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Article

A Case Study on Spatial Heterogeneity in the Urban Built Environment in Kwun Tong, Hong Kong, Based on the Adaptive Entropy MGWR Model

by
Xuejia Wei
,
Liang Huo
*,
Tao Shen
,
Fulu Kong
*,
Zhaoyang Liu
and
Jia Wu
School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
*
Authors to whom correspondence should be addressed.
Sustainability 2026, 18(1), 189; https://doi.org/10.3390/su18010189
Submission received: 20 November 2025 / Revised: 15 December 2025 / Accepted: 16 December 2025 / Published: 24 December 2025
(This article belongs to the Topic Spatial Decision Support Systems for Urban Sustainability)
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Abstract

The built environment, serving as the core spatial vehicle for human production and daily activities, constitutes a vital foundation for achieving sustainable urban development and high-quality renewal. However, amidst rapid urbanisation, certain areas continue to grapple with issues such as ageing infrastructure, inefficient land use, and imbalanced spatial structures, hindering the establishment of sustainable urban forms. Consequently, identifying the evolutionary characteristics and influencing mechanisms of the built environment from the perspective of spatial heterogeneity holds critical significance for advancing refined governance and sustainable planning. Taking Kwun Tong District in Hong Kong as a case study, this research constructs an Adaptive-Entropy Multi-Scale Geographically Weighted Regression (MGWR) analytical framework. This systematically reveals the spatial distribution patterns of built environment elements and their multi-scale spatial heterogeneity characteristics. The findings indicate the following: (1) The built environment exhibits significant spatial differentiation and clustering structures across different scales, reflecting complex spatial processes driven by multiple interacting factors (2) Compared with the OLS model at a 1000 m scale and the GWR model at a 500 m scale, the Adaptive-Entropy MGWR model at a 100 m scale demonstrated superior fitting accuracy and explanatory power. It more effectively captured local structural variations and scale effects, thereby offering greater guidance value for sustainable planning. Building upon these findings, this study further proposes pathway recommendations for urban renewal and built environment optimisation in Kwun Tong District, offering an analytical approach and technical framework that may serve as a reference for sustainable development in high-density cities.

