1. Introduction
With the ever-enriching city lives, open public places, such as pedestrian streets, commercial streets, parks, and squares, have gradually become an important part of people’s lives [
1]. These open places, without definite space boundary, are likely to cause overcrowding with the inrush of massive pedestrians in a short period, which could arise evacuation problems, leading to the occurrence of stampedes [
2,
3]. In stampedes, a huge crowd obstructs each other and people are crushed by the shock waves building up in the crowd, which may incur clogging effects at bottlenecks. The people who lose their balance and fall down become obstacles for others, which can produce piles of fallen people [
4]. Therefore, it is a great concern to understand the dynamics of pedestrian flow in open public places. It can not only help city managers implement prevention strategies to alleviate road congestion, but also provide useful information for travelers to choose appropriate travel routes and improve travel efficiency.
The definition of pedestrian flow prediction can be considered as follows. Given a sequence of observed flow data in the road network, the task is to predict the pedestrian flow in the next moments [
5,
6,
7,
8]. The pedestrian can be affected by miscellaneous factors which pose great challenges to pedestrian prediction [
9,
10]. From the temporal dependencies, the crowd flow always repeats over time, such as weekends and weekdays and the rush hours in the day. Concerning the spatial dependencies, the flow in a region is similar and relevant with its neighborhood rather than the far regions. Besides, the weather condition has an influence on the pedestrian features [
11].
There are three kinds of forecasting methods in existing research, namely traditional statistical model, machine learning-based model and deep learning-base model. In the early stages, classic forecasting approaches were mainly based on the assumption of linearity and stationarity to infer future pedestrian trends [
12,
13,
14,
15,
16]. The models consider the dynamic change of historical data and extract the crowd features for the prediction task, and require large efforts on parameter inference, which may result in lower prediction accuracy and efficiency. Serval non-linear prediction models in the artificial intelligence field, such as Gaussian maximum likelihood model [
17], Bayesian networks [
18], decision trees [
19,
20], support vector machines (SVM) [
21,
22] and neural networks [
23,
24,
25,
26], have shown the great application prospect and received wide popularity in the field of crowd flow prediction. The machine learning-based models discover complex non-linearities in data and outperformed the traditional methods with a lower error rate and higher accuracy rate. Despite the above methods have produced compelling results, it remains unsatisfactory for the rapid development of intelligent transportation systems in practice. Recently, deep learning has made groundbreaking progress on classification tasks, pattern recognition, and natural language processing [
27]. Due to its high computational efficiency and interpretability, deep learning models, such as convolutional neural network (CNN) [
28,
29,
30,
31,
32] and recurrent neural network (RNN) [
33,
34,
35,
36], have been applied widely to capture the crowd flow features with a squared tessellation of tiles.
However, the above methods by assuming a convolution filter in the form of a grid structure and ignore modeling the physical roadway network topological structures. In the real world, the road network cannot be regarded as a regular gridded structure [
37,
38,
39]. With the powerful ability to capture the spatio-temporal features of graph-structured data, graph convolutional network (GCN) and its extensions have been widely applied to prediction tasks [
40,
41,
42,
43,
44,
45,
46]. By constructing the road network as a graph and aggerating the features of neighborhood, the GCN model can capture characteristics of the crowd data in the deep layer among the irregular regions. Many researchers used the trajectories of bicycle sharing [
47,
48], mobile phone positioning data [
49,
50], taxi GPS records data [
51,
52], or the number of passengers on public transportation systems (e.g., metro, railway or airport) [
53,
54,
55,
56,
57] to predict the crowd flow in a city. It is relatively scarce on the pedestrian in open public spaces.
In this study, we introduce the GCN model to predict the pedestrian flow in a walking street in Shenzhen metropolitan area. The GCN model can handle the issues that CNN cannot be applied to graph structures of the road network. The graph is built based on the existed road structures to capture the spatial dependency of the crowd by calculating the coefficient between nodes. We further compare the GCN model with baseline methods to validate the performance of pedestrian flow prediction. The experiments show that the GCN model improves the prediction precision and decreased the prediction error. The accurate and timely pedestrian flow prediction results can help managers to take precautions in advance and ensure the public safety, which is beneficial for building a smart city. Since the pedestrian flow could be impacted by temporal dependencies and other factors, we conduct the sensitive analysis of the GCN model with the consideration of these related factors such as weekends and weekdays, the rush hours in the day and the weather conditions. It is found that the model has the ability to capture pedestrian congestion peaks with high accuracy. Understanding the dynamic of pedestrian flow can be beneficial for crowd control systems to manage and direct the optimal detours in advance.
