ST-TAR: An Efficient Spatio-Temporal Learning Framework for Traffic Accident Risk Forecasting

1 Introduction

Urbanization and the proliferation of vehicles have caused traffic accidents to become one of the world's largest publichealth threats. The Global Plan for the Decade of Action for Road Safety 2021-2030 [Organization and others, 2021] reports nearly 1.3 million avoidable deaths and around 50 million injuries worldwide yearly due to road accidents. Moreover, as it stands without intervention measures, there will be an estimated 13 million deaths and 500 million injuries in the next decade. In light of these disconcerting statistics, advanced accident prediction mechanisms are urgently needed to identify and mitigate risks as early as possible, safeguarding public health and safety.

∗Corresponding authors.

Traffic accidents are influenced by various spatio-temporal factors [Bergel-Hayat et al., 2013; Trirat et al., 2023]. Traditional statistical learning-based methods [Sharma et al., 2016; Barba et al., 2014] struggle to capture the complex correlations, while deep learning modules such as Graph Convolutional Networks (GCN) [Kipf and Welling, 2017] and Transformers [Vaswani, 2017] have emerged as powerful tools for modeling spatial dependencies and temporal patterns. Deep learning-based methods [Wang et al., 2021; An et al., 2022; Wang et al., 2023; Chen et al., 2024] integrate these modules with customized designs to achieve better performance. Although existing methods have made great advances in traffic accident forecasting, they still have three major limitations.

The first limitation is the problem of zero-inflated data. Traffic accidents are low-probability events in a city, with most regions and time intervals labeled as 0 due to their infrequent occurrence. In the deep learning models, the resulting excessively imbalanced label distribution tends to lead all predictions to be 0, reducing their utility [Bao et al., 2019]. Existing solutions [Wang et al., 2023; Chen et al., 2024] follow a process where they build multi-level graphs and then aggregate fine-grained features to obtain high-level features with a smaller proportion of zero labels. In addition, weighted loss function [Wang et al., 2021; Chen et al., 2024] is introduced to assign higher weights to samples with high accident values. However, the weighted loss function only enhances the importance of non-zero data but ignores a large amount of zero-label data that can be further mined.

The second limitation is a lack of modeling of the spatiotemporal heterogeneity. As illustrated in Figure 1, A and B are schools and residential areas in New York City with different urban functions. We collect and calculate the frequency of traffic accidents at each hour of the day during February 2013 1 , presenting these data as a heat map. We observe a significant inconsistency in accident frequency between the two regions at the same hour of the day. In area A, the peak hours for traffic accidents are from 4 p.m. to 5 p.m. and from 6 p.m. to 7 p.m., while in area B, the peak hour of traffic accidents occurs from 8 a.m. to 9 a.m. Thus, there are distinct spatial differences between the two areas. Meanwhile, the frequency of accidents in both regions fluctuates significantly over time, indicating obvious temporal dynamics within each region. Existing methods that model spatial differences and temporal dynamics through shared parameters without any explicit handling face difficulty in effectively capturing spatio-temporal heterogeneity.

The third limitation is insufficient efficiency. Traffic accident forecasting is highly time-sensitive. As the spatial and temporal granularity of predictions becomes more refined, existing approaches may struggle to meet the demands for timeliness and resource consumption in the future. Many existing studies [Wang et al., 2021; Wang et al., 2023; Chen et al., 2024] combine long-term and short-term data into single sequential input, and simultaneously feed sequence data into grid-based modules (e.g., CNN) and graph-based modules (e.g., GCN) to enhance model performance. Although these two types of modules each have unique advantages, their simultaneous use not only requires additional hardware resources but also increases the training time, which may be a bottleneck for large-scale data applications.