1. Introduction

The built environment of cities constitutes a vital product of human civilisation, providing fundamental spatial support for production and daily life activities [1]. Its core elements encompass land use patterns and transport systems [2]. As demands for high-quality urban development continue to rise, the built environment now transcends basic material functions, directly influencing a city’s liveability, resource efficiency, ecological resilience, and sustainable development [3]. A bidirectional coupling exists between the built environment and human behaviour: on one hand, environmental factors such as facility accessibility, road connectivity, and functional diversity shape residents’ travel, consumption, and spatial activity patterns, significantly influencing energy consumption, carbon emissions, and public resource utilisation [4]; on the other, human behaviour reflects demands for urban spatial structures, guiding planning authorities to optimise, renew, and rebalance the built environment [5]. Currently, under China’s urbanisation and ‘New Urbanisation’ strategy, built environment quality has become a key indicator for measuring urban sustainability, liveability, and governance capacity [6]. National initiatives such as ‘people-centred urban renewal’ and the development of ‘liveable [7], resilient, and smart cities’ increasingly emphasise the need for precise governance and sustainable optimisation of urban spatial structures through the scientific identification of spatial variations within the built environment [8,9].
The spatial distribution of the urban built environment is jointly driven by natural conditions and socio-economic activities [10,11], encompassing multiple factors such as land use intensity [12], building density [13], road network structure [14], economic vitality, population concentration, and ecological constraints. Existing research has accumulated substantial findings in analysing the spatial patterns of the built environment. Early studies predominantly employed statistical methods such as OLS, spatial autocorrelation analysis [15], and kernel density, primarily revealing spatial disparities at the macro-scale. However, single-scale approaches struggle to meet the requirements of sustainable planning for ‘tailored solutions based on local conditions’ [16,17]. With advances in geographic information technology and spatial statistical methods, GWR, MGWR, and multi-source data fusion have progressively become mainstream tools for exploring spatial heterogeneity in the built environment, offering richer perspectives for understanding spatial processes and resource utilisation efficiency within complex urban systems.
Early research on spatial heterogeneity within the built environment primarily relied on traditional statistical models such as ordinary least squares regression (OLS) [18]. While this approach can reveal overall relationships between built environment elements and urban socio-economic activities [19], its assumptions of fixed parameters and spatial independence struggle to capture the local variations and spatial non-stationarity prevalent in urban systems. Consequently, it proves inadequate for supporting contemporary sustainable urban planning, which emphasises ‘precise identification of differences’ and ‘tailored governance’. With advances in Geographic Information Systems and spatial econometric methods, researchers introduced Geographically Weighted Regression (GWR) models [20,21,22]. By applying geographic weights in the spatial dimension to achieve localised parameter estimation, these models better identify spatial heterogeneity between the built environment and urban functions. However, GWR’s uniform bandwidth assumption overlooks the multi-scale variations exhibited by different factors across urban spaces, hindering the characterisation of complex urban systems’ hierarchical structures and spheres of influence. To overcome this limitation, the Multi-Scale Geographically Weighted Regression (MGWR) model was proposed [23,24,25,26,27]. This allows different independent variables to be fitted at their respective optimal spatial scales, thereby revealing the multi-scale spatial built environment with greater precision. This capacity to recognise spatial process scale differences renders MGWR highly significant in sustainable urban development research. It aids in clarifying the operational mechanisms of diverse built environment factors at both broad and local scales, thereby providing more targeted scientific evidence for optimising urban spatial structures, rational resource allocation, and sustainable planning. In recent years, scholars have continuously expanded upon this methodology. For instance, Wang Zimeng employed the GBDT-SHAP model to reveal the non-linear impact of the built environment on urban vitality [28]; Wang Bo analysed the spatiotemporal heterogeneity of built environment factors on urban vitality using the GTWR model [29]; Sun Honghu combined resident activity big data with the MGWR model to identify spatial patterns of urban vitality [30]; and Li Congying explored the spatiotemporal travel influenced by the built environment using OLS, GWR, and GTWR models [31]. Overall, the OLS model is computationally straightforward but lacks spatial sensitivity; GWR can reveal local variations but is constrained by the single-scale assumption while MGWR enhances spatial fitting capability through multi-scale mechanisms. However, traditional MGWR exhibits shortcomings in handling multi-source data and non-linear relationships [32]. To address this, this study proposes an adaptive information entropy-based MGWR model. By utilising information entropy to measure variable uncertainty and implementing bandwidth adaptive optimisation, it more effectively identifies multi-scale spatial heterogeneity in the urban built environment, providing novel methodological support for spatial cognition and optimisation within complex urban systems [33,34].
This study takes Kwun Tong District in Hong Kong as a case example. This area exhibits characteristics of both a traditional industrial zone and a modern commercial district, with significant land use transformation, making it a crucial sample for researching sustainable spatial optimisation in high-density urban environments. Current systematic, multi-scale research on the spatial heterogeneity of the built environment in Kwun Tong remains relatively scarce, hindering the provision of refined evidence for urban renewal and sustainable governance. To address this, this study constructs an MGWR spatial heterogeneity analysis framework based on adaptive information entropy to more precisely reveal the spatial distribution patterns of the built environment and its multi-scale variations. The research comprises: (1) establishing a multi-scale spatial analysis framework at 100 m, 500 m, and 1000 m scales; (2) developing an indicator system covering land use, transport accessibility, and building morphology; (3) analysing the multi-scale spatial distribution characteristics of the built environment; (4) utilising the MGWR model to identify the spatial mechanisms and scale differences of key influencing factors; (5) proposing optimisation strategies for urban renewal, spatial governance, and sustainable planning in Kwun Tong District. This research provides data support and decision-making references for spatial resource allocation, functional renewal, and sustainable development in high-density cities, while also offering a generalisable multi-scale analytical method for sustainable urban studies.

2. Materials and Methods

2.1. Research Area

This study selected Kwun Tong District in the eastern part of Kowloon Peninsula, Hong Kong Special Administrative Region, as its research area [35]. Covering a total area of approximately 11.4 km2, it is situated between 22°18′ and 22°20′ north latitude and 114°13′ and 114°14′ east longitude. Bordered to the north by Lion Rock and Kowloon Bay hills, it faces Victoria Harbour to the south across the water from Hong Kong Island. To the west lies Wong Tai Sin District, while Sai Kung District adjoins it to the east. The terrain generally exhibits a north-high, south-low gradient, with hills, terraces and reclaimed land coexisting to form a complex spatial structure. In recent years, driven by urban renewal initiatives and the implementation of the ‘Kowloon East Strategy’, Kwun Tong has undergone a transformation from a traditional industrial zone into a hub for innovation, technology, and commerce [36,37]. This shift has catalysed significant evolution in its urban spatial form and built environment structure. The area exhibits high building density, a complex road network, and significant land use mixing, demonstrating pronounced spatial heterogeneity and multi-scale structural characteristics. Consequently, this study focuses on Kwun Tong, employing multi-source spatial data to construct an urban built environment indicator system. It then analyses the spatial heterogeneity and multi-scale interaction mechanisms using an adaptive information entropy MGWR model. As shown in Figure 1.

