Study on the spatial relationship between road network and the diversity of urban public facilities: the case of the central area of Changsha City

Abstract

In the context of contemporary urbanization, the significance of diversifying urban public facilities has attracted significant attention. This study examines the relationship between road network and the diversity of urban public facilities in Changsha City. These factors are measured through the Shannon-Weiner Index and Space Syntax method. To provide greater specificity, the study employs Random Forest and Geographically Weighted Regression models to analyze the relationship between road networks and the diversity of urban public facilities. The results identify a nonlinear relationship between these variables. In addition, high accessibility exhibits a stronger association with diversity than accessibility alone, and this correlation is reflected in varying degrees of inconsistency across different study areas. Finally, the cartographic depiction of diversity clusters is overlaid on the road network, demonstrating a significant relationship between the configuration of the road network and diversity patterns. In conclusion, this research emphasizes the robust correlation between the roadway network and the diversity of urban public facilities. It prompts local governments to focus beyond mere equality, with a greater commitment to enhancing the quality of life for residents through diversity.

Introduction

Urban public facilities (UPFs) are typically defined as services or amenities provided directly or indirectly by the local government for the welfare of all residents while addressing their fundamental physical and mental needs locally [1, 2]. A global consensus exists regarding the equitable provision of UPFs [3]. For instance, the United Nations’ 2030 Agenda for Sustainable Development advocates for universal access to adequate, secure, and affordable essential services. However, China’s rapid urbanization has given rise to challenges such as “the contradiction between unbalanced and insufficient development of public service facilities and the ever-increasing aspirations of the populace for an improved quality of life” [4, 5]. Research into the optimal arrangement of UPFs holds immense significance in UPF equalization and the promotion of social equity [6, 7].

Existing literature concerning UPF equality and fairness revolved around their spatial distribution [7, 8]. However, the demand for public services among residents has grown increasingly diverse and personalized. This necessitates the provision of diversified and optimized facilities in urban environments to cater to the multi-level daily needs of residents in their respective service areas [9, 10]. For instance, in terms of dimension, there is a need for sports and cultural amenities besides essential educational and healthcare facilities. On the level, of urban households, large supermarkets are essential for planned shopping requirements characterized by low frequency but substantial quantities and varieties. Simultaneously, smaller shops close to residential areas are essential to address immediate shopping needs with a relatively limited range of items [11]. Therefore, the study of spatial distribution and allocation equilibrium across diverse facility types and scales is critical for equal allocation of basic public service amenities.

Urban roads represent a critical component of urban infrastructure, facilitating human social and economic activities in urban settings [12]. The complex road network closely interconnects the city’s facilities and significantly affects the layout of functional land zones, including commercial, residential, employment, and public service areas [13]. In addition, the spatial configuration of urban functional facilities guides the planning and construction of urban transportation facilities, leading to a symbiotic relationship between the two [14]. Conventionally, accessibility critically assesses UPF distribution fairness and transportation system interaction [7, 15]. The prevailing notion posits that an imbalanced coverage of a city’s transportation network or an underdeveloped transportation system significantly reduces UPF accessibility. Nonetheless, empirical validation regarding whether the diversified configuration of UPFs aligns with the spatial morphology of road networks remains scarce.

Accordingly, this study seeks to quantitatively analyze the correlation between the diversity of UPFs and the configuration of the road network. Employing Changsha as an example, this paper employs a diversity index model to assess its spatial distribution and spatial diversity attributes using a large dataset. Concurrently, spatial syntax is employed to quantify the spatial distribution characteristics of the road network morphology. Thereafter, the Random Forest (RF) model is leveraged to explore the relationship between these variables. This research yields several contributions: (1) it delves into the diversity of UPFs, categorizing it into comprehensive diversity and facility diversity, followed by spatial analysis. (2) Random Forest and Geographically Weighted Regression (GWR) models are adopted, and their accuracy and fitting degree are compared to determine the superior model. (3) This study unravels the nonlinear correlation effect (specifically the effective range and threshold), between the road network configuration and the diversity of UPFs. (4) It offers valuable insights for scientifically and judiciously aligning the spatial distribution of UPFs with the road network.

Methods

Research design

As illustrated in Fig. 1, the research methodology can be segmented into several components. Firstly, the Shannon-Wiener Index, a conventional metric for measuring land use diversity, is employed to assess the diversity of UPFs in this study. For the road network, the sDNA model, grounded in graph theory, is leveraged to establish topological relationships in urban areas. Specifically, Network Quantity Penalized by Distance in Radius Euclidean (NQPDE) and Betweenness Euclidean (BTE) measures the form of the road network, accessibility, and traversability, respectively.

