The Nonlinear Relationship and Synergistic Effects between Built Environment and Urban Vitality at the Neighborhood Scale: A Case Study of Guangzhou’s Central Urban Area

Abstract

Investigating urban vitality and comprehending the influence mechanisms of the built environment is essential for achieving sustainable urban growth and improving the quality of life for residents. Current research has rarely addressed the nonlinear relationships and synergistic effects between urban vitality and the built environment at the neighborhood scale. This oversight may overlook the influence of key neighborhoods and overestimate or underestimate the influence of different factors on urban vitality. Using Guangzhou’s central urban area as a case study, this research develops a comprehensive urban vitality assessment system that includes economic, social, cultural, and ecological dimensions, utilizing multi-source data such as POI, Dazhong Dianping, Baidu heatmap, and NDVI. Additionally, the XGBoost-SHAP model is applied to uncover the nonlinear impacts of different built environment factors on neighborhood vitality. The findings reveal that: (1) urban vitality diminishes progressively from the center to the periphery; (2) proximity to Zhujiang New Town is the most critical factor for neighborhood vitality (with a contribution of 0.039), while functional diversity and public facility accessibility are also significant (with contributions ranging from 0.033 to 0.009); (3) built environment factors exert nonlinear influences on neighborhood vitality, notably with a threshold effect for subway station accessibility (feature value of 0.1); (4) there are notable synergistic effects among different built environment dimensions. For example, neighborhoods close to Zhujiang New Town (feature value below 0.12) with high POI density (feature value above 0.04) experience significant positive synergistic effects. These findings can inform targeted policy recommendations for precise urban planning.

1. Introduction

When high-quality infrastructure and resources in a city are underutilized, urban spaces can become monotonous and lack distinctiveness, leading to the phenomenon of ghost cities [1]. This underscores the need to enhance urban vitality to improve livability and attractiveness [2]. Currently, while urbanization in China has made significant progress, cities face numerous challenges. These include mismatches between resource limitations and urban economic and population growth [3], issues arising from the cumulative effects of short-term behaviors, and unreasonable urban infrastructure configurations. These factors significantly impact human activities, thereby reducing the sustainability of urban vitality. In 1961, Jane Jacobs was the pioneer in introducing the idea of urban vitality [4], which signifies human activities occurring at diverse locations and times [5]. Urban vitality is defined as an area’s capacity to attract people to engage in diverse activities, covering aspects like economic development, social interactions, cultural diversity, and overall livability [6]. Research across various disciplines, including urban planning, design, human geography, spatial information science, sociological studies, public policy, and urban management, demonstrates that vibrant urban areas not only enhance resident interaction but also strengthen social capital and community engagement [7]. Therefore, studying urban vitality helps improve residents’ well-being and the city’s capacity for sustainable development.

The perception and assessment of urban vitality encompass multiple dimensions [8], including sociology (interaction between people and places, street vitality, and social dynamics) [9], economics (population, employment, and economic landscape) [10], culture (cultural facilities, creative industries) [11], and ecology (environmental quality, biodiversity, and sustainability) [12]. However, previous studies have primarily used population mobility to represent urban vitality [13,14,15,16]. This approach may result in imprecise measurements of urban vitality. Additionally, numerous studies have examined vitality within individual cities, urban agglomerations, and at the community and street levels [17,18,19,20]. These scale choices may limit the understanding of broader or different levels of urban vitality characteristics, leaving the vitality of smaller neighborhoods or individual buildings underexplored. This oversight may overlook the guiding role of key neighborhoods, as neighborhoods are also an essential dimension for understanding urban characteristics [21,22]. Currently, neighborhood-scale studies have shown promising results in areas such as the cooling effects of greening on underground gas storage [23], contributions to urban environmental cooling [24], and life-cycle carbon emission assessments of buildings [22]. However, empirical research related to the vitality of urban neighborhoods remains relatively scarce [25].

