Abstract
Polycentric urban development is promoted by urban planners and policy makers for its perceived benefits of alleviating urban issues. Theoretically, a polycentric urban structure is formed when different demographic groups present a collection of diverse and unique housing location preferences. Yet, only limited empirical studies have fully captured the complex effects of demographic characteristics on urban polycentric structures. Our study utilizes detailed demographic data and employs interpretable machine learning models to elucidate the nonlinear and synergistic relationship between demographic characteristics and the urban polycentric structure in the context of a city of 10 million population in China. When characterizing urban centers, the three most important demographic groups are young females, senior married couples, and middle-aged single individuals with basic education. Each urban center presents distinctive demographic compositions; for instance, middle-aged married individuals exerting a stronger influence in certain contexts, whereas in senior resident groups, married individuals have a more pronounced impact. Spatial heterogeneity is observed in the demographic profiles of urban centers; for instance, primary central cores are predominantly young, single females, whereas peripheral and secondary centers have stronger presence of highly educated residents.
Keywords: Demographic characteristics, Nonlinear effects, Synergistic effects, Urban polycentric structure, Explainable machine learning
Subject terms: Sustainability, Environmental impact, Socioeconomic scenarios, Information theory and computation
Introduction
The current global urbanization process has entered a phase of decelerated growth. Since 1950, global urbanization has transitioned from over two-thirds of the population residing in rural areas to a gradual shift where urban populations began surpassing rural populations in 20101,2. In 2022, the global urbanization rate reached 55.3%, signifying a gradual deceleration in the urbanization process3,4. The optimization of urban internal spatial structures has gradually become a focal point in spatial planning. Urban polycentric structures are gaining increasing prominence in urban development as they play a central role in shaping urban organization and functionality.
Urban polycentric structures can effectively alleviate pressures on urban centers related to population, transportation, environment, and more. They promote the rational allocation of urban resources and balance socio-economic development5,6. Existing research has employed theoretical deduction, empirical judgment, statistical data, and spatiotemporal big data to measure the spatial form and performance of polycentricstructures7–10. However, cities are complex and evolving systems and polycentric structures that dynamically change with urban development11. Therefore, without a complete understanding of influencing factors and mechanisms, relying solely on current state measurements may not provide a comprehensive grasp of the development trends in polycentric structures, the identification of potential risks, or the formulation of forward-thinking strategies.
From a logical perspective on the spatial formation of urban polycentric structures, residential population demand is a key driving factor in their evolution. The mechanisms through which the demographic characteristic affects urban polycentric structures have nonlinear and synergistic effects, and primarily include population size, population structure, and spatiotemporal population changes12–14. Relevant research suggests that population size significantly impacts the formation and development of urban polycentric structures. Some researchers argue that as the population size increases, the size and number of urban centers will correspondingly increase, thereby promoting the development of urban polycentric structures15. Additionally, population mobility is another key consideration in the context of its impact on urban polycentric structures. Research indicates that population mobility is an important driver for the formation and development of urban centers16.On the other hand, demographic characteristic is also a critical factor influencing urban polycentric structures. For instance, cities with a higher degree of aging may see the development of more advanced industries related to healthcare, elderly care, and related sectors, thereby forming corresponding urban centers17.
For spatiotemporal population changes, firstly, population growth can stimulate the prosperity of urban centers and the development of secondary centers18,19. Some scholars have found that population growth can significantly increase the number of commercial and service establishments in urban centers, elevating their level of economic activity20. Second, population agglomeration can enhance the polarization effect of urban centers and drive the development of related industries21. For example, the concentration of high-tech industries can attract more tech talent, creating a positive feedback loop22. Moreover, population distribution and mobility can also influence the distribution and evolution of urban centers. For instance, some researchers have pointed out that rural-to-urban population migration can drive the urbanization process in peripheral areas of cities23. Additionally, studies indicate that population redistribution and re-agglomeration can lead to subcenter formation after population disperses from the core city areas24.
Both qualitative and quantitative research methods have been employed. In qualitative research, scholars primarily use in-depth case analysis, observation, and interviews to investigate how demographic characteristics influence the formation and development of urban polycentric structures. For instance, Ludek Sýkora and Martin Ourednek conducted a case study to explore population growth trends and the concentration of commercial and service industries in Prague and Brno metropolitan areas25. They found that population growth significantly influences the development of commercial and service industries in urban centers, particularly in terms of creating employment opportunities. However, qualitative research methods have limitations when examining the impact of population on urban polycentric structures, such as limited data sources and subjectivity in results26. In quantitative research, scholars use statistical models, spatial analysis, and data sources like demographic data, mobile phone signals, and location-based services (LBS) data to analyze the relationships between population and urban polycentric structures27–29.
Traditional methods such as multiple linear regression and geographically weighted regression (GWR) perform well in handling linear relationships30. However, in the study of polycentric urban structures, interactions among multiple features like land use, economic activity, and population density are often highly complex22. Machine learning methods, such as gradient boosting and random forests, can capture these more intricate nonlinear relationships and often provide better accuracy31. They offer the flexibility to model these interactions without the need for strict linear assumptions, this flexibility allows us to gain a more comprehensive understanding of the factors influencing polycentricity and uncover patterns that might otherwise be overlooked32. A common criticism of machine learning models is their lack of interpretability, often referred to as the "black box" problem. SHAP (Shapley Additive exPlanations) provides an interpretable framework for understanding the contributions of individual features and their interactions. SHAP values can decompose the predictions of machine learning models into the contributions of each variable, while Shapley interaction values help explain the interactions between variables, making the decision-making process of the model more transparent33. This interpretability is crucial for understanding how different factors influence urban polycentricity and helps urban planners and policymakers better understand the study’s findings. Given the advantages of accuracy, nonlinear relationship fitting as well as interpretability, the use of machine learning and SHAP in urban studies has been increasing. Examples include analyzing the nonlinear impact and synergy effects of Transit-Oriented Development (TOD) on urban vitality34, the influence of urban form on urban heat islands35, and the role of urban morphology in shaping sustainable transportation36. These studies highlight the theoretical and practical advantages of machine learning in urban analysis, especially in handling high-dimensional data and revealing non-obvious relationships, demonstrating promising application prospects.