Fig. 1

Research design

Moreover, to explore the relationship between road networks and diversity, we employ the RF model and Geographically Weighted Regression (GWR) to identify the nonlinear or linear effects of factors. Notably, the RF model is associated with a black box phenomenon, rendering limited interpretability [16, 17]. Therefore, we introduce Shapley Additive Explanations (SHAP) to evaluate the RF model. SHAP values indicate the relationship between the road network and diversity, akin to the regression coefficients in the GWR model.

Study area

Changsha, nestled in the heart of China’s Hunan culture, features a rich cultural heritage and a blend of mountains, waterways, forests, and urban landscapes. It is a renowned historical and cultural city, positioned for the advancement of central China and the urban agglomeration in the middle reaches of the Yangtze River. Embracing the concept of age-friendly urban planning, recent years have witnessed significant enhancements in UPFs in the city. Therefore, taking Changsha as an example offers both theoretical and practical significance. The study area is outlined by the Bypass Highway and comprises approximately 879.826 km², including Furong District, Yuelu District, and Tianxin District, among others, as depicted in Fig. 2.

Fig. 2

Study area in Changsha, China

Data sources and preprocessing

The UPFs are primarily sourced from POIs on Amap (https://lbs.amap.com). In accordance with research [11], the raw POI data is transformed into the specified types in the planning standards, as presented in Table 1.

Table 1 Reclassification of urban public facilities

Additionally, OpenStreetMap is employed to acquire the road network data for the sDNA model calculations. This dataset is compared with Gaode maps, including expressways, national highways, provincial highways, and urban roads. To mitigate boundary effects, the road network is extended by approximately 5 km beyond the study area.

Diversity index of UPFs

The diversity of UPFs is dissected into several components for definition purposes. Building on relevant research [11], it is further subdivided into comprehensive diversity (CD) and facility diversity (FD), with calculations based on the Shannon–Wiener index [18]. Moreover, for spatial statistical analysis, prior studies have recommended the utilization of hexagons as a suitable spatial unit [19]. In line with these recommendations [17], a 10-min walking radius of 0.8 km is selected as the search radius, and 0.8 km × 0.8 km hexagonal grids are constructed for spatial statistics of POI data. The specific equation and definition are as follows:

$${CD}_j=-\sum P_{ij}\;\text{ln }P_{ij}$$

(1)

$${FD}_j=-\sum P_{mj}\;\text{ln }P_{mj}$$

(2)

${CD}_{j}$ represents the diversity of sub-categories of UPFs in $j$ th cell, and it ranges from [0, $\text{ln}N$]. In this formula, $N$ refers to the number of sub-categories summed in each mid categories of UPFs, and ${P}_{ij}$ denotes the ratio of the number of $i$ th type of UPFs to the number of total facilities in $j$ th cell.

${FD}_{j}$ is nearly identical to ${CD}_{j}$, while the $m$ refers to the order of mid-categories, and ${P}_{mj}$ means the proportion of the $m$ th sub-categories to their mid-categories in $j$ th cell. The more diverse the UPFs in the cell are, the higher the diversity.

Form index of road network

The sDNA model was employed to compute accessibility and traversability across various scales, represented by the NQPDE and BTE indicators [20]. In the sDNA framework, NQPDE represents a form of proximity, often referred to as a gravity model, including both the quantity of network weight. Meanwhile, BTE determines the count of geodesic paths passing through a vertex, indicating the number of times a vertex appears on the shortest path between other pairs of vertices. In addition, a search radius of 0.8 km and the value N were utilized in this model, mirroring the typical range of residents’ daily outdoor activities. These calculations are as follows:

$$\text{NQPDA}\left(x\right)= \sum\nolimits_{y\in {R}_{x}}\frac{(W(y)P(y))}{{d}_{M}(x,y)}$$

(3)

where $W(y)$ is the weight of chain $y$; $P(y)$ is the weight of node $y$ in search radius R; ${d}_{M}(x,y)$ is the shortest topological distance from node $x$ to node $y$.

$$\text{Betweeness}\left(x\right)= \sum\nolimits_{y\in N}\sum\nolimits_{z\in {R}_{y}}W(y)W(z)P(z)OD(y,z,x)$$

(4)

$${OD}_{(y,z,x)}=\left\{\begin{array}{c}1,if\;x\;\mathrm{is}\;\mathrm{on}\;\mathrm{the}\;\mathrm{first}\;\mathrm{geodesic}\;\mathrm{found}\;\mathrm{from}\;y\;to\;z\\1/2,\;if\;x=y\neq z\\1/2,\;if\;x=z\neq y\\1/3,\;if\;x=y=z\\0,\;\mathrm{otherwise}\end{array}\right.$$

(5)

where ${OD}_{(y,z,x)}$ is the shortest topological path from $y$ to $z$ through node $x$ in the search radius; $W(y)$ is the total weight of $y$ in the radius.