The main contributions of this paper are as follows:
- (1)
We employ the GCN model to predict the pedestrian flow. The graph-structure-based deep learning model, in which the detectors are regarded as nodes, and edges represent the relationship of the road network, can capture the complex topological dependency. Moreover, we assign different weights to road segments to identify the influence of road network structure to capture the spatial dependencies.
- (2)
We compare the GCN model with baseline methods selected from the existing methods to validate the performance of pedestrian flow prediction in terms of three evaluation metrics. The experimental effectiveness of the GCN model show that proper integration of the road topology could considerably improve the pedestrian flow prediction precision in real-world applications.
- (3)
We further conduct comparative experiments of pedestrian flow prediction between weekdays and weekends, and different hours during the day to capture the temporary dependencies. Sensitive analysis on the effect of weather conditions is also conducted. The robustness of the GCN model to predict the pedestrian flow would help practitioners and managers to improve road efficiency.
The remainder of this paper is organized as follows.
Section 2 details the study area and the data preprocessing procedures. The detail of the GCN model is also formulated in this section.
Section 3 shows the experimental results.
Section 4 discusses the advantage and sensitivity of the model. The conclusions are presented in
Section 5.
4. Discussion
4.1. The Advantage of the GCN Model for Pedestrian Flow Prediction
Pedestrian flow spontaneously resides in the network topological structure of the road, and the network structure might fundamentally influence the distribution patterns of the crowd. The pedestrian flow of the road segments has a geographical association with the road which is connected. Road network-based prediction task is determined by not only the features of that road segment, but also the features of its neighbors. Normally, the stronger the relationship of the road junction is, the more people move from one junction to another. The distances between pairwise detectors were employed to describe this relationship. The crowd is most likely to move towards its neighborhood instead of the faraway places. The existing methods in pedestrian flow prediction lose sight of the topological structure of the road. Compared with other methods assuming the convolution filter as the grid structure, the GCN model is competent to capture the graph structure. The model, in which the detectors are regarded as nodes, and edges represent the relationship of the road network, can capture the pedestrian flow characteristics hidden in the topological structure. In order to identify the influence of road network structure, we employed the adjacent matrix by assigning different weights to road segments. The experimental effectiveness of the GCN model to capture the spatial dependencies was validated in terms of three prediction evaluation metrics. The lower error and higher accuracy rate of the model show that proper integration of the road topology could considerably improve the pedestrian flow prediction precision in real-world applications. To further illustrate the better and robust performance of the GCN model, we conducted comparative experiments of pedestrian flow prediction between weekdays and weekends, and different hours during the day to capture the temporary dependencies. We also analyzed the effect of weather conditions on the pedestrian features.
4.1.1. Comparison between Weekdays and Weekends
As presented in
Figure 2, the pedestrian flow has a marked weekly periodicity pattern that the crowd count on weekends is larger than on weekdays. In this section, we measure the performances of the GCN model on weekends and weekdays respectively. Further, to have a better understanding of the prediction performance, we sample the head 200 rows of the dataset and visualize the ground-truth and predicted crowd count, as shown in
Figure 5.
The values of on weekends and weekdays are all above 0.93, proving the effectiveness of the GCN model for pedestrian flow forecasting. Moreover, the weekend dataset, compared to the weekday dataset, achieves higher prediction precision in terms of . Since the pedestrian flow on weekends is much heavier than on weekdays, we can conclude that the GCN model has better prediction performances under larger flow volumes. The changes of and are opposite to that of , in which the weekend dataset occurs the higher error. This is mainly because and are absolute error metrics, and the greater crowd count on weekends results in a higher value of and . From the visualization results, we can see that the GCN model can accurately forecast the pedestrian flow in multiple local peaks and nadirs. And the model achieves satisfying results in predicting the variation trend of pedestrian flow in comparison with the ground-truth data.