Existing research suffers from shortcomings in population data with high spatial accuracy and detailed demographic characteristics. There is a limited exploration of the spatial demands arising from different age structures, gender structures, and educational levels and their impact on urban polycentric structures. Additionally, Challenges lie in quantitatively explaining the complex effects and influences of demographic characteristics on urban polycentric structures. Given these limitations, the use of big data combined with explainable machine learning are helpful. This study utilizes point of interest (POI) data, high spatial accuracy, and detailed demographic characteristics of the residential population as the foundational data. Random Forest is used to train a binary classification model that distinguishes urban central areas. Decision rules are generated to explore how the population supports urban centers, and Shapley additive explanations (SHAP) interpretative analysis is used to reveal the influence of different demographic features on urban centers. And take the case study of Xiaoshan District in Hangzhou, China, provides a valuable reference for similar regions or cities of comparable scale in their development efforts.
Methodology
Conceptual framework
The threshold effect concept serves as the foundation for constructing a demographic characteristics spatial model. This concept stems from the notion that establishing public centers requires a local consumer base, that primarily consists of the residential population in the surrounding area37. A specific population threshold near public centers is essential, as show in Fig. 1. Given the population’s spatial autocorrelation, different demographic traits create varied agglomeration and dispersion patterns, forming distinct local spatial structures, which also lead to the nonlinear and synergistic effects on polycentric structure.
Fig. 1.
Comparative Analysis of Models Predicting Urban Centers Based on Demographic Data. Central Panel: The grid highlights the study area’s urban center (Cluster 0) with the red squares denoting the higher density urban zones as identified by the models. A magnified section within this urban area illustrates the density of an urban center, showing a concentrated impact in the central squares. Left Section: The relationship between population growth and urban service provision, where the intersection of the two red broken lines represents the threshold at which the population is sufficient to support the density of urban services and form an urban center. Bottom Panels: Three distinct models are compared in terms of their predictive abilities: the Total Population Model, the Age Group Model, and the Demographic Factors Model. Each model is represented by a set of icons correlating to demographic categories—individuals, families, and diverse population groups, respectively. Right Section: Bar charts show the number of population groups in grids. Grey bars represent the actual number of diverse population groups, while the overlaid red line indicates the threshold population structure for supporting urban centers.
This research is divided into three main sections, as show in Fig. 2: center identification, model training and validation, and the explanation of influencing factors.
Fig. 2.
Overview of Model Frameworks and Analytical Techniques. Left Panel: the process of urban center identification. Central Panel: the data process and training of the three main modeling approaches used in the study: the Total Population Model, the Age Group Model, and the Demographic Factors Model. Right Panel: the process of explanation analysis.
(1) Center identification
The study identifies urban centers based on the theory that centers have a higher density than their surroundings. It utilizes a two-step approach, starting with data collection from Amap API and generating POIs in ArcMap. The kernel density method is then applied to transform POI points into a density distribution, which is imported into a 100 × 100 m2grid for center area identification. Finally, the Local Moran’s Index is used to calculate the kernel density within the grid, identifying High-High (H–H) clusters as urban centers.
(2) Model training and validation
To assess the impact of demographic characteristics, three comparative models based on Random Forest are employed: a total population model, an age group model, and a demographic model (including age, gender, and education). Population data is grouped based on different characteristics for model input, with parameter optimization during training. The accuracy of the models is then tested and compared.
(3) Explanation of influencing factors
The aim is to explore the contribution of individual factors and their interactions. Decision rules from the Random Forest model indicate demographic thresholds for center formation. The mean SHAP values assess the overall contribution of factors, with the most significant ones highlighted. SHAP interaction values analyze the contribution of factor interactions. Lastly, K-means clustering groups center grids based on demographic similarities, with individual samples from different clusters analyzed to observe commonalities and differences in factor influence.
Research methods
Shapley additive explanation (SHAP)
SHAP is a representative local interpretation method38. The core of SHAP is to calculate Shapley values based on the classic cooperative game theory. Machine learning predictions are somewhat analogous to games. For every prediction, Shapley values can offer a solution for fairly distributing the effects of explanatory variables by calculating their average marginal contributions across all possible variable value coalitions. The Shapley value is defined as:
| 1 |
where is the Shapley value that reflects the effect of variable on the single prediction compared to the average value of overall predictions, is the set of possible variable orderings, is the number of variables, is the variables that come before the variable in the ordering , and is the values of explanatory variables.
Then, the single prediction is explained by:
| 2 |
where denotes the average value of overall predictions.
The relative importance of variables is calculated by averaging absolute Shapley values per variable:
| 3 |
where is the importance of variable , is the Shapley value for variable k in the single prediction i. Shapley values can estimate the local effects of explanatory variables on final predictions. The local effects of an explanatory variable (i.e., Shapley values) can be further decomposed into the main local effects and the local interaction effects with other variables (i.e., Shapley interaction values). Shapley interaction values capture local interaction effects by allocating credits among pairs of variables. The Shapley interaction value is defined as:
| 4 |
when ,
| 5 |
where is the Shapley interaction value that reflects the interaction effect between variable and variable on a single prediction, is the number of variables, is the set of input variables, is the possible variable coalitions, and is the input variable values for the prediction.
Synergism is a ubiquitous phenomenon around the world which deserves attention. Synergism emerges when a cooperation or interaction causes an increase in the whole so that the whole is greater than the sum of parts. In this research, two variables generated synergistic effects (i.e., positive interaction effects) on the urban centers when the Shapley interaction values are above zero; otherwise, they had negative interaction effects on the urban centers.
