-DHL) model represents the latest advancement in self-supervised
accident prediction by addressing the sparsity issue with hypergraph. It
employs a cross-regional dynamic hypergraph learning approach to identify
global spatiotemporal dependencies of accdient data and introduces contrastive
learning to provide supervisory signals, thereby enhancing model performance.

Experiment Configuration and Hyperparameter Settings: The proposed SMA-Hyper
model is implemented using PyTorch, and all training and testing are conducted
on an NVIDIA A40 GPU. We use the Adam optimiser to optimise model parameters,
with a learning rate set to 0.001. The batch size is adjusted to 4, 8, 16
based on GPU memory usage. The ratio of hyperedges to regions is set to 0.1,
retaining the top 40 regions with the highest weights in each hyperedge. The
embedding dimension is uniformly set to 32, and the number of attention heads
is set to 8. To learn high-order complex spatiotemporal relationships, we
stack 2 layers each of spatiotemporal encoders and convolutional decoders. In
the loss function, we choose the coefficients as 0.001. The sequence length is
set to 12 steps, with an 80% training ratio.

Evaluation Metrics: We employ Root Mean Squared Error (RMSE) and Mean Absolute
Error (MAE) to measure the accuracy of accident risk predictions, as well as
Recall at top K (Rec@K) to evaluate the ability to identify high-risk regions
wherereal accidents happen. For our evaluation, we choose $K=20\%$. The
formulas for multi-step predictions are as follows:

$\text{RMSE}=\sqrt{\frac{1}{L}\sum_{t’=T+1}^{T+L}(y_{t’}-\hat{y}_{t’})^{2}}$
(21)

$\text{MAE}=\frac{1}{L}\sum_{t’=T+1}^{T+L}|y_{t’}-\hat{y}_{t’}|$ (22)

$\text{Rec@K}=\frac{1}{L}\sum_{t’=T+1}^{T+L}\frac{|R_{t’}\cap\hat{R}_{t’}|}{|R_{t’}|}$
(23)

where $y_{t’}$ and $\hat{y}_{t’}$ are the true and predicted risk scores of
all districts in the time interval $t’$, respectively; and $L$ is the duration
of the prediction. $R_{t’}$ and $\hat{R}_{t’}$ are the sets of the top actual
and predicted districts of the highest risk $K$, respectively. Given that
accident risk data are zero-inflated with a large amount of nonrisk (zero)
entries and is very left-skewed, lower RMSE values indicate more accurate
predictions by heavily penalising larger errors, making RMSE particularly
sensitive to extreme error values. Lower MAE values reflect more accurate
predictions by providing a straightforward average error measure, which is
less influenced by extreme values compared to RMSE, making it useful for
understanding average prediction accuracy across all regions. Higher Rec@K
values indicate the effectiveness of the model in identifying high-risk
districts where real accidents occur.

###  4.3 Results

####  4.3.1 Overall Performance

To comprehensively evaluate the effectiveness of the proposed SMA-Hyper model,
we conducted experiments on two temporal scales of the London accident
dataset: 12-hour and 24-hour intervals. For these experiments, the model uses
12 input steps to generate multi-step predictions over 6 output steps. The
sparsity of the data is indicated by the ratio of non-zero instances within
the tensor of each dataset, reflecting the inherent challenges of predicting
rare events.

MultiStep Overall Performance: Table 1 summarises the performance metrics of
the models, averaged over the multiple time horizons. This provides a clear
comparison of the overall predictive accuracy of each model across multiple
time horizons. Our SMA-Hyper model consistently demonstrates superior average
performance compared to both traditional and state-of-the-art baseline models.
Specifically, it achieves over 50% improvement in regression metrics such as
RMSE and MAE, and approximately 13.79% and 13.96% improvements in accurately
identifying scenarios where accidents occurred within the predicted high-risk
regions. In particular, Table 1(a) shows that the SMA-Hyper model yields more
accurate prediction results for the 12-hour interval compared to the 24-hour
interval. However, the improvements are more pronounced in the 24-hour
interval, which has a higher occurrence of accidents (6.01% non-zero
instances) as indicated in Table 1(b). The increased improvement in the
24-hour interval can be attributed to the higher volume of accidents,
providing a richer accident scenario that allows the model to be sensitive to
accident patterns.