4.1.2. Comparison between Different Hours of the Day
It must be noticed that the throng in open public place changes over time, with the characteristics of the high crowd count in the afternoon and evening and the low value at midnight. To further evaluate the influence of the high or low pedestrian flow on the model performance, we compare the evaluation metrics under different hours during the day, and the results are listed in
Table 5.
For the table, we can find that the values of and are quite small in the early morning (from 00:00–05:59), while the values are relatively big in the afternoon. It is noteworthy that the prediction accuracy () under various time intervals has no significant difference between weekdays and weekends. Specifically, no matter on weekends or weekdays, the model does not achieve satisfactory precision from 06:00 to 08:59. The value of during the evening peak (from 16:00 to 21:59) are all above 0.9, indicating the GCN model can predict the pedestrian flow accurately when there are massive travelers, which is beneficial for road managers to prevent or alleviate pedestrian congestion.
As previously mentioned, the value of crowd count has a significant impact on the value of
and
. We depict the relationship between them in
Figure 6, and further employ the scatter plot and linear regression analysis on these indices. There are a larger crowd of people thronged into the walking street in the afternoon and evening on weekends. The peak of pedestrians per 100 square meters on weekdays is about 15, while the number on weekends is above 20. On weekdays, the maximum value of
and
occurs from 17:00 to 17:59, of which the values are 4.452 and 2.727, respectively. The peak error occurs from 15:00 to 17:59 on weekends, and the value is larger than the one on weekdays. More importantly, the slopes in the linear regression equations are positive, indicating the prediction error has a positive correlation with crowd count. The intercept on weekends is larger than the value on weekdays, reflecting the heavier pedestrian flow on weekends could lead to a higher prediction error compared to weekdays. And the fitness of regression equations are 0.9628, 0.9551, 0.9517 and 0.9506, respectively. It provides an insight that
and
have a strong correlation with crowd count.
Therefore, the relative metric (
) is adopted to measure the model effectiveness under different hours. We further investigate the reason why the model performances differ under various hours in the aspect of the interval distribution of datasets. The datasets of which
is less than 0.8 (highlighted in bold) are selected as poor performance sets. And the remainder datasets,
more than 0.8, are grouped as good performance sets. By considering the distribution characteristics of the collected ground-truth data, we partition the crowd count with an interval of 5, then calculate the proportion of the flow on the given interval. The statistical diagrams are pictured in
Figure 7.
From the figure, it can be noticed that the good performance sets () have a smaller proportion in the interval of from 0 to 5, where the pedestrian flow is quite low. On weekdays, about 60% of the crowd are lower than 5 in terms of good performance sets while the percent of poor performance sets is above 90%. This kind of phenomenon is more perceivable on weekends. The percentage of the two sets are 55% and 93%, respectively. More importantly, the poor performance sets reach the 99th percentile in the previous two intervals both on weekdays and weekends—that is, only 1 percent of crowd count is larger than 10. On the good performance sets, the percent of the previous two intervals account for 79% and 72% respectively on weekdays and weekends. It reaches the 99th percentile when the number of pedestrians per 100 square meters is above 50. It is concluded that the GCN model achieves a better prediction when the crowd count is high, which proves the effectiveness of the model to find the pedestrian flow peaks.
4.1.3. Comparison between Different Weather Conditions
It is known that the pedestrian flow fluctuates under various weather situations. Therefore, in this section, dealing with weather conditions data over the study period, we apply sensitive analysis to validate the model effectiveness. We used the weather and temperature data from Meteorological Bureau of Shenzhen Municipality (
http://weather.sz.gov.cn/ (assessed on 1 March 2021)) and the data were obtained every day. The summary of the temperature and weather conditions is shown in
Figure 8.