We used the SHAP package (Python 3.9) to interpret the Random Forest model. The SHAP package contains an improved TreeExplainer method that efficiently calculates both Shapley and Shapley interaction values39. Based thereon, patterns of model behavior can be uncovered by globally summarizing the relative importance of centers variables, locally demonstrating nonlinear and interaction effects, and clustering center grids by similarity of demographic characteristics.
Research area and data source
Research area
The study area was Xiaoshan District on the south bank of the Qiantang River in the south of Hangzhou City, as show in Fig. 3. It became one of the main urban districts of Hangzhou City in 2001 after the original city was abolished and the district was established. According to the statistical yearbook, the residential population in the research scope was 2.11 million by the end of 2022, with an area of 959 km2, and the urbanization rate was 81.1% by the end of 2022.
Fig. 3.
Geographic Context and Subdivision Mapping of Xiaoshan District. Left Panel (Detailed Subdivision Map): This map showcases the detailed administrative divisions within Hangzhou City. The areas labeled in pink represent different sub-districts, while the blue regions represent various towns within the district. Each area is named accordingly, providing a clear visual representation in research area. Top Right Panel (Location Map of Hangzhou in Zhejiang Province): This map places Hangzhou City within the broader context of Zhejiang Province, China. Hangzhou is highlighted, allowing for an immediate understanding of its geographic location within the province. Bottom Right Panel (Focus on Research Area in Hangzhou): This map zooms into the specific research area within Hangzhou City, highlighted research area in red.
Research data
Point of interest (POI)
The data source for urban polycentric structure was POI from amap API. Polycentric structure can be assessed through different dimensions, such as land use, building density, population statistics and economic activity density40,41. From the perspective of its definition, polycentricity can be categorized into two types: the first emphasizes morphological characteristics, identifying polycentricity based on the scale, density, and spatial distribution of urban areas; the second views polycentricity as a function-oriented concept, focusing on the structure of urban functions and the flows, communications, and networks of cooperation between different urban units42.
POI data, which became popular around 2010, is characterized by geographic coordinates and functional labels. It can accurately reflect changes in urban building density and effectively represent the distribution of urban functions, thereby satisfying both morphological and functional measurements of polycentric structure43. Compared to traditional statistical data, POI data has the advantages of higher spatial precision, broader coverage, better accessibility, and more timely updates, making it more effective in reflecting the current state of urban polycentric development44. As a result, POI data has gained extensive attention and application in the study of polycentric structures.
According to the service content provided by the urban public centers in relevant studies, a total of 70,661 POIs in 10 categories were collected within the research scope, including catering services, scenic spots, shopping services, science and education, culture services, life services, sports and leisure services, medical and health services, accommodation services, government agencies and social organizations, financial and insurance services. POI data is mature in urban spatial applications with a high spatial accuracy and is commonly used to identify existing polycentric structures.
Grouping of demographic characteristics
Age significantly shapes urban center development due to varying service demands and consumer preferences across age groups. Urban centers are also influenced by gender, education, and marital status, which intersect with age demographics, affecting service consumption and needs. For example, gender imbalances can arise from social norms and demographic factors like migration, influencing urban structures. Additionally, educational attainment varies by gender, affecting service preferences. In this study, we quantified these characteristics as independent variables within a defined spatial context, acknowledging their complex interplay in urban dynamics.
The research data was sourced from the Population Database of the Hangzhou Municipal Planning Bureau (anonymous). In addition to age and residential spatial location, the database included characteristics such as gender, marital status, and the education level of the residential population.
Age structure was divided into five groups based on considerations of public service utilization and urban residents’ consumption behavior characteristics: these groups include the juvenile group (0–18), the youth group (19–29), the adult group (30–49), the elderly group (50–69), and the senior elderly group (70 +), totaling 2,041,460 individuals.
Gender structure was categorized into two groups: male and female. Educational structure was divided into three groups: those uneducated (illiterate or semi-literate), those with basic education (including primary, middle school, high school, or equivalent), and those with tertiary education (including bachelor’s, master’s, doctoral degrees, or the equivalent). The marital status structure was divided into two groups: married and single.
The initial grouping for the age group model was based on age data, and then other characteristics are grouped based on this foundation. In the juvenile group, as their gender awareness is still developing, many have not completed their education, and their consumption behavior often depend on their guardians, is not further subdivided. To ensure that overly small groups with total counts below 10,000 are not split, which could result in overly specific and imbalanced features, a hierarchy or upward merging of groups was considered. In this context, the young and elderly groups prioritize gender, while middle and senior age groups prioritize educational attainment. Therefore, the middle age and elderly group are primarily divided by educational attainment, while the young group and elderly group are primarily divided by gender. Many individuals in the young group have not completed their education, so their educational structure is not further subdivided. In the end, this results in 22 feature combinations. The grouping labels and sample sizes are shown in Table 1. For easy presentation, abbreviations in parentheses will be used in the rest of this paper to refer to demographic characteristics. For example, ‘YM’ refers to a young male group, and ‘MHMF’ refers to a middle-aged, highly educated, married women group.
Table 1.
Cross-categorizing demographic characteristics.