However, despite the greater improvements, the 24-hour interval data show less
accuracy compared to the 12-hour data. This is likely due to the coarser
temporal resolution of the 24-hour interval, which aggregates accident data
over longer periods, potentially smoothing out finer details that could be
crucial for precise predictions. The 12-hour interval, with its finer temporal
granularity, retains more detailed encoding information about accident
occurrences, leading to higher accuracy in predictions. In particular, the
adaptive graph learning component and the contrastive fusion of multi-urban
views in both setwise graph and pairwise Hypergraph modules enable our model
to effectively learn spatial heterogeneities and overcome spatial-temporal
oversmoothing issues associated with sparsity. This results in better recall
scores for accident identification(around 40% in both temporal resolution
datasets), demonstrating the robustness and effectiveness of the SMA-Hyper
model in handling complex urban traffic accident prediction tasks with multi-
urban views.

Moreover, in the baseline models, we observe an overall inferior performance
with the 24-hour data compared to the corresponding 12-hour data, due to the
fact that there are less data available for sufficient training with coarse-
grained temporal levels. Despite this, the hypergraph-based models continue to
lead the baselines in individual metrics. In particular, SST-DHL, the state-
of-the-art hypergraph model for accident prediction, demonstrates a promising
approach in predicting overall accident risk scores with lower errors in RMSE
among all baselines. However, its performance is restricted by relying solely
on self-supervised learning from historical accident data, lacking integration
of urban configuration views (Cui et al.,, 2024).

The STGCN model shows the highest Recall performance compared to hypergraph-
based baseline models. This superior Recall performance can be attributed to
the effective use of spatial convolutions by STGCN, which aggregate feature
information from adjacent geographical locations, and gated convolutions with
enhanced temporal feature extraction. This dual approach allows STGCN to
capture more relevant spatiotemporal patterns, making it more adept at
identifying high-risk regions where actual accidents occur. In contrast, while
hypergraph-based models like SST-DHL can capture higher-order relationships
and offer robust predictions, their complexity might lead to overfitting,
especially in sparse datasets. The intricate nature of hypergraphs can
sometimes obscure the direct spatiotemporal correlations needed for accurate
high-risk identification, thus affecting their Recall performance (Wang and
Zhu,, 2024). It shows the need for the sparsity-considered hypergraph learning
framework.

Timewise Stability Performance: To gain a comprehensive understanding of our
SMA-Hyper model’s consistent strengths in predicting the risks of traffic
accidents under varying conditions, Figure 5 presents the timewise
performance. Specifically, the 24-hour baseline models exhibit more
fluctuations, as indicated by Figure 5(b), due to limited training data. When
comparing all the metrics across the four major types of models, the
hypergraph-based models demonstrate relatively stable performance over time.
Among these, the SMA-Hyper model shows the highest stability in Recall. This
stability can be attributed to the high-order spatial relationships captured
by hypergraphs, which enable the model to maintain consistent performance
despite the variability in data. Thus, By effectively capturing complex
spatiotemporal patterns in a reliable way, SMA-Hypercan better support the
multi-steps management and planning of traffic safety interventions.

Spatial Robustness Performance: Figure 6 illustrates the spatial robustness
performance of the SMA-Hyper model across various regions, encompassing non-
risk, low-risk, and high-risk accident occurrences. The accident density map
(Figure 4(a)) reveals that accidents predominantly occur in central London and
a few regions in outer London, surrounded by a large number of non-accident
regions. The SMA-Hyper model integrates urban configurations as external
supplementary information and transcends local spatial constraints by
capturing high-order relational similarities among different regions. This
approach enhances global fairness in encoding performance, mitigating issues
such as overfitting or oversmoothing for outputs, particularly in critical
locations.