To overcome these limitations, we propose a SpatioTemporal Learning framework for Traffic Accident Risk forecasting (ST-TAR). The ST-TAR leverages hierarchical multi-view GCN and long short-term cross-attention mechanism to encode spatio-temporal traffic correlations. More specifically, ST-TAR models long-term and short-term historical data respectively for spatio-temporal contrastive learning to capture spatio-temporal heterogeneity. The zero-inflated data issue is alleviated through hierarchical structure and adaptive risk-level weighted loss function. In particular, we propose an efficient auxiliary label processing algorithm that exploits locality-sensitive hashing to reduce the label distribution imbalance. By exploiting contextual spatio-temporal information, ST-TAR effectively addresses the aforementioned limitations to improve the effectiveness and efficiency of traffic accident risk forecasting.

The main contributions are summarized as follows:

• We propose a novel spatio-temporal learning framework named ST-TAR that effectively utilizes short-term proximity and long-term periodicity with hierarchical multi-

1 https://opendata.cityofnewyork.us/

• view GCN and long short-term cross-attention mechanism for traffic accident risk forecasting.
• We introduce spatio-temporal contrastive learning and adaptive risk-level weighted loss function with an efficient auxiliary label processing algorithm that can capture spatio-temporal heterogeneity and alleviate the zero-inflated data issue.
• We report on an extensive experimental study on two real-world datasets. The results demonstrate that our proposed ST-TAR model outperforms baseline models while utilizing fewer computational resources and requiring less runtime. This underlines the effectiveness and efficiency of ST-TAR in forecasting traffic accident risk from large-scale spatio-temporal data. The source code of our ST-TAR implementation is publicly available at https://github.com/wanghyhy/ST-TAR.

2 RelatedWork

Existing methods can generally be categorized into statistical learning-based methods and deep learning-based methods. Statistical learning-based methods such as K-Nearest Neighbors (KNN) [Lv et al., 2009], decision trees [Lin et al., 2015], Support Vector Machine (SVM) [Sharma et al., 2016], and Autoregressive Integrated Moving Average Model (ARIMA) [Barba et al., 2014] make predictions on smallscale traffic accident data with limited features, and they are unable to capture complex spatio-temporal dependencies in historical data.

To model spatio-temporal correlations in traffic data more effectively, recent methods utilize deep learning modules such as graph convolutional networks [Guo et al., 2021; Luo et al., 2022; Han et al., 2021]. These methods demonstrate advantages by effectively capturing complex temporal and spatial dependencies that are inherent to traffic data. Hetero-ConvLSTM [Yuan et al., 2018] employs an ensemble method with a convolutional long short-term memory network to handle the spatial heterogeneity, but manuallyselected regions limit the spatial patterns. Therefore, HintNet [An et al., 2022] devises a multi-level risk-based spatial partitioning with a hierarchical knowledge transfer network to capture irregular spatial heterogeneity patterns. To alleviate the zero-inflated data issue, GSNet [Wang et al., 2021] presents a geographical and semantic spatio-temporal network with a weighted loss function. Further, MVMTSTN [Wang et al., 2023] leverages a multi-task learning framework to predict fine and coarse-grained traffic accidents jointly to contend with data sparsity. More recently, MGHSTN [Chen et al., 2024] introduces multi-level hierarchical structures with multivariate hierarchical loss function, and incorporates remote sensing images to make a comprehensive traffic accident risk prediction. In addition to efficiency, none of these studies explicitly consider the challenges of zeroinflated data issue and spatio-temporal heterogeneity simultaneously for traffic accident forecasting.

3 Preliminaries and Definitions

Definition 1 (Grid and Region). A city is partitioned into a regular grid with I × J cells based on longitude and latitude.

Since cities typically exhibit irregular shapes, only a subset R = {r1, r2, . . . , rN} contains road segments (i.e., N ≤ I × J), and each ri in the subset R is defined as a region.

Definition 2 (Spatio-temporal Features). Spatio-temporal features xti ∈X of region ri in time interval t are categorized into static and dynamic features. Static features are the POI distribution, while dynamic features include temporal information, weather data, traffic flow, and accident risk values.

Definition 3 (Traffic Accident Risk). Three types of traffic accidents are defined based on the number of casualties in traffic accidents, i.e., minor accidents, injured accidents, and fatal accidents, with corresponding risk values set to be 1, 2, and 3, respectively [Wang et al., 2021]. The traffic accident risk yt i ∈ Y is equal to the sum of the risk values of accidents that occurred in region ri in time interval t.