| Age group | Demographic characteristics group | Number | Percent |
|---|---|---|---|
| 0–18 | Child (C) | 144,183 | 7.06% |
| 19–29 | Young male (YM) | 257,453 | 12.61% |
| Young female (YF) | 214,433 | 10.50% | |
| 30–49 | Middle age uneducated (MU) | 7041 | 0.34% |
| Middle age basic educated married male (MBMM) | 360,916 | 17.68% | |
| Middle age basic educated single male (MBSM) | 63,955 | 3.13% | |
| Middle age basic educated married female (MBMF) | 315,545 | 15.46% | |
| Middle age basic educated single female (MBSF) | 39,280 | 1.92% | |
| Middle age high educated married male (MHMM) | 25,297 | 1.24% | |
| Middle age high educated single male (MHSM) | 10,808 | 0.53% | |
| Middle age high educated married female (MHMF) | 19,511 | 0.96% | |
| Middle age high educated single female (MHSF) | 6,856 | 0.34% | |
| 50–69 | Senior age uneducated (SU) | 9412 | 0.46% |
| Senior age basic educated married male (SBMM) | 237,864 | 11.65% | |
| Senior age basic educated single male (SBSM) | 9254 | 0.45% | |
| Senior age basic educated married female (SBMF) | 198,354 | 9.72% | |
| Senior age basic educated single female (SBSF) | 11,081 | 0.54% | |
| Senior age high educated (SH) | 7736 | 0.38% | |
| 70 and above | Elderly married male (EMM) | 44,858 | 2.20% |
| Elderly single male (ESM) | 4321 | 0.21% | |
| Elderly married female (EMF) | 38,729 | 1.90% | |
| Elderly single female (ESF) | 1573 | 0.71% |
Results
Distribution of urban centers in Xiaoshan District
The final identification results include 40 centers (the range of spatial contiguous adjacent grids identified as a single center), with a total of 3533 grids, accounting for 3.75% of the research area, as show in Fig. 4. The distribution of centers is basically consistent with the existing empirical evidence of urban multi-centers in Xiaoshan District26.
Fig. 4.
The process of detecting urban center in research area. Top Left Panel (Kernel Density Map): centrality density from kernel density of muti-data. The blue to red spectrum indicates increasing centrality density, with red areas highlighting the highest density regions. Legend for Kernel Density: Blue: Low density (< 0.523199) Green: Moderate density (0.523199 to 0.708735) Yellow: High density (0.708735 to 0.856058) Red: Very high density (> 0.856058) Bottom Left Panel (Local Moran’s I Analysis): This map displays the results of the Local Moran’s I statistical analysis to identify spatial clusters of similar values (High-High or Low-Low) and outliers. High-High clusters are indicated in dark blue, suggesting areas of significant urban agglomeration, while Low-Low clusters in light blue show less dense areas. Grey areas denote non-significant values. Legend for Local Moran’s I: Dark Blue: High-High (H-H) cluster Light Blue: Low-Low (L-L) cluster Grey: Not significant Right Panel (Research Area and Urban Center Mapping): This map provides a geographic overview of the research area, with specific urban center areas highlighted in pink. These areas represent significant urban density clusters identified through the kernel density and Local Moran’s I analyses. Legend for Right Panel: Pink: Urban center area Dashed outline: Research area.
Model comparison
To evaluate the effectiveness of different classification models in predicting urban center areas, we compared logistic regression, decision tree, and random forest models, the models took girds type as y (normal grid or center grid) and took total population as x. The comparison experiments results presented in Table 2. The classification results provided valuable insights into the strengths and weaknesses of each model, especially in the context of imbalanced data. The logistic regression achieved an overall accuracy of 97.38%, with a recall of 40.23% for the minority class (Center grid). The decision tree achieved an overall accuracy of 96.69%, but its recall for the Center grid was 39.23%, indicating that its performance was still suboptimal. These results suggest that while both the decision tree and logistic regression were effective at classifying the majority class (Normal grid), they were limited in their ability to identify minority class, resulting in low recall. This indicates their limitations in handling complex relationships within the data.
Table 2.
Confusion matrices of logistic regression, decision tree and random forest.
| Model | Logistic regression | Decision tree | Random forest | |||
|---|---|---|---|---|---|---|
| Samples | Normal grid | Center grid | Normal grid | Center grid | Normal grid | Center grid |
| Normal grid | 18,399 | 76 | 18,260 | 215 | 18,190 | 290 |
| Center grid | 426 | 275 | 419 | 282 | 336 | 360 |
| Accuracy | 97.38% | 96.69% | 96.73% | |||
| Recall | 39.23% | 40.23% | 51.72% | |||
In contrast, the random forest classifier performed significantly better in identifying the minority class, with a recall of 51.72%. This demonstrates that the random forest model is more effective at capturing the complex relationships within the data, which is crucial for accurately identifying samples from urban center areas. The recall for the Normal grid was 98.43%, indicating the model’s strong ability to correctly classify the majority class as well. This improvement in recall for both classes highlights the effectiveness of the ensemble approach in reducing overfitting and capturing more complex patterns in the data.
Accuracy of center grid classification
The total population model achieved 98.84% accuracy on the test set and 96.61% on the training set, as show in Table 3. Yet, for center grids, the recall rate was notably lower. In the training set, 487 out of 1793 center grid samples were misclassified, yielding a 72.84% recall rate. The center grid accuracy in the test set was only 51.72%, significantly lower than for general grids, indicating potential overfitting.
Table 3.
Confusion matrices of total population model and age group model.
| Total population Model | Age group Model | ||||
|---|---|---|---|---|---|
| Normal grid | Center grid | Normal grid | Center grid | ||
| Training set | Normal grid | 46,079 | 67 | 46,216 | 0 |
| Center grid | 487 | 1306 | 1 | 1722 | |
| Test set | Normal grid | 45,474 | 725 | 45,906 | 223 |
| Center grid | 840 | 900 | 627 | 1183 | |
Age group model is better than total population model, misclassification of center grids in the training set dropped to nearly zero, and the test set’s recall rate for center grids rose to 65.36%, with general grid accuracy reaching 99.52%. This highlights the substantial role of age demographics in identifying center grids.
The demographic model shows a significant improvement in accuracy, as show in Table 4. For the test dataset, misclassifications dropped to 97 for center grids and 168 for general grids, enhancing the recall rate of center grids to over 90% and achieving an overall accuracy above 99%. This marked improvement in accuracy and significant reduction in misclassification, with general grids decreasing by 24.66% and center grids by 87.50%.
Table 4.