2.2. Method

2.2.1. Information Entropy

Calculate the information entropy value for each grid. For grid i and metric j,
H i , j = − ∑ k = 1 c j P i , j , k   l n   ( P i , j , k )
Cj: Number of categories for indicator j Pi,j,k: Proportion of category k within indicator j in grid i [38,39].
P i , j , k = t h e   k t h   c a t e g o r y   q u a n t i t y Indicator   j .   total   quantity
This yields the information entropy for each indicator within each grid cell, describing the degree of dispersion and complexity of that indicator within the local spatial domain. A higher value indicates greater spatial heterogeneity of the variable within that region.

2.2.2. Multi-Scale Geographically Weighted Regression Model

Multi-scale Geographically Weighted Regression represents an extension and refinement of the classical Geographically Weighted Regression. Unlike GWR, which employs a single spatial bandwidth for all explanatory variables, MGWR permits each independent variable to possess its own spatial bandwidth. This enables the model to capture the distinct spatial influence ranges and scale characteristics of different influencing factors. The calculation formula is as follows:
y i = β h ( x i , y i ) + ∑ j = 1 k β j ( x i , y i ) x i j + ϵ i
In the formula, y denotes the global variable; (x, y) represents the spatial coordinates of point i; β(x, y) constitutes the regression constant term, where β(x, y) signifies the regression coefficient for point j; x indicates the value of independent variable j; k denotes the number of independent variables; and ϵ represents the residual.

2.2.3. Adaptive Information Entropy and MGWR Fusion Method

To further enhance the interpretability and robustness of multi-scale geographically weighted regression models in analysing multi-source urban built environment data, this study introduces adaptive information entropy weights W into the traditional MGWR framework, thereby constructing an adaptive information entropy–MGWR hybrid model. This approach employs a dynamic adjustment mechanism for entropy weights to differentially assign importance to explanatory variables across distinct spatial units, thereby achieving adaptive optimisation of variable scale and spatial influence.
First, the information entropy of each indicator undergoes normalisation processing. Adaptive variable weights are then derived.
W i , j = H i , j ∑ j = 1 m H i , j
where m denotes the number of independent variables. This weighting serves to reflect the relative importance of different variables at varying spatial locations, thereby enabling dynamic adjustment of variable influence.
On this basis, construct a weighted independent variable matrix.
X i , j ‘ = w i , j × X i , j
By substituting the weighted variables into the MGWR model, adaptive optimisation of the model can be achieved. The improved adaptive information entropy MGWR model can be expressed as:
Y i = β 0 ( u i , v i ) + ∑ j = 1 m β j ( u i , v i ) ⋅ ( w i , j ⋅ X i , j ) + ϵ i
Here, Y represents the dependent variable, ( u i , v i ) denotes spatial position coordinates, β j ( u i , v i ) is the local regression coefficient, and ϵ i is the error term.

2.3. Data Source

This study employs a comprehensive approach utilising multi-source spatial data, including building data, road data, and land use data, to support multi-scale spatial analysis of the built environment in Kwun Tong District. These datasets primarily originate from the Hong Kong Government Open Data Platform, the Survey and Mapping Office, the Planning Department, and field survey results from research institutions. Building data is derived from the ‘Building Outline Dataset’ published by the Hong Kong Survey and Mapping Department; road data utilises the ‘Road Centreline Dataset’ provided by the Hong Kong Government Open Data Platform; and land use data is selected from the ‘Hong Kong Land Use Status Map Dataset’ released by the Hong Kong Planning Department.

2.4. Spatial Unit Delineation and Indicator Development

2.4.1. Spatial Unit Division

To thoroughly elucidate the spatial heterogeneity of Kowloon Bay District’s built environment, this study employs a regular grid partitioning method to establish a unified spatial analysis unit [40,41,42]. This approach effectively mitigates spatial shape inconsistencies arising from administrative boundaries or parcel divisions, facilitating the integration of multi-source data and spatial statistical analysis. Taking into account the study area’s size, data resolution, and spatial complexity, three spatial scales were established: 100 m, 500 m, and 1000 m. This facilitates multi-scale comparative analysis from micro- to meso- to macro-levels. The 100 m grid primarily delineates micro-structural features such as buildings and roads. The 500 m grid focuses on regional functional layouts and spatial structural connections. The 1000 m grid represents the macro-scale of urban structure, being suitable for analysing Kwun Tong District’s overall spatial pattern and functional zone agglomeration characteristics.

2.4.2. Indicator Construction

In constructing the indicator system, comprehensive consideration was given to the spatial structural characteristics, functional attributes, and overall performance of the built environment. Spatial variations were characterised from multiple dimensions, resulting in the establishment of four indicator systems: morphological, structural, functional, and comprehensive. This classification approach systematically reflects the multidimensional characteristics of the built environment across different levels—morphological features, spatial organisation, functional connections, and overall standards—facilitating a comprehensive assessment of its spatial heterogeneity. Specifically, building density, building compactness, road density, road accessibility, and land use density were employed as independent variables in the model, with the built environment composite index serving as the dependent variable [43,44]. This quantitative analysis examined the influence of each factor on the overall level of the urban built environment. The extraction and calculation methods for each indicator are detailed in Table 1.