Traditional graph neural networks (GNNs) are constrained in accident
prediction primarily due to their reliance on pairwise relationships (Cui et
al.,, 2024). These models aggregate information from immediate neighbours
based on predefined spatial links, which may not adequately capture the
complex, non-local interactions inherent in urban traffic systems (Li et al.,,
2024). Given the highly localised nature of accident data, with a significant
concentration in central regions and sparse occurrences in others, GNNs often
struggle to generalise throughout the spatial landscape. This limitation is
exacerbated by the zero-inflation issue, where the predominance of non-
accident regions leads to oversmoothing and reduced model sensitivity to
actual accident hotspots.

On the other hand, pure hypergraph models that focus solely on accident data
are also constrained. While hypergraphs can capture higher-order relationships
and provide a richer representation of complex interactions, models that rely
exclusively on historical accident data lack the contextual information
provided by urban configurations (Wang and Zhu,, 2024). This limitation
reduces their ability to generalise and predict accidents in regions where
historical data is sparse or non-existent. Additionally, self-supervised
learning frameworks based solely on accident data may not fully leverage the
spatial and urban heterogeneities that influence accident occurrences.

The SMA-Hyper model addresses these limitations by integrating both
traditional graph-based approaches and hypergraph learning. By incorporating
urban configuration data and capturing high-order spatial relationships
through hypergraphs, the SMA-Hyper model effectively learns from the complex,
multi-faceted nature of urban environments. This comprehensive approach allows
the model to handle the inherent sparsity and variability in traffic accident
data, leading to improved predictive accuracy and spatial fairness.
Consequently, the SMA-Hyper model offers a more reliable and equitable
foundation for urban traffic management and decision-making processes,
supporting the development of targeted interventions and policies to enhance
road safety.

Model Class | Model | 12 Hours (3.07%)
---|---|---
RMSE | MAE | Recall@20%
Traditional Models | ARIMA | 0.4315 | 0.2046 | 11.20
SVR | 0.4198 | 0.3109 | 12.22
Spatial/Temporal Deep Learning Models | Hetero-Convlstm | 0.2319 | 0.0686 | 26.91
GRU | 0.2319 | 0.0645 | 27.08
GCN | 0.2317 | 0.0703 | 32.68
Spatiotemporal Graph Models | STGCN | 0.2322 | 0.0581 | 35.40
DSTGCN | 0.2331 | 0.0572 | 34.92
Spatiotemporal HyperGraph Models | HyGCN | 0.2337 | 0.0562 | 26.36
SST-DHL | 0.2316 | 0.0664 | 26.01
SMA-Hyper(Ours) | 0.1140 | 0.0277 | 40.28
| Improvements | 50.77%$\downarrow$ | 50.71%$\downarrow$ | 13.79%$\uparrow$
(a) Performance comparison for 12 Hours time interval.

Model Class | Model | 24 Hours (6.01%)
---|---|---
RMSE | MAE | Recall@20%
Traditional Models | ARIMA | 0.5918 | 0.3860 | 11.98
SVR | 0.5654 | 0.3966 | 15.95
Spatial/Temporal Deep Learning Models | Hetero-Convlstm | 0.3335 | 0.1329 | 25.88
GRU | 0.3247 | 0.1224 | 24.06
GCN | 0.3234 | 0.1226 | 32.90
Spatiotemporal Graph Models | STGCN | 0.3242 | 0.1112 | 34.32
DSTGCN | 0.3394 | 0.1485 | 27.27
Spatiotemporal HyperGraph Models | HyGCN | 0.3249 | 0.1136 | 26.66
SST-DHL | 0.3238 | 0.1108 | 24.47
SMA-Hyper(Ours) | 0.1527 | 0.0462 | 39.11
| Improvements | 52.84%$\downarrow$ | 58.30%$\downarrow$ | 13.96%$\uparrow$
(b) Performance comparison for 24 Hours time interval.