The built environment, unlike the natural environment, is shaped by human activities such as urban design, transportation systems, and land use [26]. Urban morphologists argue that the built environment not only shapes the layout of cities but also influences urban life and activities [27]. Scholars have highlighted that features of the built environment, such as building density, accessibility, and diversity, significantly impact urban vitality [13,14,19,28]. Therefore, the built environment and urban vitality are considered closely related and complexly intertwined social processes [29]. Understanding how the built environment affects urban vitality and formulating adaptive and resilient urban planning strategies are crucial for sustainable urban development. A wealth of empirical research has established a robust connection between features of the built environment and the vitality of urban streets [30]. However, most studies rely on traditional linear regression models such as OLS, GWR, and MGWR [6,31,32], which typically assume linear relationships between variables or follow predefined patterns, and are affected by multicollinearity among indicators. Such studies might fail to account for the nonlinear dynamics in the impact of the built environment on urban vitality. This oversight occurs despite the probability of complex and synergistic interactions involving the built environment and urban vitality [33,34,35]. Machine learning techniques are adept at uncovering the intricate connections between human activities and the built environment [36]. Many scholars have demonstrated that machine learning methods outperform traditional regression methods in studying urban vitality and the built environment [37,38,39,40]. XGBoost is one of the commonly used machine learning methods, known for its exceptional stability in various data processing scenarios [41]. In contrast to traditional statistical regression methods, the XGBoost model can modify the weights of independent variables through learning, fitting the complex relationships between dependent and independent variables, thereby enhancing prediction accuracy. Additionally, it exhibits high tolerance to multicollinearity, outliers, and missing values [42]. Since machine learning models often operate as black boxes, deciphering their internal mechanisms and decision-making pathways can be challenging. This opacity can result in models that excel during training but underperform in real-world scenarios [43]. Currently, machine learning interpretation techniques are broadly categorized into global methods and local methods. Wang et al. [13] examined the intricate interactions between built environment indicators and urban vitality in the core urban area of Guangzhou using machine learning techniques, employing global methods to evaluate the influence of individual variables on model accuracy. In contrast, techniques like SHAP offer localized interpretations for individual predictions [44], preserving the uniqueness of each case and providing more detailed explanations than global methods. SHAP, inspired by Shapley values, is an interpretable model that provides deeper insights than the feature importance scores from XGBoost itself. The main advantage of SHAP values is their ability to show the specific impact of each feature on individual samples and distinguish whether these impacts are positive or negative [45]. Many studies have been conducted to explore the nonlinear relationships between urban characteristics and phenomena such as metro passenger flow [46], house price [47] and surface temperature [48] using the XGBoost-SHAP model. This suggests that some urban characteristics and phenomena exhibit nonlinear interactions, indicating a need for further investigation to reveal their complexity and potential mechanisms of influence. However, only a limited number of studies have applied the model to explore the intricate interactions and combined effects related to the built environment and urban dynamics. This study primarily explores the following research questions: (1) In contrast to prior studies at the township or grid scale, does examining at the more granular neighborhood level reveal significant spatial heterogeneity in the economic, social, cultural, and ecological vitality of cities? Additionally, do key neighborhoods with varying vitality levels demonstrate notable radiating effects? (2) What are the specific characteristics of the nonlinear relationship between multidimensional neighborhood vitality and the urban built environment at the neighborhood scale? (3) Which interaction effects among various indicators significantly impact neighborhood vitality? Are there thresholds within these indicators and their interactions that result in different changes in neighborhood vitality? To address these questions, the central urban area of Guangzhou was selected as the study region, with neighborhoods being used as the basic research units. We constructed a comprehensive vitality assessment system based on social, economic, cultural, and ecological vitality [8] and spatially expressed it. Referring to Ewing and Cervero’s 5Ds framework [49], we established a built environment indicator system. The XGBoost-SHAP model was employed to explore the nonlinear impacts of various built environment factors on neighborhood vitality and to quantitatively analyze the synergistic and threshold effects among different built environment indicators. The aim is to provide urban planners with more precise data support and a decision-making basis to improve neighborhood vitality and foster sustainable urban growth.