3. Results

3.1. Analysis of Multi-Scale Spatial Distribution Characteristics

This study focuses on Kwun Tong District in Hong Kong, employing a regular grid division method to partition the study area into spatial units at three scales: 100 m, 500 m, and 1000 m. Based on building vector data, road networks, and land use information, indicators such as building density, building compactness, road density, road accessibility, and land use density were calculated and spatialised. GIS spatial analysis methods were employed to generate spatial distribution maps for these indicators at different scales, as illustrated in Figure 2. Results indicate that all indicators exhibit pronounced spatial differentiation across scales: at 100 m, spatial patterns are most granular with distinct local variations, reflecting micro-level spatial structures; at 500 m, local differences are partially smoothed into more continuous distributions; while at 1000 m, spatial heterogeneity significantly diminishes, enhancing regional coherence. Overall, building density and land use density exhibited high-value clusters in the central and roadside areas of the study zone, while building compactness and road accessibility showed variations in the zones. This indicates that the built environment of Kwun Tong District exhibits distinct multi-scale spatial characteristics across different spatial scales.

3.2. Comparative Analysis of Models

To validate the model’s fitting performance and ability to reveal spatial heterogeneity at different spatial scales, the results of the OLS, GWR, and MGWR models were compared at three scales: 1000 m, 500 m, and 100 m. The findings indicate that both the model’s explanatory power and fitting accuracy show a significant improvement trend as model complexity and spatial resolution increase, as shown in Table 2.
From the perspective of the coefficient of determination R2 and adjusted R2, the OLS model exhibits an R2 value of merely 0.402. This indicates that, at the global scale, the independent variables possess limited overall explanatory power for the dependent variable, rendering it difficult to discern spatial variations between regions. Following the incorporation of a spatial weighting function within the GWR model, the R2 value improved to 0.793, demonstrating a certain degree of enhancement in capturing local spatial effects. Further incorporating the MGWR model based on adaptive entropy yields an R2 of 0.893 and an adjusted R2 of 0.825. Both the explanatory power and robustness of the model are markedly enhanced, demonstrating that modelling different independent variables at their respective scales more effectively reflects the spatial heterogeneity of the urban built environment. Regarding the AIC/AICc information criteria, lower values denote superior model fit. The AIC value for the based MGWR model slightly increased compared to OLS, indicating a penalty for heightened model complexity. However, considering both R2 and RMSE, the based MGWR model retains superior precision. The root mean square error (RMSE) decreased with increasing model complexity, falling from 0.230 for OLS to 0.216 for MGWR, confirming the based MGWR model’s superior predictive accuracy. Regarding spatial scale trends, the based MGWR model at the smaller 100 m scale better captures local spatial heterogeneity, whereas models at larger scales (500 m and 1000 m) exhibit stronger overall homogeneity and averaging tendencies. This demonstrates that the spatial effects of urban built environment factors exhibit pronounced multi-scale characteristics, with significant differences in spatial dependence and spatial heterogeneity across different scales.