Modeling approach

The effect of the road network on the diversity of UPFs may exhibit a linear or nonlinear trend, which prompted the selection of two models: the GWR and RF models, as detailed in the “Study area” section 2.2 above. Regarding the RF model, the SHAP value is employed to explain its potential effect, benchmarked against the regression efficiency of the GWR model.

Geographically weighted model

The geographically weighted model method measures the heterogeneity or non-smoothness characteristics in spatial data relationships through the solution of a locally weighted regression analysis model, with varying parameter estimates based on spatial location. Numerous studies have employed this method to analyze spatial influence relationships, yielding significant research results. Therefore, this paper opts for the Geographically Weighted Regression model to analyze whether a typical spatial influence pattern exists between road network morphology and diversity. The formula is as follows:

$${H}_{j}={\beta }_{0}\left({u}_{j},{v}_{j}\right)+ \sum\nolimits_{n=1}{\beta }_{n}\left({u}_{j},{v}_{j}\right){X}_{jn}+ {\varepsilon }_{j}$$

(6)

where ${X}_{jn}$ is the diversity index in cell $j$, $n$ is the number of independent variables; $\left({u}_{j},{v}_{j}\right)$ is the value in cell $j$. ${\beta }_{n}\left({u}_{j},{v}_{j}\right)$ is the regression equation intercept and ${\varepsilon }_{j}$ is the error term.

Random forest

Random Forest is an integrated learning method based on the decision trees model, renowned for its exceptional ability to capture non-linear correlations [21]. The RF model employs the Bootstrap sampling method to randomly select $n$ samples from the training dataset, creating $m$ subsets, each of which fits a separate decision tree. The average of the prediction results from these $m$ decision trees serves as the output. The mechanism of the RF regression algorithm is illustrated in Fig. 3.

Fig. 3

Mechanism of Random Forest regression

In this research, road network indicators are represented as X and UPF diversity as y. The training process incorporates cross-validation to assess model stability and accuracy. Finally, hyper-parameters are adjusted to optimize model performance.

This paper utilizes the Classification and Regression Tree as the fundamental unit to construct a random forest regression model. The steps of the Classification and Regression Tree for generating a regression tree are as follows:

• (1) In the input space D, which includes the training dataset, the optimal j and s are selected by iterating through each feature j and its corresponding value s. The squared error minimization criterion is used for this selection, with the optimization objective as

  $${\text{min}_{j,s}}\left[{\text{min}_{C_1}}\sum\nolimits_{x_i\in R_1(j,s)}{(y_i-c_1)}^2+{\text{min}_{C_2}}\sum\nolimits_{x_i\in R_2(j,s)}{(y_i-c_2)}^2\right]$$

  (7)

• (2) Utilizing the chosen optimal j and s, the input space D is divided into two subspaces, R1 and R2, with corresponding output means C1 and C2;

• (3) Steps (1)–(2) are repeated for the two subspaces R1 and R2 until no further feature divisions are possible. At this juncture, all nodes form the regression tree.

The random forest regression model incorporates the road network form factor and control variables associated with each aspect of diversity as input variables, with the actual diversity as the output. During the modeling process, two crucial parameters must be determined: the quantity of decision trees and the number of features utilized in each decision tree. The values for these parameters are determined through a combination of grid search and cross-validation methods in the experimental phase (Table 2).