Confusion matrices of demographic model.
| Normal grid | Center grid | ||
|---|---|---|---|
| Training set | Normal grid | 46,153 | 0 |
| Center grid | 0 | 1786 | |
| Test set | Normal grid | 46,031 | 168 |
| Center grid | 97 | 1643 | |
Threshold rules (decision rules) from Random Forest
In the classification rules for center grids, different demographic characteristics groups have different lower limits, indicating that different demographic characteristics have varying levels of influence on the development of urban centers, as show in Table 5. In these rules, the most frequently appearing are YF and SBMM, and their lower limits are not always constant. For example, in some rules YF > 578, while in others, YF > 322. Similarly, SBMM varies from SBMM > 587 to SBMM > 318 in others. The lower limits for different population groups in the rules exhibit high and low configuration features. This suggests that there may be a hierarchy of influence within the rules, indicating that different demographic characteristics groups have varying degrees of impact. The sum of the lower limits for each group in the classification rules is consistently around 1000, indicating that a city center with a 1 hm2 area requires approximately 1000 people to support demand. However, the specific configuration of demographic characteristics may differ in these requirements.
Table 5.
Decision rules with high accuracy.
| Grid | Decision rules |
|---|---|
| Normal grid | MHMM ≤ 11, MHMF ≤ 8, MBMF ≤ 380 |
| EMM > 26, YM > 49, MBMF ≤ 380, MHMF ≤ 13 | |
| YM ≤ 48, MBMF ≤ 380, MHMF ≤ 13 | |
| MHSM ≤ 6, MHMM ≤ 11, YF ≤ 578 | |
| SBSM > 1, MBMM ≤ 635, MHSF > 4, MHSM ≤ 9, YF ≤ 322 | |
| Center grid | SBSF > 9, SBMM > 587, YF > 578, MHMF > 13, SH > 3 |
| MBMM > 1090, MBSF > 87, MHMF > 13 | |
| YF > 578, SBMM > 318, MBSF > 87, MHMM > 19 | |
| SBMF > 211, MBSM > 160, YF > 578, SH > 3 | |
| MHMF > 33, SBMM > 587, YF > 322 |
Influence from subordinate resident groups
The mean SHAP value indicated that the most important demographic characteristics in the predicted center grids is YF, as show in Fig. 5. The second one is SBMM, the third one is SBMF, followed by SH, MBSF, and MBSM. YF is the largest in terms of population, but even among similar age groups, YM has a significantly lower impact. One explanation is that young females exhibit prominent consumption power, which plays a crucial role in driving the development of urban centers. SBMM and SBMF are both large groups, which belong to the same age group with similar education and marital statuses. One explanation is fewer financial burdens and greater consumption potential, which can contribute to the development of urban centers. MBSF and MBSM represent smaller populations. Unlike the senior age groups, the wealth accumulation of the middle age groups could not be completed, as children may still need to be raised. The single ones may imply lower life and support pressure, potentially leading to stronger consumption power for urban services. SH is a relatively small demographic characteristics group, but they are more likely to occupy advantageous positions in terms of social wealth. Additionally, they experience lower life pressure, making them more receptive to bulk and high-quality services, which significantly contribute to urban development. MHMM and ESM were excluded due to their negligible impact.
Fig. 5.
SHAP Value Analysis of Demographic Influence on Urban Center Formation. Left Panel (Bar Chart Comparison): This panel presents a comparative analysis of SHAP values (Shapley Additive exPlanations) which quantitatively describe the impact of various demographic groups on the model’s output for predicting urban center formation. The chart is split into two classes: Class 0 (Blue Bars): Represents the impact of demographic groups when not contributing to urban center formation. Class 1 (Red Bars): Represents the impact of demographic groups when contributing to urban center formation. Longer bars indicate a greater impact on the model’s prediction, with the mean SHAP value shown on the x-axis. Right Panel (Beeswarm Plot): This plot displays individual SHAP values for each demographic group, showing the distribution of their impacts on the prediction model. Points are colored and positioned according to their impact: Blue Points: Indicate a negative impact on urban center formation. Red Points: Indicate a positive impact on urban center formation. The position on the x-axis reflects the magnitude of impact, with the center line at zero indicating no impact. Note: Each demographic group is labeled with abbreviations, such as ‘YF’ for young females, ‘SBMM’ for senior basic educated married males, etc.
From the SHAP values, the x-axis represents the variable value, and the y-axis represents the local effect. The top 5 demographic characteristics groups make positive contributions to urban centers. However, some groups have the opposite effect, such as SBSM, SU, and ESF. One possible explanation is that older single individuals in these groups may have lower demand for urban centers. They might have a smaller activity range and lower social travel needs, preferring scattered living facilities near their residences. YM makes both positive and negative contributions to urban centers. One explanation could be that young men are more tolerant of the layout of urban services, whether dispersed or concentrated in urban centers. This flexibility reflects the diversity of their preferences and needs. The contributions of all groups are less than 0.3, indicating no single group exerts the decisive impact on urban centers. Instead, a combination of different demographic characteristics groups is needed to support the development of urban centers.
Considering the top six groups with importance exceeding 0.1 for interaction importance, the local effects of an explanatory variable are composed of main local effects and local interaction effects with other variables. For each variable, we computed the interaction effects with the rest of the variables (calculated by averaging absolute SHAP interaction values per variable pair) and then screened out the one with the strongest interaction effects.
YF and SBMF are highly correlated groups, as show in Fig. 6, and their interaction indicates that once a certain threshold is reached they no longer make additional contributions. This aligns with expectations. Their interaction shows three trend lines, suggesting the formation of three different thresholds. Among these, the trend line with the lower threshold is cross-type. In this case, YF can reach the threshold with a relatively low quantity of SBMF. One possible explanation is that YF has a strong influence, and the low-level threshold can be achieved with low-frequency combinations with SBMF. The other two trend lines show synchronized interactions, where both groups need to increase together to reach a certain condition that supports urban centers. SBMM has the strongest interaction with SBMF, indicating that they are likely to be married couples and their influence is formed in a family context. Therefore, the interaction between SBMM and SBMF is also synchronized.
Fig. 6.