Definition 4 (Hierarchical Multi-view Graph). To capture spatial dependency at multiple granularities and from various semantic perspectives, a hierarchical multi-view graph G = {G(1) ,G(2) , . . . ,G(L) } is constructed, where L represents the number of layers. Each layer G(i) =(V (i) ,E(i) ,X(i) ) is a multi-view graph at a specific granularity level, which consists of three views of graph: road similarity graph G(i) D , POI similarity graph G(i) P , and risk similarity graph G(i) K . G(1) is the finest-grained graph for prediction (i.e., X(1) =X where X is the original feature).

Definition 5 (Traffic Accident Risk Forecasting). Given the historical features {X1 ,X2 , . . . ,XT }, a hierarchical multiview graph G and target time information zT+1 , our goal is to forecast the traffic accident risk ˆYT+1 in the time interval T + 1 with the model f :

4 Methodology

In this section, we present our ST-TAR model for traffic accident risk forecasting, as illustrated in Figure 2. The complete historical data is composed of long-term and short-term data. Historical data from the p most recent time intervals is short-term data, and the same time interval in the previous q weeks is long-term data (T =p+q). In contrast to most existing methods that concatenate long-term and short-term data into a single sequential input, we treat long-term and shortterm data as separate inputs, respectively, to capture spatiotemporal correlations across different time steps.

4.1 Hierarchical Multi-viewGCN

High-level features can significantly reduce the proportion of zero-label data by aggregating information from multiple low-level nodes. Moreover, these high-level features enhance fine-grained predictions by providing rich contextual information. The hierarchical multi-view GCN consists of two main stages: intra-level multi-view GCN and inter-level feature fusion.

Intra-level Multi-view GCN. To model neighbor interactions with spatial dependencies, we adopt the GCN [Kipf and Welling, 2017] for each view within a hierarchical level. The adjacency matrix is augmented with a self-connection to obtain matrix ˜A and degree matrix ˜D. Then we can get the normalized symmetric adjacency matrix ˆA = ˜D(- 12 ) ˜A˜D(- 12 ) . Then the graph convolution operation can be formulated as

where Hlc represents the l-th layer of the hidden features matrix in the GCN, Wlc and blc are learnable parameters of the l-th graph convolutional layer.

In general, we employ a two-layer GCN to learn the spatial features of each view and then aggregate them by summation, which is formulated as follows:

where X denotes the initial embeddings of regions, and Ai ∈ {AD, AP , AK} denotes the adjacency matrix of each view. Inter-level Feature Fusion. For two adjacent k-th and k+1-th levels, the nodes at the k+1-th layer aggregate multiple nodes from the k-th layer. The corresponding relationship can be represented by matrix Bk,k+1, which is represented as:

By utilizing matrix Bk,k+1 as a bridge to represent the relationships between nodes in adjacent levels, the feature fusion process is executed sequentially from the finest-grained level to the coarsest-grained level, which is consequently represented as follows:

where H(k) f and H(k+1) f represent the feature fused from the k+1-th layer to the k-th layer and from the k-th layer to the k+1-th layer, respectively. λf is hyperparameters that balance the weights between low-level and high-level layers.

4.2 Long Short-termCross-attentionMechanism

To distinguish the output of long-term and short-term data through hierarchical multi-view GCN module, we use the Hf,l and Hf,s to represent the embeddings learned from long-term and short-term data, respectively (we omit the superscripts indicating the level because the attention mechanism is implemented independently within each level). Given target time information zT+1 , we utilize Hf,l and Hf,s as the keys and values in the attention mechanism, while concatenating zT+1 and complementary embeddings as respective queries, which are represented as follows:

where WQ,WK and WV are learnable parameters, and ∥ refers to the concatenation operation. We process the above features through a multi-head attention method:

whereWO is the learnable linear transformation to merge the information from various attention heads.