Table 2 Parameters specified in the model

Shapley additive explanations

To explain the results of the RF, the SHAP model by Lundberg and Lee is employed [22]. This method aids in understanding the nonlinear relationship between road network form and UPF diversity [23]. Inspired by cooperative game theory, SHAP constructs an additive explanatory model where all features are considered “contributors” [24]. In cases of nonlinearity or interdependent input features, SHAP computes a weighted average by ranking all possible features. SHAP interprets the model's prediction as the sum of imputed values for each input feature, with the assigned values being the Shapley values [17], calculated as follows:

$$g(x)={\phi }_{0}+\sum\nolimits_{j=1}^{M}{\phi }_{j}$$

(8)

where ${\phi }_{0}$ is the constant that explains the model, and is the predicted mean of all training samples. Each feature has a corresponding Shapley value, i.e., ${\phi }_{j}$:

$${\phi }_{j}=\sum\nolimits_{S\subseteq \left\{{x}_{1},\cdots ,{x}_{p}\right\}\setminus \left\{{x}_{j}\right\}}\frac{\left|S\right|!\left(p-\left|S\right|-1\right)!}{p!}\left({f}_{x}\left(S\cup \left\{{x}_{j}\right\}\right)-{f}_{x}\left(S\right)\right)$$

(9)

where $\left\{{x}_{1},\cdots ,{x}_{p}\right\}$ is the set of all input features, $p$ is the number of all input features, $\left\{{x}_{1},\cdots ,{x}_{p}\right\}\setminus \left\{{x}_{j}\right\}$ is the set of all possible input features that do not include $\left\{{x}_{j}\right\}$, and ${f}_{x}\left(S\right)$ is the set of feature subsets $S$ of predictions. The weight $\frac{\left|S\right|!\left(p-\left|S\right|-1\right)!}{p!}$ can be interpreted as follows: the denominator $\text{p}!$ represents the combination of $p$ features in arbitrary ordering, and the numerator $\left|S\right|!\left(p-\left|S\right|-1\right)!$ denotes the combination of $p$ features under a particular ordering after determining the subset S; $\frac{\left|S\right|!\left(p-\left|S\right|-1\right)!}{p!}$ is the proportion of feature combinations of subset $S$, and the sum of all possible subsets is equal to one.

Results

Diversity and spatial distribution of road network patterns

To investigate the correlation between road network morphology and the diversity of UPFs, it is necessary to collect and calculate diversity and road network morphology parameters. After excluding grid units lacking public service facilities, the diversity and road network morphology parameters are standardized using the min–max method. The results of this calculation for diversity and road network morphology are presented in Fig. 4.

Fig. 4

Calculation of Diversity, NQPDE, and BTE at different scales

It can be observed in Fig. 4 that the diversity in the study area is concentrated in the commercial zones of the city center, such as Wuyi Square and Huangxing Pedestrian Street, among other busy areas. In addition, diversity is reduced further away from the city center, displaying the characteristics of a circular “core-edge” structure. Influenced by planning policies, traffic flow, and other factors, the diversity of the road network in the study area is notably low, a consequence of the “core-edge” structure. Additionally, the topology of the road network in the study area displays a “square-ring-radial” circular distribution, influenced by planning policies and traffic flow. This topology results from the integration of various road network forms and also shapes the spatial distribution of the NQPDE with the “core-edge” attribute.

Moreover, the results of the diversity and road network morphology calculations were integrated into both the GWR model and RF model for training in regression tasks for the following analysis. Table 3 presents the regression accuracies, indicated by ${R}^{2}$ and Adjusted R², for the GWR and RF models. The RF model displays exceptional performance with Adjusted R² values ranging from 70 to 80% across different scales. Conversely, the GWR model exhibits lower and less consistent performance. This suggests that the RF model may unveil more complex mechanisms in this research context. It has also been previously demonstrated in this research [25] that the city functions as a complex giant system, wherein several factors interact not in a simple linear manner, but rather exhibit nonlinear synergistic relationships among different factors. It can be postulated that a similarly complex nonlinear relationship exists between road network morphology and diversity a challenging task with traditional linear models. Therefore, this study will analyze the results of SHAP values derived from the RF model to provide insights into this relationship.

Table 3 R-square comparison of GWR and RF model

Relationship between the spatial distribution of diversity and road network

Theoretically, a linear correlation is expected between NQPDE and diversity when considering the same spatial distribution characteristics. However, this expectation does not hold true. As depicted in Fig. 5 (top left), NQPDE only positively affects CD in the ring-shaped area bounded by the second and fourth ring roads, consistently exhibiting relatively high values. This phenomenon occurs because this area serves as a transitional link between the city center and the periphery. The city center features a rich diversity of facilities, while the periphery experiences a gradual decrease. According to the ground-rent theory, the periphery has a larger population than the center, leading to reduced access to areas with high diversity due to the ring-like road network. In summary, an increase in NQPDE results in enhanced accessibility to the road network system, thereby increasing access to facilities. Therefore, the correlation between NQPDE and diversity is more pronounced at a global scale.