Table 1: Performance comparison for 12 & 24 Hours time interval. The bold font
means the best performance, while the underline indicates the second best
performance. The zero-inflation rate is highlighted in parentheses.

(a) Model performance at 12 hours across all evaluation metrics

(b) Model performance at 24 hours across all evaluation metrics

Figure 5: Step-wise performance on all evaluation metrics for different
models. Figure 6: Prediction Error Visualization of different methods over
MSOA regions in the entire urban space of London (12 Hours Results).

####  4.3.2 HyperEdge Examination and Analysis

Figure 7 presents a detailed analysis of hyperedges, utilizing multiple urban
views to understand how different factors contribute to accident risks. To
maintain consistency in the analysis, min–max normalization is applied to all
data, allowing us to dynamically capture complex, high-order correlations of
traffic accidents occurring both near and far among all city regions (Cui et
al.,, 2024).

Figure 7(a) illustrates the temporal dynamics of each hyperedge in the five
most relevant regions, providing a clear representation of how the dynamic
hypergraph captures higher-order correlations with time variation. Each view
captures different aspects of the urban environment, and the shades of color
reveal traffic accident risk patterns in different views. The similar colors
in each hypergraph clearly demonstrate that our SMA-Hyper model can capture
the global dependence of different geographical regions in various urban
configurations with similar traffic accident scenarios. Furthermore, the
dynamic hyperedges consistently maintain similar global dependencies over
input time, as illustrated by the nuanced changes in colors in the correlation
matrix as time shifts.

Figure 7(b) provides spatial heat maps for the encoded relations of regions
within the sampled local hyperedges. These maps illustrate the complex spatial
distribution and intensity of hyperedges across different regions, showing how
local factors influence the formation and relevance of hyperedges. Compared to
the ground truth density map in Figure 4(a), the sampled hyperedges
effectively capture similar-density accident regions within each hyperedge,
demonstrating the model’s ability to identify critical areas. For example, as
depicted by hyperedge 0 in the accident views, this ability to capture regions
with similar dense accident occurrence patterns, even if they are distant from
each other, underscores the robustness and effectiveness of the SMA-Hyper
model.

(a) Temporal evaluation of the five most relevant regions to hyperedges. These
maps highlight the temporal dynamics of hyperedges in different regions,
providing insights into how certain areas are affected over time. The five
regions on each hyperedge are expected to have similar accident risk scores,
indicating a consistent pattern of hypergraph dynamics.

(b) Spatial heat maps for the encoded relations of regions within sampled
local hyperedges. These maps show the spatial distribution and intensity of
hyperedges across different regions, illustrating how local factors influence
hyperedge formation and relevance. It is expected that each hyperedge would
capture the high-order cross-regional relations, reflecting complex spatial
interactions.

Figure 7: Visualization of relevance weights of hyperedges from hypergraph
learning. The left panel (a) provides a temporal evaluation of the five most
relevant regions to hyperedges, while the right panel (b) presents spatial
heat maps of regions to local hyperedges.

####  4.3.3 Ablation Studies with Model Configurations

To evaluate the impact of various components within our framework, including
PKDE for mitigating imbalanced accident labels, contrastive learning,
attention mechanisms, and hypergraph learning, an ablation study was
conducted. This study aimed to evaluate the contributions of these components
to the predictive precision of urban traffic accidents while integrating two
urban configurations (POI and Roads) for comprehensive node representation.
Each variable was individually added, while all other modules were kept
constant, as shown in Figure 8.

In general, PKDE demonstrated the most significant positive impact on the
improvement of the SMA-Hyper model, resulting in substantial reductions across
all metrics, particularly with an increase in recall of more than 10%. It is
important to note that the baseline models referred to in Table 1 were all
tested without the PKDE strategy. However, even when this strategy is
eliminated, the SMA-Hyper model consistently outperforms these baseline
models.