SHAP Value Interaction Plots. General Description: The series of scatter plots illustrate the interaction effects between pairs of demographic characteristics on the model’s output. Each plot shows how the SHAP value (on the left y-axis) for one feature (on the right y-axis) changes in relation to another feature (on the x-axis). Blue Dots: indicating a lower impact on the predictive outcome when both features are considered together. Red Dots: suggesting a higher impact on the predictive outcome when considering the interaction of both features.
SH has the strongest interaction with YF and exhibits two distinct trend lines. One is a fixed-type interaction. In this case, SH has a strong influence and is not constrained by population size. It can form a threshold even with a very small size. This suggests that SH’s influence is significant and does not necessarily require a large population to make impaction. Another is peak-type interaction that shows a synchronized increase followed by a synchronized decrease. One possible explanation is that SH living in close-knit communities may rely on community services, reducing their dependence on urban services, especially for elderly care. As a result, their influence reaches a peak and then goes to mean reversion.
MBSF has the strongest interaction with SBMF, and three trend lines are observed, including two fixed-type interactions with low thresholds when the SBMF population is low. The third trend is a peak-type interaction, where the peak occurs at around 200 SBMF individuals. This suggests that the influence of MBSF is limited and regresses toward the mean as the SBMF population increases.
MBSM exhibits a synchronized-type interaction with YF, possibly indicating a synergistic effect, such as that of single-parent households. Another possible explanation is that single or divorced males in this category have lower family-related financial burdens, which allows for more stable income and strong consumption preferences, similar to young females.
In these interactions, female groups tend to interact more strongly with other female groups, possibly reflecting similar consumption and service preferences. On the other hand, male groups tend to interact with either same-age female groups or younger female groups, possibly indicating family-related synergies.
Evaluating the local effects of demographic characteristics on urban center can provide useful references for fostering vibrancy in urban center areas. An important way to achieve such a goal is to reveal similar patterns of local effects among urban center areas and propose targeted strategies. This can eventually lead to more precise and nuanced interventions toward urban centers.
We take the 20 demographic characteristics groups as the input of the K-means and put the grids into two clusters: cluster 1 are in the core of the main center and the core of the second center (in Fig. 7), and the grids of cluster 2 are in the sub-centers or edge of large centers (the main center and the second center), which makes a significant spatial pattern of the clusters.
Fig. 7.
Spatial Analysis of Urban Centers and Demographic Characteristics Clusters in Xiaoshan District, Hanzhou. Left Panel: This map illustrates the spatial distribution of two clusters within Xiaoshan District, outlined as the study area. Cluster 1 is represented in pink, Cluster 2 in blue, depicting urban centers’ delineation. The black squares indicate the dense core of main urban centers. Right Panel (Top Section): The horizontal bar charts detail the influence of various demographic groups on the development of urban centers, arranged by sample order based on similarity. The bars are color-coded to indicate the level of impact, with red for higher impact and grey for lower. Right Panel (Middle Section): A force plot displays the probability distribution of areas being urban centers, with the x-axis showing sample order by similarity, and the y-axis depicting the likelihood of urban center status. Red peaks represent areas with a higher probability, and blue indicates a lower probability. Right Panel (Bottom Section): Expanded force plots for selected grids within the clusters highlight specific demographic groups’ contributions to urban center classification. The baseline indicates the threshold, with bars to the right showing a positive influence and bars to the left showing a negative influence. Note: Demographic groups are abbreviated (e.g., ‘YM’ for young male, ‘MBMF’ for middle-aged basic educated married female), with their impacts quantified on the scales next to each bar.
two grids from each cluster are selected as examples to understand cluster characteristics better. The demographic characteristics impact on both clusters is mainly positive. The SHAP values shows two patterns:
In cluster 1, which has a higher predicted probability urban center grid, the top three influences are YF, SBMM, and MBSF. This indicates that female residents, especially young females, have a significant preference for high-quality urban services, enabling them to strongly influence the development of the core areas of the urban center. Furthermore, it reaffirms the differences in influence among demographic groups when segmented by age, with single middle-aged households having a stronger influence, while married senior-aged households also exhibit substantial influence.
In cluster 2, where the top five influences are SH, SBSM, SBMF, SBSF, and MBSM. In the senior age group, the influence of higher education is clear. One possible explanation is that they tend to make more rational choices, seeking lower rent but better-quality residential spaces. Additionally, they have a wider range of urban service needs, which strongly drive the development of local education, culture, sports, and other urban services, leading to the formation and growth of secondary centers. Furthermore, both single men and women exhibit active influence in both clusters, including MBSF, SBSM, MHSF, SBSM, SBMF, SBSF, and MBSM. One explanation is that the awakening of individual preferences and reduced family responsibilities give single households more choices in urban services, significantly contributing to the growth of consumer-oriented urban services.
Discussion and conclusions
This study analyzed how demographic traits affect urban centers using POI data and residential demographics, including age, gender, marital status, and education, to form 22 demographic groups. It trained three Random Forest models for urban center identification, using population data, age structure, and the demographic groups. After testing for accuracy and comparing models, the best model’s decision rules were used to understand demographic distributions. The study also assessed the significance of these groups and their interactions through SHAP values and cluster analysis, focusing on Xiaoshan District, Hangzhou, China.
By comparing the confusion matrices of the three models, the demographic model exhibits the highest precision, considering the explanatory power of population structure features is crucial. The generated decision rules are all based on combinations of multiple rather than single features, indicating that the development of urban centers relies on diverse population demands. Different population groups have varying lower limits, implying that different groups have varying degrees of influence on the development of urban centers. The population thresholds in the rules are all around 1000, suggesting that each km2 of urban center area requires approximately 1000 people to support demand. The most prominent groups affecting urban centers are YF, SBMM, SBMF, SH, MBSF, and MBSM, with no single decisive feature among them. Nonlinear correlation is the primary characteristic of demographic impact on urban polycentric structure, including differences between age groups, where middle age single households have more influence, but senior age married households have stronger influence. Synergistic effects significantly contribute to the development of polycentric structures, with female groups often interacting more strongly with other female groups, indicating convergence in consumption and service preferences. Male groups tend to interact with female groups of the same age or younger, possibly indicating family-based synergies. Spatial heterogeneity exists in the demographic mechanisms, according to the analysis of sample influence after clustering reveals two patterns: (1) the core area of the main center is more influenced by young women and single women and (2) the peripheral area and secondary centers of the main center are more influenced by highly educated populations.