Fig. 5

Distribution of spatial relationships revealed by SHAP

In addition, there is a noticeable correlation between BTE and FD, especially at local scales, particularly at radial-like traffic nodes, as depicted in Fig. 5 (bottom right). The BTE represents high-level roads, such as national and provincial roads, where individuals do not linger but rather facilitate the flow of traffic across the area, resulting in a reduced probability of visitation. Therefore, areas with high BTE are likely to exhibit lower levels of diversity. Overall, the NQPDE demonstrates a predominantly positive relationship with diversity globally and locally, while BTE exhibits a negative effect.

Relationship between the quantity distribution of diversity and road network

The numerical impact of road network morphology on diversity is illustrated in Fig. 6. In this section, the x-axis represents the values of road indicators, with the y-axis representing the SHAP value, and the diversity values are color-coded. This figure emphasizes the significant relationship between NQPDE and diversity globally, and the relationship between BTE and diversity locally. This relationship can be specified as follows:

Fig. 6

Distribution of numerical relationships revealed by SHAP

As depicted in Fig. 6 (top left), the contribution of NQPDE to CD initially tends to increase, then stabilizes after surpassing the threshold of approximately 0.4. It can be inferred that a clear threshold exists, beyond which NQPDE significantly contributes to CD. Lower values of NQPDE exhibit a significant negative relationship with diversity, which gradually reduces to nearly zero as NQPDE increases and peaks in the range of x [0.4, 0.6], where the relationship becomes positive.

Locally, there appears an evident relationship between BTE and FD, as illustrated in the bottom right of Fig. 6. The SHAP values decrease steadily as BTE increases, starting from x and y at 0, and then the effect tends to decrease steadily, indicating a negative relationship with diversity. It can be inferred that as FD increases, indicating a higher-level road network, traffic flows through this area more freely. In conclusion, the reduction in accessibility caused by traversal traffic has a direct association with the richness of FD.

Relationship between the agglomeration distribution of diversity and road network

As presented in Fig. 7, both CD and FD exhibit highly agglomerative phenomena in the central area, while faint in the peripheral areas display sporadic high and low clustering distribution.

Fig. 7

Different agglomerations with their features

Upon comparing the road network indicators in Fig. 4 with the results of agglomeration in Fig. 7, a significant relationship is observed between the spatial aggregation characteristics of CD and FD and the topological features of the road network. This relationship exhibits grid-like, ring-like, and radial-like patterns as the distance increases from the city center. Specifically, in the central area where the road network is grid-like, there is an HH (high-high) agglomeration feature due to its accessibility and topology. The horizontal and vertical backbone of the road network reduces the cost of outdoor activity with convenient access to all areas, resulting in a strong ability to integrate surrounding regions. For the ring-like road area, low–high agglomeration emerges, as there are numerous ring roads to alleviate traffic pressure from directly passing through the city, albeit increasing the cost of entering the city and reducing opportunities for diversity in the central area. Finally, in the radial-like road area, the agglomeration feature tends to be low-low, primarily due to the functional nature of radial roads. These roads mainly transport peripheral traffic flow to the ring-like roads, and their traversing nature does not bring traffic to the periphery itself, resulting in low-low agglomeration and insignificance in the periphery.

Discussion

To enhance the living and working environment in urban areas, it is necessary to ensure that UPFs cater to the diverse needs of residents on a broader scale. When planning UPFs, the focus should shift from merely providing a certain quantity of services to guaranteeing the quality and variety of services. Moreover, considering the unequal distribution of UPFs between urban and rural areas and the differing demands of various regions, it is crucial to leverage the positive effect of urban road network patterns on public facilities. The urban road infrastructure forms the foundation for residents' outdoor activities, significantly impacting their perception of distance, time, and recreational opportunities. Through the utilization of a machine learning model, this study has analyzed the spatial heterogeneity and continuity of the road network effect on the diversity of UPFs, offering a basis for making more scientific and rational decisions. The primary focus of this study revolves around the spatial arrangement of UPF diversity and its correlation with road networks.

Firstly, in terms of model accuracy measured by adjusted R², the RF regression model consistently maintains a strong fit between various road network morphology variables and diversity, achieving values between 70 and 80%. In contrast, the GWR model yields lower accuracy, ranging from 40 to 60% and exhibiting more significant fluctuations. This discrepancy highlights a nonlinear relationship between UPF diversity and road network morphology, represented by the RF model [26].