3.3. Analysis of Influence Factors at Various Scales

3.3.1. Analysis of MGWR Model Results Based on Adaptive Entropy at the 100 m Scale

To further elucidate the spatial variability of built environment elements in Kwun Tong District, this study employs the MGWR model at a scale to visually represent the spatial regression coefficients of each variable. As illustrated, distinct spatial influences in both intensity and direction are evident across different variables, reflecting the non-stationary and multi-scale heterogeneity inherent in urban built environments, as depicted in Figure 3.
The regression coefficients for building density exhibit an overall spatial gradient decreasing from northwest to southeast. Within the densely built core development zone in Kwun Tong’s northwest, building density exerts a significant positive influence on the overall built environment quality. This indicates that high-density building clusters play a constructive role in fostering spatial agglomeration effects and enhancing residential vitality. Conversely, in the southeast coastal and mountainous fringe areas, the coefficient markedly weakens or even turns negative. This suggests that in low-density zones, the agglomeration effect diminishes, limiting its positive contribution to the built environment. The spatial distribution pattern of building compactness resembles that of building density, though its positive influence is more concentrated within the high-intensity development zones of the northwest. This suggests that intensified building forms within core areas enhance land use efficiency and spatial integration. However, in peripheral zones or overly intensive areas, excessive compactness may lead to issues such as restricted ventilation and spatial oppression, thereby diminishing its positive impact on the built environment. Land use density regression coefficients exhibit an overall negative spatial distribution with minimal variation. This indicates a negative correlation between excessive land use intensity and built environment quality within Kwun Tong District. Particularly in areas with single-use land functions or overdevelopment, excessive land use intensity may lead to declining environmental quality and insufficient public space. The spatial distribution of road density exhibits a pronounced positive gradient, with higher coefficients in the northern and northwestern zones. This indicates that the road network exerts a more significant positive influence on the built environment within core functional areas. Higher road density typically correlates with enhanced transport convenience and accessibility, thereby boosting regional spatial vitality. Conversely, in the southeastern mountainous and coastal areas, sparse road networks and inadequate connectivity result in relatively weaker contributions from transport conditions to the built environment. The spatial distribution of the road accessibility coefficient exhibits an inverse trend to road density, generally increasing from northwest to southeast. This indicates that in peripheral areas, enhanced transport accessibility exerts a more pronounced driving effect on improving built environment quality whereas in core zones, where the transport network is already relatively well-developed, the marginal benefit of increased accessibility is comparatively lower. The intercept term remains consistently high and uniformly distributed across the entire district, reflecting Kwun Tong’s generally high baseline level of built environment quality. Localised R2 values exhibit pronounced spatial differentiation: higher values in the northwest indicate stronger explanatory power of the model for variables in that area, whereas relatively lower values in the southeast suggest weaker model fit. This spatial variation reflects significant local heterogeneity in the influence mechanisms across different spatial locations, providing spatial guidance for subsequent refined factor analysis and model optimisation tailored to distinct zones. In summary, the formation mechanisms of Kwun Tong District’s built environment exhibit pronounced spatial non-stationarity. Building density and compactness drive spatial aggregation and functional intensification in the core area, while transport factors—road density and accessibility—play a pivotal role in enhancing the built environment in peripheral zones. The negative effect of land use density reveals the potential risk of declining spatial environmental quality associated with high-intensity development.

3.3.2. Analysis of Influencing Factors for the 100 m-Scale GWR Model

A heatmap illustrating the correlation between factors influencing the built environment at the scale is presented in Figure 4. This visualises the linear relationship characteristics among building density, building compactness, road density, road connectivity, land use density, and the composite index at this small scale. Overall, significant variations in correlations between variables are evident, reflecting the multidimensional and complex interactions within the small-scale built environment of the study area. Specifically, building density exhibits extremely strong positive correlations with both road density and land use density, indicating that at this scale, the spatial distribution of building development intensity is highly synchronised with the development of the road network and land use intensity. Similarly, road density shows an extremely strong positive correlation with land use density, reflecting the strong coupling between the road system and land use at this scale. By contrast, building compactness exhibits weaker correlations with other variables overall. It shows weak negative correlations with building density (−0.138) and road density (−0.138), indicating limited independent contribution to the composite characteristics of the built environment. The composite index exhibits an extremely strong negative correlation with land use density (−0.944) and strong negative correlations with building density (−0.932) and road density (−0.932), demonstrating an inverse relationship between the composite index and building, road, and land use indicators at the small-scale level.

3.3.3. Impact Factor Analysis of the MGWR Model Based on Adaptive Entropy at the Scale

Table 3 presents the statistical characteristics of each variable within the multi-scale geogewicht regression model, weighted by adaptive information entropy, at a spatial scale of 100 m. Overall, the mean values of different indicators at this scale are generally low, indicating that spatial features are relatively dispersed within fine grid cells, with significant local variations. Among these, Building Compactness exhibits the highest mean (0.276918) and a relatively low standard deviation (0.035567), suggesting a more balanced distribution across the study area and making it the most stable spatial variable. Road Accessibility The mean for road accessibility was 0.0744 with a standard deviation of 0.0589, indicating substantial spatial variation and marked disparities in transport accessibility across different areas. In contrast, both building density and road density exhibited extremely low means, with standard deviations approaching tens of times the mean. This suggests the presence of localised areas with exceptionally high densities, yet most grid cells exhibited low densities, resulting in a markedly skewed spatial distribution. Furthermore, the minimum value for land use density is non-zero, indicating that all units exhibit some degree of land use coverage, reflecting Kwun Tong District’s overall high development intensity. Overall, the standard deviations for all indicators at this scale are generally high, reflecting significant spatial heterogeneity and structural differences within the built environment at the micro-scale. This provides a robust basis for variable differentiation, enabling the MGWR model to capture local spatial effects.