4.3 Feature Fusion and Prediction

In general, short-term proximity and long-term periodicity influence the target time to different degrees. Consequently, we employ two trainable weight matrices W(k) s andW(k) l in each level to dynamically integrate the outputs of long shortterm data and employ a fully-connected (FC) layer to make the risk prediction at each granularity:

4.4 Spatio-Temporal Contrastive Learning

With the proposed hierarchical multi-view GCN and long short-term cross-attention mechanism, we obtain two feature representations of short-term proximity and long-term periodicity as S and L, which contribute to the prediction at the target time from different perspectives. Therefore, we regard the short-term embedding and long-term embedding in the same region for the same target time as positive pairs (sti , lti ), while the embeddings at different regions (i.e., ri ̸= rj) and for different target time (i.e. t ̸= t′ ) as spatial-negative pairs (sti , ltj ) and temporal-negative pair (sti , lt′ i ).

Following this criterion, the correlation between shortterm proximity and long-term periodicity is manifested as a complementary relationship in the contrastive learning process, which promotes representations in both views that retain spatio-temporal heterogeneity to match each other. The spatio-temporal contrastive learning task is optimized with BCEWithLogitsLoss, which is defined as follows:

Here, D(·) is a discriminator that evaluates the matching scores between two input embeddings. Specifically, we implement it with a fully connected network fed by the concatenation of the input, which is defined as:

where Wd and bd are learnable parameters of the discriminator.

4.5 Adaptive Risk-level Weighted Loss Function

Zero-inflated data causes common loss functions (e.g., mean squared error) to disproportionately focus on zero-label data, thereby neglecting non-zero data. To alleviate this issue, we classify the data labeled as 0 at the finest-grained level (i.e., Y(1) =0, we omit the level superscripts for simplicity) into high-risk and low-risk based on the feature similarity. The resulting auxiliary labels serve as soft targets [Hinton et al., 2015] to implicitly optimize the label distribution to enhance the discriminative ability of the model.

An intuitive approach is to set a threshold for distinguishing high-risk and low-risk labels by calculating pairwise feature similarities (e.g., cosine similarity) between the accident-occurred and non-accident intervals in a given region. However, this is extremely time-consuming when processing large-scale spatio-temporal data.

To improve efficiency, we utilize the hash collisions of Locality Sensitive Hashing (LSH) [Indyk and Motwani, 1998] for approximate similarity search. LSH is an algorithmic technique that employs hash functions to efficiently map similar data points into the same bucket with high probability, reducing the computational cost of similarity search. Due to its simplicity and effectiveness, we adopt random projection hash [Charikar, 2002] as the specific LSH method. Given the spatio-temporal features xti , we obtain a random vector u from the Gaussian distribution (i.e., each coordinate is drawn from the 1-dimensional Gaussian distribution). Then the hash value p(xti ) is calculated as follows:

In our model, we construct a hash table by sampling K independent random projection hash functions, denoted by P = {p1, p2, . . . , pK}. As a single random projection hash function returns a one-bit output (0 or 1), the hash table returns a K-bit output. Given that A and B are represented as feature vectors, the collision probability in this condition conforms as follows [Goemans and Williamson, 1995]:

Therefore, according to the power law, the collision probability declines sharply as K increases, ensuring that similar embeddings have a high probability of obtaining identical outputs. In a specific region, we initialize hash buckets and map the accident-occurred hash values into buckets. For accident-occurred intervals, we label them as accident (cti = 2). For non-accident intervals, if the K-bit hash values match a non-empty bucket, we label them as high-risk (cti =1); otherwise, we label them as low-risk (cti =0). We obtain three types of auxiliary labels, and the relationship with traffic accident values is as follows:

Time complexity. The time complexity of auxiliary label processing algorithm is O(N ×M ×K ×dh +2×N ×M) = O(N × M × K × dh), where N, M, and K denote the number of regions, time intervals, and hash functions, respectively, and dh denotes the feature dimensionality. Compared with the intuitive solution, which has a complexity of O(N ×Ma ×Mn × dh) (Ma and Mn denote the number of time intervals with and without accident occurrences, which satisfy M = Ma +Mn), our method has a better complexity. Moreover, our method is more suitable for online risk prediction due to the O(K×dh) complexity of an update operation, while the intuitive solution has a complexity of O(M × dh).