The temperature in the study area is stabilized during the third quarter (from 1 July 2020 to 30 September 2020). Overall, the highest and the lowest temperature are above 30 and 25 degrees Celsius respectively in most cases. From the statistical table, the cloudy weather accounted for more than half (50/92) of the study period and the temperature variation under diverse weather conditions has little difference. Comparing to the sunny days, it attracts more visitors in cloudy days. It is mainly because Shenzhen is the subtropics climate, and the cloudy days are suitable for people to travel along the road while the sunny days are too scorching heat to sightsee. Since the weather records are time-series data in every day, we embed weather features into pedestrian flow data. The time interval is 1 min in our experiment, which means the 1440 intervals share the recorded weather data in a day. We further conduct the comparative experiments under different weather conditions and the results are shown in
Table 6.
Taking the mean crowd count in
Figure 8 into consideration, we found that all three metrics have a positive correlation with the mean value. Specifically speaking, the heavy pedestrian flow may result in high prediction error (
and
), and the model has a greater prediction precision (
) when the flow is heavier. The model achieves the best accuracy in cloudy days, and its prediction precision is 0.947, higher than the value of
in other weather conditions.
is the lowest in the overcast days, whose value is still above 0.92. It validates the model’s effectiveness to predict the pedestrian flow in open public places, especially when there is a large crowd of pedestrians thronged into the walking street.
4.2. The Limitation and Prospects of the Study
There are some limitations of this study. The primary concern is that we employ the number of pedestrians within the monitoring area. As the detectors are installed on the pole by the road, the monitoring area may be blocked by the buildings or leaves, resulting in the underestimation of crowd count. Besides, we equipped 25 detectors to monitor the pedestrian in the walking street, covering the main road and crossroad but ignoring the throng in the sideway. High-density spatial sampling would capture the pedestrian features across the board. Finally, there are three dominated indices in the field of pedestrian traffic, i.e., density, speed and direction. This study concentrates on the crowd count within a definite area. It will be beneficial to improve the prediction precision considering the relationship between the three indices.
With respect to the prospects of the study, it can go in three directions. First, compared to the characteristics of vehicle flow in complying with specified roadway, the pedestrian could move freely and even change direction at any time. It would be meaningful to consider the features of pedestrian movement and construct the adjacency matrix besides the distances of pairwise detectors. In addition, the road topology is represented as a static graph in this study. The present model could be improved with an in-depth exploration of the dynamic graph based on variable matrices, further enhancing its accuracy and robustness for crowd count prediction. Finally, we applied a standard GCN model to predict the pedestrians in this study. Many GCN extensions addressing the prediction tasks are proposed to improve the computation accuracy. It is meaningful to utilize these state-of-the-art methods for practical application after decreasing the model complexity.
5. Conclusions
In this paper, we have introduced the GCN model to predict pedestrian flow in open public places. In contrast to traditional grid matrices, the model forecasts the crowd count depending on the road spatial topology relationship, and the graph is constructed to describe the relationships among detectors. Experimental results show that the GCN model consistently and significantly outperforms s baseline models, namely HA, ARIMA, SVM, CNN, LSTM and STGCN. For 1, 5, 10, 15, 20, 25, 30 min pedestrian flow prediction, the values of are 0.937, 0.928, 0.921, 0.916, 0.911, 0.906 and 0.902, respectively. We further analyze the sensitivity of the GCN model in pedestrian flow prediction. The model obtains superior performances with higher prediction precision on weekends and the precision during the evening peak is above 0.9, demonstrating the superiority of the model, especially when there is a large crowd of pedestrians thronged into the walking street.
The proliferation of various data mining technology creates unprecedented opportunities to better understand crowd distribution patterns using the collected data. The accurate prediction results help road managers take flexible and effective measures to meet the requirements for security management of open public places. More specifically, the massive crowds of pedestrians are similar to shock waves, and people may be crushed by the high pressure building up in the crowd, especially for the older, juvenile and women, who have the tendency to scream and cause psychological uneasiness, even lose their balance and fall down. The managers can shield or divert these vulnerable individuals into the vast square in advance to prevent the occurrence of stampedes. Besides, people often rely on their preferences to choose the route while neglecting the whole story in the walking street during the huge crowd. The regulators can release the road capacity information through public display screens and broadcast facilities, which is effective to avoid the crowd gathering due to the scarcity and distortion of information. It also has the potential to provide accurate and timely flow information for pedestrians to choose appropriate travel routes and decrease the travel time.