3.4. 500 m Scale Influence Factor Analysis

3.4.1. Correlation Analysis of the 500 m Scale Influence Factor

A scale heatmap of correlations between urban built environment factors was employed to reveal linear relationships among different spatial indicators, along with their direction and strength of association with composite metrics, as illustrated in Figure 5. Overall, significant variations in correlations between variables were observed, reflecting the multidimensional interactive characteristics and complex spatial structure of Kwun Tong District’s built environment indicators at the mesoscale. The results indicate a remarkably strong positive correlation between building density and land use density, with a correlation coefficient of 0.993. This indicates a high degree of spatial alignment in their distribution patterns, where areas of high building density are frequently accompanied by high land use intensity. This strong coupling reflects the synchronous growth of building mass and land development density within Kwun Tong’s high-intensity development zones. By contrast, building compactness exhibits overall weaker correlations with other variables, displaying a mere –0.061 correlation coefficient with the composite indicator. This suggests its spatial variation contributes relatively little to the overall composite characteristics of the built environment. Road-related variables demonstrate more complex correlations. Road density exhibits a moderate negative correlation with road accessibility (r = –0.349), indicating that increased road quantity does not necessarily enhance overall accessibility, potentially influenced by road hierarchy and spatial layout. Furthermore, road accessibility shows a weak negative correlation with the composite indicator (r = –0.161), suggesting that transport accessibility has a negligible impact on overall spatial quality at this scale, manifesting more as functional disparities within localised areas. The correlations between the composite indicator and most factors were generally weak (|r| < 0.2). This indicates that at the 500 m scale, the composite characteristics of the built environment are influenced by multiple factors with pronounced non-linear interactions, making it difficult for any single variable to explain its spatial distribution patterns.

3.4.2. Analysis of Influencing Factors for the 500 m Scale GWR Model

The built environment indicators at the scale within Kwun Tong District exhibit relatively pronounced spatial variations, as shown in Table 4. Overall, the mean building compactness was highest at 0.2231, indicating relatively concentrated building layouts and dense spatial utilisation within the area. Conversely, the means for building density and land use density were 0.0085 and relatively low values suggesting limited overall building coverage. However, substantial local variations exist, reflecting pronounced built environment differentiation between core and peripheral zones. The mean road density was 0.0196 with a high standard deviation, indicating pronounced unevenness in road distribution. The mean road accessibility score of 0.1333 placed it at a moderate level overall, suggesting generally balanced transport accessibility within the study area, albeit with localised traffic concentration zones. Collectively, Kwun Tong District exhibits pronounced spatial heterogeneity at the 500 m scale.

3.5. 1000 m Scale Influence Factor Analysis

3.5.1. Correlation Analysis of the 1000 m Scale Influence Factor

A heatmap illustrating the correlation between factors influencing the built environment at the 1000 m scale reveals linear relationships among building density, building compactness, road density, road connectivity, land use density, and the composite index at this large scale, as depicted in Figure 6. Overall, significant variations in correlations between variables are evident, reflecting the multidimensional and complex interactions within the large-scale built environment of the study area. Specifically, building density exhibits a moderate positive correlation with road density (correlation coefficient 0.397) and with the composite index (0.368), indicating a degree of synergy between development intensity and road network development alongside the overall built environment quality at this scale. Road density shows a moderate positive correlation with land use density (0.400), reflecting a close association between the road system and land use patterns at this scale. In contrast, building compactness exhibits weaker correlations overall with other variables, showing low associations with building density (0.125) and road density, and making a limited independent contribution to the composite characteristics of the overall built environment. The composite index exhibits a weak positive correlation with land use density (0.216), and moderate positive correlations with building density (0.368) and road density (0.226). This demonstrates the positive association between the composite index and building, road, and land use indicators at the large scale. This multi-factor correlation pattern provides quantitative support for subsequent large-scale analyses of built environment spatial heterogeneity and investigations into multi-factor synergistic mechanisms, while also highlighting the scale-specific nature of inter-factor relationships at large scales.

3.5.2. Analysis of Influencing Factors for the 1000 m Scale GWR Model

Regarding the correlation characteristics between individual indicators and the composite index, as shown in Table 5 the correlation coefficient of 0.3924 and regression coefficient of 0.2599 for building compactness both demonstrate significant prominence, exerting a positive influence on the composite index. This establishes compact building layout as the most crucial practical factor driving the research objective, indicating its positive promotional effect on the study subject. Although building density exhibits a moderate positive correlation (0.3080) with the composite index, it demonstrates a negative influence (−0.2593) in multiple regression analysis, suggesting a potentially complex non-linear relationship between the twoThe correlation coefficient of road density (0.2364) and regression coefficient (0.1011), alongside the correlation coefficient of land use density (0.2164) and regression coefficient (0.1950), all exerted positive effects on the composite index. This indicates that moderate increases in road network density and heightened land use intensity yield favourable outcomes for the composite index. The correlation coefficient for road accessibility (0.1706) and regression coefficient (0.1814) also exerted a positive influence on the composite index, albeit with relatively weaker impact. Overall, the direction and intensity of influence exerted by various indicators on the composite index exhibited marked differences, reflecting the multidimensional and complex spatial interaction mechanisms of the research subject.