Finally, the adaptive risk-level weighted loss function based on Mean Squared Error (MSE) can be divided into two parts: zero-label data and non-zero data. For non-zero data, we classify them into three levels according to the accident risk value Inz = {Y=1, Y=2, Y≥3} and assign them different weights, which are expressed as:

where Nnz is the number of non-zero samples, λnz k are hyperparameter weights of three risk value levels.

For zero-label data, we classify them into two levels according to the auxiliary labels Iz = {C=0, C=1} and assign them different weights, which are expressed as:

where Nz is the number of zero-label samples, λzk are hyperparameter weights of high-risk and low-risk data.

The overall adaptive risk-level weighted loss function is defined as follows:

4.6 Model Optimization

In the training process, adaptive risk-level weighted loss and spatio-temporal contrastive loss are jointly optimized with the hierarchical loss. Therefore, the total loss of multi-task learning is represented as follows:

where Lh represents the hierarchical loss following existing hierarchical studies [Wang et al., 2023; Chen et al., 2024]. λr, λc and λh are the hyperparameters of the loss function to balance the importance of the different tasks.

5 Experimental Study

We conduct extensive experiments on real-world datasets to evaluate the effectiveness and efficiency of the proposed model. Moreover, we conduct the ablation study and create visualizations to assess and illustrate the impact of the different components on the model.

5.1 Experimental Settings

Datasets. Experiments are conducted on two public realworld traffic accident datasets collected from New York City

(NYC) 2 and Chicago 3 . Statistics of the datasets are presented in Table 1. The POI data includes seven categories: residence, school, culture facility, recreation, social service, transportation, and commercial area. Due to the absence of POI data in the Chicago dataset, we only constructed neighborhood, risk similarity, and road similarity graphs for this dataset. The weather data includes temperature and weather conditions, including sunny, rainy, cloudy, snowy, and misty days. We employ the taxi trip data to calculate the inflow and outflow of each region as the human mobility data.

Experimental Setup. Following existing studies of traffic accident forecasting [Wang et al., 2021; Wang et al., 2023], we divide the data on the timeline into training, validation, and test sets in a ratio of 6:2:2. A city is partitioned into grid cells of size about 2km × 2km. The length of short-term input data p and of long-term input data q are set to 3 and 4, respectively. The time interval length is set to 1 hour.

Baselines. We compare ST-TAR with eight baselines for traffic accident risk forecasting: (1) statistical methods: ARIMA, (2) grid-based learning methods: MLP, ConvLSTM [Shi et al., 2015], Hetero-ConvLSTM [Yuan et al., 2018] (3) graph-based learning methods: GSNet [Wang et al., 2021], HintNet [An et al., 2022], MVMT-STN [Wang et al., 2023], MGHSTN [Chen et al., 2024].

Evaluation Metrics. We adopt Root Mean Square Error (RMSE), Recall, and Mean Average Precision (MAP) to assess the performance. Due to the high frequency of traffic accidents during rush hours (i.e., 7:00-9:00 and 16:00-19:00), we independently use RMSE*, Recall*, and MAP* to evaluate the performance during these periods to evaluate the performance of our model more comprehensively.

5.2 Effectiveness Comparison

Table 2 presents the performance comparison of all methods on the two datasets. Our model achieves the best performance in most metrics on all datasets, which demonstrates the superiority of ST-TAR. We attribute the performance improvement to spatio-temporal contrastive learning and adaptive risk-level weighted loss function for capturing spatiotemporal heterogeneity and alleviating the zero-inflated data issue simultaneously. More specifically, the ST-TAR model performs well both throughout the entire day and during rush hours, demonstrating its robustness under diverse conditions.