It is verified that the significant role that population plays in the formation and development of urban centers. Even in contemporary life, with the advancement of Internet technology and the Internet of Things (IoT), the decentralized way of life has become important. However, residential life still depends on urban public spaces and modes of public consumption, and urban centers are expected to remain a crucial part of urban structures in the foreseeable future. Furthermore, this study delves into the analysis of demographic characteristics such as age, gender, marital status, and education level, and their influence on urban centers. An exploration of the local impact of demographic characteristics groups, interactions between multiple groups, and the explanatory differences of individual samples after clustering sheds light on the nonlinear contributions of demographic characteristics to urban centers. This work lays the foundation for understanding the mechanisms through which population affects urban centers. This contributes to the formulation of effective urban planning and management strategies, including the consideration of the diverse impacts of population structures on multi-center layouts and the configuration of urban functional facilities.
In future work, we plan to conduct further comparative analyses to evaluate the applicability of more models and provide a deeper theoretical discussion. Additionally, we intend to explore the inclusion of more advanced machine learning techniques, such as deep learning models, to assess their effectiveness in capturing the complex, non-linear relationships inherent in urban data. We also plan to investigate the potential for incorporating geospatial data from different sources, including remote sensing and social media, to enhance the robustness of our analysis. Furthermore, we aim to expand the scope of our research by applying our methods to different urban contexts, such as smaller cities or rural–urban transition areas, to evaluate the generalizability of our findings. By doing so, we hope to better understand how different population and economic structures impact polycentric urban development across various geographic scales. We will also engage in a more in-depth theoretical exploration of the mechanisms through which demographic characteristics influence urban spatial structures, thus providing comprehensive insights that can be used to formulate data-driven urban planning strategies.
Author contributions
Yichen Ruan wrote the main manuscript text and prepared figures. Xiaoyi Zhang did the research and data collection and prepared Figs. 1, 2. Mingyu Zhang developed the manuscript. Yichen Ruan did data analysis. Feiyang Sun and Qiuxiao Chen checked the main manuscript text. Xiaoyi Zhang did the survey. All authors reviewed the manuscript.
Funding
Joint Funds of the Zhejiang Provincial Natural Science Foundation of China, LHZY24A010001, Incubation Fund of Hangzhou City University, X-202211, National Key R&D Program of China, 2018YFD1100302.
Data availability
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Vlahov, D. Urbanization, Urbanicity, and Health. Journal of Urban Health: Bulletin of the New York Academy of Medicine79, 1S – 12 (2002). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Wang, H., He, Q., Liu, X., Zhuang, Y. & Hong, S. Global urbanization research from 1991 to 2009: A systematic research review. Landsc. Urban Plan.104, 299–309 (2012). [Google Scholar]
- 3.Ouyang, Z. et al. Albedo changes caused by future urbanization contribute to global warming. Nat Commun13, 3800 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4.Tian, Y., Tsendbazar, N.-E., Van Leeuwen, E., Fensholt, R. & Herold, M. A global analysis of multifaceted urbanization patterns using Earth Observation data from 1975 to 2015. Landscape and Urban Planning219, 104316 (2022). [Google Scholar]
- 5.Lv, Y., Zhou, L., Yao, G. & Zheng, X. Detecting the true urban polycentric pattern of Chinese cities in morphological dimensions: A multiscale analysis based on geospatial big data. Cities116, 103298 (2021). [Google Scholar]
- 6.Zhang, W., Derudder, B., Liu, X., Sun, B. & Wang, Y. Defining ‘centres’ in analyses of polycentric urban regions: the case of the Yangtze River Delta. Regional Studies56, 87–98 (2022). [Google Scholar]
- 7.McDonald, J. F. The identification of urban employment subcenters. Journal of Urban Economics21, 242–258 (1987). [Google Scholar]
- 8.Meijers, E. J. & Burger, M. J. Spatial Structure and Productivity in US Metropolitan Areas. Environ Plan A42, 1383–1402 (2010). [Google Scholar]
- 9.Zhang, W., Fang, C., Zhou, L. & Zhu, J. Measuring megaregional structure in the Pearl River Delta by mobile phone signaling data: A complex network approach. Cities104, 102809 (2020). [Google Scholar]
- 10.McMillen, D. P. Employment Densities, Spatial Autocorrelation, and Subcenters in Large Metropolitan Areas. Journal of Regional Science44, 225–244 (2004). [Google Scholar]
- 11.Liu, X. et al. Characterizing the polycentric spatial structure of Beijing Metropolitan Region using carpooling big data. Cities109, 103040 (2021). [Google Scholar]
- 12.Huang, D., Liu, Z., Zhao, X. & Zhao, P. Emerging polycentric megacity in China: An examination of employment subcenters and their influence on population distribution in Beijing. Cities69, 36–45 (2017). [Google Scholar]
- 13.McMillen, D. P. & Smith, S. C. The number of subcenters in large urban areas. Journal of Urban Economics53, 321–338 (2003). [Google Scholar]
- 14.Aguilera, A. Growth in Commuting Distances in French Polycentric Metropolitan Areas: Paris. Lyon and Marseille. Urban Studies42, 1537–1547 (2005). [Google Scholar]
- 15.Lv, Y., Lan, Z., Kan, C. & Zheng, X. Polycentric Urban Development and its Determinants in China: A Geospatial Big Data Perspective. Geogr Anal53, 520–542 (2021). [Google Scholar]
- 16.Doyle, J., Hung, P., Farrell, R. & McLoone, S. Population Mobility Dynamics Estimated from Mobile Telephony Data. Journal of Urban Technology21, 109–132 (2014). [Google Scholar]
- 17.Zhu, H. Spatial Matching and Policy-Planning Evaluation of Urban Elderly Care Facilities Based on Multi-Agent Simulation: Evidence from Shanghai. China. Sustainability14, 16183 (2022). [Google Scholar]
- 18.Lai, Y., Lv, Z., Chen, C. & Liu, Q. Exploring Employment Spatial Structure Based on Mobile Phone Signaling Data: The Case of Shenzhen. China. Land11, 983 (2022). [Google Scholar]
- 19.Jiang, L. & Wu, F. A Study on Guangzhou’s Employment Subcentres and Polycentricity. Urban Planning Forum 75–81 (2009).