4. Discussion

Our research findings indicate that the spatial distribution of the built environment in Kwun Tong District, Hong Kong, exhibits pronounced multi-scale spatial heterogeneity, with distinct spatial characteristics and driving mechanisms across different scales. Analysis using the MGWR model reveals that factors such as building density, building compactness, road density, road accessibility, land use density exert primary influence on the spatial patterns of the built environment. Building density and land use density exhibit strong local spatial clustering, reflecting regional variations in land intensification and spatial development intensity. Road density and accessibility significantly influence spatial reachability and urban connectivity, demonstrating the regulatory effect of transport networks on optimising built-up area structures. Differences in influence intensity and spatial distribution across scales indicate that the formation mechanism of the urban built environment exhibits distinct multi-scale coupling characteristics. Smaller scales better reveal details of micro-spatial structures, while larger scales reflect the overall patterns of regional spatial organisation.
Based on an analysis of multi-scale spatial heterogeneity characteristics, this paper proposes the following strategies for optimising the urban built environment: Firstly, promote spatial form optimisation and functional integration. Vertical space utilisation and mixed-use development should be encouraged in high-density built-up areas to enhance land use efficiency and spatial vitality. Secondly, improve road networks and transport accessibility structures. For areas with low connectivity, road layouts and public transport systems should be optimised to strengthen spatial connectivity and travel convenience. Thirdly, guide coordinated development across multiple scales. At the macro level, spatial structure and land use allocation should be coordinated to establish a rational spatial zoning pattern. At the micro level, attention should be paid to enhancing spatial quality at the community scale, fostering the synergistic development of living, ecological, and transport systems. Overall, a quantifiable, diagnosable, and optimisable urban built environment assessment system should be established, underpinned by multi-source data-driven and adaptive modelling methodologies.

5. Conclusions

Although this paper utilises multi-source spatial data and introduces an MGWR model to reveal the spatial heterogeneity of the urban built environment from a multi-scale perspective, several limitations remain. On the one hand, the data employed in the study is predominantly static, lacking dynamic temporal analysis, which makes it difficult to comprehensively reflect the evolutionary process of the urban built environment. On the other hand, while the model can reveal spatial scale differences, it does not yet fully account for the non-linear interactive relationships between variables. Future research may explore the following avenues: firstly, incorporating multi-temporal remote sensing and social perception data to analyse the dynamic evolution and spatiotemporal coupling characteristics of the built environment; secondly, integrating machine learning with spatio-temporal deep modelling methods to investigate nonlinear driving mechanisms within complex urban systems; thirdly, expanding the geographical scope and sample dimensions to enhance the model’s generalisability and transferability, thereby providing more adaptive decision support for urban spatial planning and sustainable development.