2 https://opendata.cityofnewyork.us/

3 https://data.cityofchicago.org/

Furthermore, the statistical learning method ARIMA has the worst performance, which is due to its limited capability in capturing complex spatial and temporal correlations. Among the deep learning models, the performance of basic MLP is inferior to ConvLSTM and Hetero-ConvLSTM, which utilize convolutional networks and LSTMs to capture spatial and temporal dependencies. The graph-based models (GSNet, HintNet, MVMT-STN, MGHSTN, and STTAR) perform better than grid-based models (ConvLSTM and Hetero-ConvLSTM), indicating the effectiveness of modeling non-Euclidean spatial structure for traffic accident forecasting. However, these baseline methods do not simultaneously address the zero-inflated data issue and capture spatiotemporal heterogeneity. Therefore, ST-TAR achieves superior performance compared to baselines.

5.3 Ablation Study

To validate the effectiveness of the different components in ST-TAR, we conduct an ablation study with three variants: (1) ST-TAR-LS combines long-term and short-term data into a single sequential input. (2) ST-TAR-CL removes the spatio-temporal contrastive learning. (3) ST-TAR-WL replaces the adaptive risk-level weighted loss function with a classic MSE loss function. Figure 3 shows the experimental results between ST-TAR and these variants. We observe that ST-TAR outperforms the three variants across all metrics, indicating that each component contributes to the model. Specifically, the deteriorated RMSE and MAP of both datasets in ST-TAR-CL suggest that separately considering long-term and short-term data benefits long-term periodicity and short-term proximity modeling. Furthermore, ST-TARCL outperforms ST-TAR-WL in regression prediction on the NYC dataset while the converse is observed on the Chicago dataset, proving both capturing spatio-temporal heterogeneity and alleviating the zero-inflated data issue can enhance model performance across different scenarios.

5.4 Efficiency Comparison

We compare the training time per epoch and the inference time of our ST-TAR model and the three best prediction performing baselines: GSNet, MVMT-STN, and MGHSTN. We also record the GPU memory usage of these models for training. The results are shown in Table 3 and Figure 4. Moreover, the auxiliary label processing procedure takes 10.8 seconds and 5.2 seconds on NYC and Chicago datasets respectively, roughly equivalent to one training epoch time, indicating that the pre-processing does not impose a significant overhead. Compared to the baselines, ST-TAR saves more than 25% of running time with minimal GPU usage. Different from the baselines that handle long-term and short-term data as a concatenated input and predict their results by fusing the outputs of their respective grid-based and graph-based modules, STTAR processes long-term and short-term data separately and performs risk prediction solely based on graph-based feature learning, thus significantly improving the efficiency.

5.5 Visualization

To illustrate the impact of auxiliary labels on the zero-inflated data issue intuitively, we visualize the spatial label distribution before and after processing on the NYC dataset from 10 p.m. to 11 p.m. on February 2, 2013. As presented in Figure 5, accidents only occurred in a small fraction of regions. Our auxiliary label processing algorithm classifies non-accident regions as high-risk and low-risk, resulting in a more balanced label distribution. Notably, high-risk regions are mainly concentrated near the accident-occurred regions, which aligns with Tobler's first law of geography [Tobler, 1970] as geographically close regions tend to have similar characteristics in terms of traffic flow, weather, and other factors, making accidents more likely to occur near the accidentoccurred regions.

Figure 5: Visualization of label distribution of the city before and after the auxiliary label processing procedure on the NYC dataset.

6 Conclusion

We propose an efficient spatio-temporal learning framework, called ST-TAR, for traffic accident risk forecasting. We introduce hierarchical multi-view GCN and long short-term crossattention mechanism to capture spatio-temporal correlation by considering long-term periodicity and short-term proximity separately. To capture spatio-temporal heterogeneity and contend with the zero-inflated data issue, spatio-temporal contrastive learning and adaptive risk-level weighted loss function are devised to achieve a multi-task framework. Extensive experimental studies on two real-world datasets demonstrate that ST-TAR achieves superior performance with improved efficiency.

Acknowledgments

This work was supported by the National Key R&D Program of China 2024YFE0111800, NSFC U22B2037, and NSFC U21B2046.