Regarding the ablation performance of cCL, hypergraph learning, and the
attention mechanism, three key elements of our framework, the absence of
hypergraph learning resulted in the most significant decrease in performance.
Specifically, the reduction ratios ranged from 7.98% to 9.47% in RMSE, 155.59%
to 87.00% in MAE and 7.1% to 7.7% in Recall. Furthermore, the 24-hour data
set, with its limited training data, showed greater sensitivity to all
framework modules, further underscoring the importance of these components in
our model.

For the urban view, incorporating the POI and Road data resulted in improved
performance, although the improvement was modest. However, the Road view
played a more significant role in contributing to better results. In
particular, the inclusion of road information results in an improvement in
MAE, highlighting the importance of road characteristics in accurately
predicting accident risks, which also corresponds to previous studies
(Mannering and Bhat,, 2014; Wang et al.,, 2021; Yang et al.,, 2022). This is
likely due to the direct influence that the types, conditions, and
infrastructure of roads have on traffic safety, making them critical factors
in the predictive capabilities of the model.

(a) RMSE at 12 Hours and 24 Hours.

(b) MAE at 12 Hours and 24 Hours.

(c) Recall at 12 Hours and 24 Hours.

Figure 8: Performance comparison of different model configurations evaluated
using MAE, RMSE, and Recall metrics at 12-hour and 24-hour intervals.

####  4.3.4 Sensitivity studies for hyperperameter

We evaluated the model using different hyperparameters, including the loss
parameter $\lambda_{1}$, the length of the input sequence, the training ratio,
and the number of GCN layers, to justify our choices in corresponding
settings. The experiments are carried out on 12-hour and 24-hour intervals,
and performance is assessed using RMSE, MAE, and Recall metrics. The results
are summarised in Table 2.

The parameter $\lambda_{1}$ controls the ratio of cross-graph and hypergraph
contrastive learning, achieving balanced performance at 0.1. Although the RMSE
is slightly lower for the 24-hour prediction at $\lambda_{1}=1$, metrics such
as MAE and Recall are more sensitive to accurate and precise predictions. The
value of $\lambda_{1}=0.1$ achieves superior results in these metrics compared
to $\lambda_{1}=1$, indicating that this setting helps the model better
identify high-risk regions and maintain lower prediction errors. This is
crucial for practical applications where accurately pinpointing accident-prone
areas is more important than marginal improvements in RMSE.

A similar situation occurs with the GCN layers. We chose 2 layers as the
optimal parameter, although 3 layers show slightly lower RMSE for the 24-hour
interval. Increasing the number of GCN layers can lead to over-smoothing,
where node representations become indistinguishable due to excessive
aggregation of information. This degrades the ability of the model to
distinguish between different nodes, leading to poorer performance on metrics
such as MAE and Recall, which are sensitive to precise predictions.
Furthermore, adding more layers increases the complexity of the model, which
can lead to overfitting, especially when training data is sparse, such as in
the case of 24-hour intervals. Overfitting can result in the model capturing
noise rather than meaningful patterns, negatively affecting generalisation
performance.

For sequence length and training ratios, these hyperparameters are all about
the quality of training data. Although higher training ratios show better
results, longer input sequence lengths are not always optimal. Longer
sequences can introduce more noises and uncertainties into the training
process, potentially degrading model performance(Trirat et al.,, 2023).

$\lambda_{1}$ | 12 Hour / 24 Hours
---|---
|  RMSE |  MAE |  Recall (%)
0.001 |  0.1302/0.1648 |  0.0667/0.0849 |  37.55/36.33
0.01 |  0.1164/0.1604 |  0.0304/0.0857 |  37.74/37.17
0.1 |  0.1140/0.1527 |  0.0277/0.0462 |  40.28/39.11
1 |  0.1143/0.1525 |  0.0288/0.0476 |  39.85/38.49
(a) Performance on different tests of $\lambda_{1}$ as loss parameters.