- 20.Heikkila, E. et al. What Happened to the CBD-Distance Gradient?: Land Values in a Policentric City. Environ Plan A21, 221–232 (1989). [Google Scholar]
- 21.Shi, B. Polarization And Flattening Of City Center System: The Evolution With The Effect Of Agglomeration-difusionConvection. Planners34, 85–90 (2018). [Google Scholar]
- 22.Li, Y. & Du, R. Polycentric urban structure and innovation: evidence from a panel of Chinese cities. Regional Studies56, 113–127 (2022). [Google Scholar]
- 23.Zhu, C. et al. Urban–rural construction land transition and its coupling relationship with population flow in China’s urban agglomeration region. Cities101, 102701 (2020). [Google Scholar]
- 24.Wang, H., Yuan, F., Wei, Y. D., Chen, W. & Wang, L. Understanding spatial and compositional dynamics of employment centers in urban China: Empirical evidence from Nanjing. Growth and Change52, 2635–2661 (2021). [Google Scholar]
- 25.Sýkora, L. & Ourednek, M. Sprawling post-communist metropolis: Commercial and residential suburbanization in Prague and Brno, the Czech Republic. in Employment Deconcentration in European Metropolitan Areas (eds. Razin, E., Dijst, M. & VÁZquez, C.) vol. 91 209–233 (Springer Netherlands, Dordrecht, 2007).
- 26.Ruan, Y., Liu, S. & Li, W. Public Center System Identification Based on Multiple Data : The Case of Xiaoshan District in Hangzhou. Economic Geography39, 103–109 (2019). [Google Scholar]
- 27.Long, Y., Song, Y. & Chen, L. Identifying subcenters with a nonparametric method and ubiquitous point-of-interest data: A case study of 284 Chinese cities. Environment and Planning B: Urban Analytics and City Science49, 58–75 (2022). [Google Scholar]
- 28.He, X., Zhou, C., Zhang, J. & Yuan, X. Using Wavelet Transforms to Fuse Nighttime Light Data and POI Big Data to Extract Urban Built-Up Areas. Remote Sensing12, 3887 (2020). [Google Scholar]
- 29.Xiao, Y., Wang, Y., Miao, S. & Niu, X. Assessing polycentric urban development in Shanghai, China, with detailed passive mobile phone data. Environment and Planning B: Urban Analytics and City Science48, 2656–2674 (2021). [Google Scholar]
- 30.Wang, S., Fang, C., Ma, H., Wang, Y. & Qin, J. Spatial differences and multi-mechanism of carbon footprint based on GWR model in provincial China. J. Geogr. Sci.24, 612–630 (2014). [Google Scholar]
- 31.Zhou, L., Dang, X., Sun, Q. & Wang, S. Multi-scenario simulation of urban land change in Shanghai by random forest and CA-Markov model. Sustainable Cities and Society55, 102045 (2020). [Google Scholar]
- 32.Dabove, P., Daud, M. & Olivotto, L. Revolutionizing urban mapping: deep learning and data fusion strategies for accurate building footprint segmentation. Sci Rep14, 13510 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33.Li, W. et al. Widespread increasing vegetation sensitivity to soil moisture. Nat Commun13, 3959 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 34.Xiao, L., Lo, S., Liu, J., Zhou, J. & Li, Q. Nonlinear and synergistic effects of TOD on urban vibrancy: Applying local explanations for gradient boosting decision tree. Sustainable Cities and Society72, 103063 (2021). [Google Scholar]
- 35.Bansal, P. & Quan, S. J. Examining temporally varying nonlinear effects of urban form on urban heat island using explainable machine learning: A case of Seoul. Building and Environment247, 110957 (2024). [Google Scholar]
- 36.Wagner, F. et al. Using explainable machine learning to understand how urban form shapes sustainable mobility. Transportation Research Part D: Transport and Environment111, 103442 (2022). [Google Scholar]
- 37.Mulligan, G. F. Agglomeration and Central Place Theory: A Review of the Literature. International Regional Science Review9, 1–42 (1984). [Google Scholar]
- 38.Lundberg, S. M. & Lee, S.-I. A Unified Approach to Interpreting Model Predictions.
- 39.Lundberg, S. M. et al. From local explanations to global understanding with explainable AI for trees. Nat Mach Intell2, 56–67 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 40.Ouwehand, W. M., Van Oort, F. G. & Cortinovis, N. Spatial structure and productivity in European regions. Regional Studies56, 48–62 (2022). [Google Scholar]
- 41.Cai, J., Huang, B. & Song, Y. Using multi-source geospatial big data to identify the structure of polycentric cities. Remote Sensing of Environment202, 210–221 (2017). [Google Scholar]
- 42.Wei, L. et al. Multiscale identification of urban functional polycentricity for planning implications: An integrated approach using geo-big transport data and complex network modeling. Habitat International97, 102134 (2020). [Google Scholar]
- 43.Deng, Y., Liu, J., Liu, Y. & Luo, A. Detecting Urban Polycentric Structure from POI Data. IJGI8, 283 (2019). [Google Scholar]
- 44.Jiang, L., Wu, Y., Wang, J., Han, H. & Shi, K. A nonparametric approach for detecting urban polycentric spatial structure in China using remote sensing nighttime light and point of interest data. GIScience & Remote Sensing61, 2383461 (2024). [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.