In addition, regarding spatial distribution characteristics, it is generally observed that NQPDE exhibits a positive correlation with diversity, while BTE displays a negative correlation. Nevertheless, the connection between NQPDE and CD on a global scale is predominantly significant in the Second and Third Ring Roads, creating a spatial distribution pattern resembling a “circular” structure. This pattern is attributed to the fact that this area is positioned in the transitional zone between the central city and its periphery, with its critical role directly facilitating the “link” between the city center and its outskirts. Accordingly, it is apparent that this area is situated in the transition zone between the central city and its periphery, and its role as a “link” directly contributes to its partial access to the benefits of the diversity of the central city [27, 28]. However, it is inadequate in fully satisfying the residents' needs, as peripheral traffic congestion in the central city simultaneously reduces residents' access opportunities to enjoy diversity [11].

Finally, in terms of aggregation characteristics, the topological features of road systems are closely associated with the diversity of aggregation characteristics. Specifically, the diversity of aggregation in the chevron road network is predominantly characterized as “high-high aggregation,” while the ring road network exhibits “low-high” aggregation tendencies. In contrast, the radial road network displays “low-low aggregation” or minimal aggregation. This relationship is also correlated with the pros and cons of different transportation road layout configurations. The square road network, for instance, offers a regular traffic network structure that facilitates the clustering of public service facilities in its framework. On the other hand, the ring road network occupies a transitional position between the central city and its outskirts, forming a circular structure at the periphery. This placement can result in the “low-high agglomeration characteristic” of diversity. Conversely, the radial network is typically situated on the outskirts of the city and primarily focuses on “low-high agglomeration” or exhibits insignificant aggregation [29, 30]. It primarily serves the peri-urban area with fewer public service facilities, and is more distant from the city center, thus displaying a “low-low” agglomeration characteristic.

In light of the aforementioned findings, it is necessary for city managers to gain a comprehensive understanding of how the overall morphology of the road network impacts diversity. To ensure equitable access, they should focus on constructing an efficient, integrated, and well-designed public transportation system. Additionally, in urban planning, it is crucial to allocate residential land based on the significant differences in road network morphology variables. For instance, the degree of road network integration, from a global perspective, more significantly and positively affects the diversity of public service facilities on the second and third ring roads. Therefore, it is necessary to optimize the road network structure in these areas to enhance regional road connectivity. Moreover, the topological form of the road network also affects the accessibility and associated costs of accessing public service facilities. When planning the placement of such facilities, a comprehensive assessment of road accessibility is essential, with a preference for grid-shaped configurations and smooth transitions between ring roads. Attention should be paid to ensuring fairness and suitability in the facility distribution. This study, utilizing quantitative methods to analyze the effect of road network morphology on the diversity of UPFs, suggests the need for further research. Specifically, an in-depth study is valuable for enhancing diversity at the elemental level and strengthening diversity management planning through road network structure to better fulfill residents’ requirements for refinement, diversity, and quality, and the creation of a “pleasant city to live in and pleasant to work in.” This topic warrants further exploration and study.

Conclusions

This research adopts multi-source data and machine-learning models to explore the relationship between UPF diversity and road network morphology. The Shannon–Wiener diversity index is utilized to assess both comprehensive and facility-specific diversity in urban facilities, while the SDNA model measures road network proximity and traversability. Firstly, in comparison to the GWR and RF models, the RF model reveals the spatial scales of influence of various variables and is more suitable for exploring the correlation between road network morphology and UPF diversity in Changsha. This study reveals a complex nonlinear relationship between diversity and road network form. Secondly, both globally and locally, high accessibility is more positively correlated with diversity than high traversal, which exhibits a negative correlation. Finally, clusters are also related to road network form, with HH clusters commonly found in square-grid road networks.

However, this paper is not without several limitations. Firstly, it assumes that all residents have equal demands for facilities, overlooking that specific areas may have varying needs. Future research should consider the varying demands of different regions in order to gain a more nuanced understanding of the relationship between road networks and the diversity of UPFs. Additionally, the study does not consider the size, capacity, or weight of facilities, which could introduce errors in the results. Future research could incorporate these factors to provide a more accurate assessment of the relationship. Finally, due to limited data sources, the study does not comprehensively consider all relevant variables, nor interactions between the road network and other factors. Incorporating additional data sources and technical approaches would enhance the analysis and provide a more comprehensive understanding of the relationship between road networks and the diversity of UPFs. Furthermore, there is a need for an understanding of the mechanisms through which road network systems affect diversity with more detailed planning strategies, thus contributing to a more in-depth and insightful analysis of the subject.