Sequence |  |  |
---|---|---|---
Length | 12 Hour / 24 Hours
|  RMSE |  MAE |  Recall (%)
8 |  0.1142/0.1531 |  0.0293/0.0488 |  39.02/37.00
10 |  0.1145/0.1530 |  0.0288/0.0518 |  39.63/37.77
12 |  0.1140/0.1527 |  0.0277/0.0462 |  40.28/39.11
14 |  0.1143/0.1529 |  0.0284/0.0501 |  39.69/38.41
16 |  0.1145/0.1533 |  0.0279/0.0505 |  40.09/38.61
(b) Performance on varying input sequence length.

Training |  |  |
---|---|---|---
Ratio | 12 Hour / 24 Hours
|  RMSE |  MAE |  Recall (%)
0.5 |  0.1161/0.1533 |  0.0305/0.0477 |  38.22/38.83
0.6 |  0.1154/0.1528 |  0.0294/0.0499 |  39.74/38.93
0.7 |  0.1172/0.1544 |  0.0291/0.0495 |  39.94/38.81
0.8 |  0.1140/0.1527 |  0.0277/0.0462 |  40.28/39.11
(c) Performance on training ratio.

GCNs |  |  |
---|---|---|---
Layers | 12 Hour / 24 Hours
|  RMSE |  MAE |  Recall (%)
1 |  0.1306/0.1636 |  0.0655/0.0842 |  37.89/36.93
2 |  0.1140/0.1527 |  0.0277/0.0462 |  40.28/39.11
3 |  0.1145/0.1502 |  0.0283/0.0488 |  40.07/38.89
4 |  0.1149/0.1539 |  0.0284/0.0478 |  39.92/38.90
5 |  0.1145/0.1508 |  0.0286/0.0499 |  40.07/38.91
(d) Performance on the number of GCNs layers.

Table 2: Ablation study: Comparison of performance on different tests of
$\lambda_{1}$ as loss parameters, varying input sequence length, training
ratio and GCNs layers for 12-hour and 24-hour intervals. Each table presents
the RMSE, MAE, and Recall metrics.

##  5 Conclusion

The SMA-Hyper framework consistently demonstrates superior and robust
performance in multistep urban traffic accident prediction by effectively
addressing the challenges posed by data sparsity and the need for precise
identification of high-risk areas. It integrates adaptive graph learning and
employs both setwise and pairwise contrastive graph representation learning
techniques to dynamically capture spatial heterogeneities and homogeneities.
Additionally, with the help of PKDE, the framework overcomes the limitations
of traditional and state-of-the-art models. By leveraging hypergraph learning,
the SMA-Hyper model effectively captures high-order spatiotemporal dynamics,
offering a comprehensive understanding of the complex interactions between
various urban factors. Incorporating diverse urban configurations, such as POI
and road network data, the model achieves a more feasible and explainable
representation of the urban environment. This multiview fusion approach
enables the model to adapt to the dynamic nature of urban traffic patterns,
thereby improving predictive accuracy across different temporal scales.

Extensive experiments on the London traffic accident dataset reveal that the
SMA-Hyper model significantly improves key performance metrics, including
RMSE, MAE, and Recall. The model’s ability to maintain high performance under
varying temporal conditions and data sparsity underscores its robustness and
reliability for practical applications in urban traffic management.

Despite its strengths, the SMA-Hyper model has some limitations. The
complexity of the model increases computational requirements, which may be a
constraint in real-time applications. Furthermore, while the model integrates
multiple urban views, it may still miss certain contextual nuances that could
further enhance prediction accuracy. Future work could explore the inclusion
of more diverse data sources and the optimisation of computational efficiency.

Overall, the SMA-Hyper model represents a significant advancement in multistep
traffic accident prediction, providing valuable insights and a solid
foundation for the development of targeted interventions and policies aimed at
enhancing road safety in urban environments.

##  6 CRediT authorship contribution statement

##  7 Declaration of Competing Interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

##  8 Data availability

Data could be downloaded publicly.

##  9 Acknowledgments

The authors thank Dr. Lu Yin, Mr. Zheyan Qu, and the anonymous referees for
their insightful comments.

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