Author Contributions

X.W. and F.K. methodology; T.S. validation; T.S. formal analysis; L.H. investigation; L.H. resources; Z.L. and X.W. data curation; X.W. writing—original draft; J.W. writing—review and editing; T.S. and F.K. visualization; X.W. supervision; F.K. and T.S. project administration; X.W. funding acquisition. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. The location of Kwun Tong District in Hong Kong. (a) Map of China (b) Map of Hong Kong (c) Map of Kwun Tong.
Figure 1. The location of Kwun Tong District in Hong Kong. (a) Map of China (b) Map of Hong Kong (c) Map of Kwun Tong.
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Figure 2. Spatial distribution characteristics of various built environment indicators at different scales.
Figure 2. Spatial distribution characteristics of various built environment indicators at different scales.
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Figure 3. Spatial regression coefficients for respective variables in the MGWR model: (a) patial regression coefficient for building density; (b) patial regression coefficient for building compactness; (c) patial regression coefficient for road density; (d) patial regression coefficient for road accessibility; (e) patial regression coefficient for land use density; (f) patial regression coefficient for local R2.
Figure 3. Spatial regression coefficients for respective variables in the MGWR model: (a) patial regression coefficient for building density; (b) patial regression coefficient for building compactness; (c) patial regression coefficient for road density; (d) patial regression coefficient for road accessibility; (e) patial regression coefficient for land use density; (f) patial regression coefficient for local R2.
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Figure 4. Correlation heatmap of factors influencing the urban built environment at the scale.
Figure 4. Correlation heatmap of factors influencing the urban built environment at the scale.
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Figure 5. Correlation Heatmap of Factors Influencing the Urban Built Environment at the Scale.
Figure 5. Correlation Heatmap of Factors Influencing the Urban Built Environment at the Scale.
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Figure 6. Correlation Heatmap of Factors Influencing the Urban Built Environment at the Scale.
Figure 6. Correlation Heatmap of Factors Influencing the Urban Built Environment at the Scale.
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Table 1. Extraction and Calculation Methods for Indicators.
Table 1. Extraction and Calculation Methods for Indicators.
Indicator TypeIndicator NameCalculation FormulaSignificance
Morphological Building DensityBuilding Density = (Floor Area of Building Basements/Total Construction Land Area) × 100%Measures the intensity of urban spatial development and reflects the degree of building coverage per unit area
Building CompactnessBuilding Compactness = Building Floor Area/Building PerimeterCharacterizes the regularity of building form and the efficiency of space utilization
StructuralRoad DensityRoad Density = Total Length of All Roads/Total Regional AreaMeasures the development level of the road network
Road Accessibilityd = s/(2L) (where d = influence distance, s = built-up area, L = total length of primary and secondary trunk roads)Evaluates the connectivity of the road network and travel efficiency
FunctionalLand Use DensityLa = Σ(Ai × Ci) (where La = comprehensive index of land use intensity; Ai = classification index of land use intensity at level i; Ci = percentage of area classified by land use intensity at level i)Reflects the intensity of land use and embodies the overall development level of land use types
ComprehensiveComprehensive Built Environment IndexComprehensive Built Environment Index = Σ(wi × Xi) (where wi = weight of the i-th indicator, Σwi = 1; Xi = standardized value of the i-th indicator)Reflects the different contributions of each indicator to the comprehensive level of the built environment and realizes the weighted integration of multiple indicators
Table 2. Comparison of OLS Model, GWR Model and MGWR Model Based on Adaptive Entropy.
Table 2. Comparison of OLS Model, GWR Model and MGWR Model Based on Adaptive Entropy.
ModelR2Adjusted R2AIC/AICcRMSEScale
OLS0.4020.3081958.4020.2301000 m
GWR0.7930.7541957.9470.229500 m
MGWR based on Adaptive Entropy0.8930.82511956.5680.216100 m
Table 3. Impact factor analysis results of the MGWR model based on adaptive entropy at the scale.
Table 3. Impact factor analysis results of the MGWR model based on adaptive entropy at the scale.
Indicator NameMeanMedianStandard DeviationMinimum Regression CoefficientMaximum Regression Coefficient
Building Density 0.0001510.157690.0031310.000000.11576
Building Compactness0.2769180.287710.0355670.000000.30165
Road Density0.0002980.000680.0046180.000000.17077
Road Accessibility0.0743770.057220.0588790.000000.286127
Land Use Density0.0001790.0000310.0033950.0000130.125670
Table 4. Impact Factor Analysis Results of the MGWR Model Based on Adaptive Entropy at the 500 m Scale.
Table 4. Impact Factor Analysis Results of the MGWR Model Based on Adaptive Entropy at the 500 m Scale.
Indicator NameMeanMedianStandard DeviationMinimum Regression CoefficientMaximum Regression Coefficient
Building Density 0.0085060.0422290.0022210.000000.362397
Building Compactness0.2231060.1371790.2414030.000000.643982
Road Density0.0195590.0381880.0125000.000000.314028
Road Accessibility0.1333320.0705580.1348910.000000.263861
Land Use Density0.0050320.0332470.0005250.000000.286677
Table 5. Impact factor analysis results of the MGWR model based on adaptive entropy at the 1000 m scale.
Table 5. Impact factor analysis results of the MGWR model based on adaptive entropy at the 1000 m scale.
Indicator NameCorrelation CoefficientRegression CoefficientImpact Direction
Building Density 0.39240.2599Positive Impact
Building Compactness0.3080−0.2593Negative Impact
Road Density0.23640.1011Positive Impact
Road Accessibility0.17060.1814Positive Impact
Land Use Density0.21640.1950Positive Impact
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Wei, X.; Huo, L.; Shen, T.; Kong, F.; Liu, Z.; Wu, J. A Case Study on Spatial Heterogeneity in the Urban Built Environment in Kwun Tong, Hong Kong, Based on the Adaptive Entropy MGWR Model. Sustainability 2026, 18, 189. https://doi.org/10.3390/su18010189

AMA Style

Wei X, Huo L, Shen T, Kong F, Liu Z, Wu J. A Case Study on Spatial Heterogeneity in the Urban Built Environment in Kwun Tong, Hong Kong, Based on the Adaptive Entropy MGWR Model. Sustainability. 2026; 18(1):189. https://doi.org/10.3390/su18010189

Chicago/Turabian Style

Wei, Xuejia, Liang Huo, Tao Shen, Fulu Kong, Zhaoyang Liu, and Jia Wu. 2026. "A Case Study on Spatial Heterogeneity in the Urban Built Environment in Kwun Tong, Hong Kong, Based on the Adaptive Entropy MGWR Model" Sustainability 18, no. 1: 189. https://doi.org/10.3390/su18010189

APA Style

Wei, X., Huo, L., Shen, T., Kong, F., Liu, Z., & Wu, J. (2026). A Case Study on Spatial Heterogeneity in the Urban Built Environment in Kwun Tong, Hong Kong, Based on the Adaptive Entropy MGWR Model. Sustainability, 18(1), 189. https://doi.org/10.3390/su18010189

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