2. Materials and Methods

2.1. Overview of the Study Area

Guangzhou, the capital of Guangdong Province, is situated at the northern boundary of the Pearl River Delta, near the South China Sea. As the economic and transportation hub of southern China, it has a permanent population exceeding 15 million. The “Guangzhou 2049 Urban Development Strategy” envisions goals such as “southward expansion towards the oceans, eastward progress along the two rivers, upgrading the old city, and demonstrating key points.” The central urban area, as the spatial carrier of the “upgrading the old city” strategy, extends from the Northern Second Ring Expressway in the north to the boundaries of Liwan and Haizhu districts in the south, from the city boundaries of Guangzhou in the west to the boundary of Tian-he District in the east. With high economic density and a significant population con-centration, the central urban area shows notable vitality changes, making it conducive to evaluating and analyzing urban vitality in this study. Therefore, researching the urban vitality of Guangzhou’s central urban area is highly pertinent and representative.

Since the neighborhood scale can more finely and accurately capture the spatial heterogeneity within a city, it reveals differences in vitality among different neighborhoods and the intricate interactions between these neighborhoods and built environment elements. Therefore, this study references the methodology of Huang and Xiao [50], who combined remote sensing imagery and OSM road network data to divide the study area into basic research units, resulting in 5,142 neighborhood units. The specific division is illustrated in Figure 1.

2.2. Overview of the Study Area Research Framework

In this research, we utilize multiple data sources to explore the connection between built environment characteristics and urban vitality. It evaluates vitality through four aspects: economic, social, cultural, and ecological, each quantified by specific indicators, and examines the spatial patterns of vitality within these aspects. Additionally, we develop a built environment indicator system and use the XGBoost-SHAP model to explore the complex nonlinear relationships and synergistic effects between the built environment and urban vitality. The goal is to provide urban planners with actionable insights. The process of this study is depicted in Figure 2.

2.3. Data Sources and Processing

2.3.1. Basic Dataset

As shown in

Table 1. Description of various datasets.

Data Name	Year	Data Source
Guangzhou Administrative Boundaries	2023	https://www.webmap.cn/, accessed on 6 February 2023.
Guangzhou Main Urban Area Road Network	2023	https://www.openstreetmap.org/, accessed on 19 February 2023.
GF-2 Data	2023	https://www.cpeos.org.cn/, accessed on 7 December 2023. https://www.cpeos.org.cn/, accessed on 29 April 2024.
GF-6 Data	2024
Guangzhou Baidu Heatmap Data	2023	https://map.baidu.com/, accessed on 26 March 2024.
Guangzhou Social Perception Data	2023	https://www.dianping.com/, accessed on 15 January 2024.
Guangzhou Main Urban Area POI	2023	https://ditu.amap.com/, https://map.baidu.com/, accessed on 23 January 2024.
Guangzhou Main Urban Area Building Data	2023	https://www.tianditu.gov.cn, https://ditu.amap.com/, accessed on 21 April 2023.
Guangzhou Main Urban Area Transportation Stations	2023	https://ditu.amap.com/, https://map.baidu.com/, accessed on 29 April 2023.
Guangzhou Main Urban Area Housing Price Data	2023	https://www.anjuke.com/, accessed on 7 December 2023.
Guangzhou Population Data	2022	https://landscan.ornl.gov/, accessed on 1 September 2023.

, the primary data sources for this study include OSM road network data, GF-2 satellite imagery, GF-6 satellite imagery, Baidu heatmap data, social sensing data, POI data, and building data. The Baidu heatmap data, sourced from Baidu Huiyan, offer advantages such as continuity and dynamism. The 2023 POI data were obtained from the Gaode Map API and Baidu Map API interfaces using crawler technology. Redundant, duplicate, and incomplete POI points were removed, and the data were classified. Road network data were obtained from the OpenStreetMap website, with the raw OSM road network converted into a single-line network and subjected to topological correction. This was further refined manually using GF-2 imagery to delete or trim dangling nodes and remove excessively short isolated roads, which were then used to delineate block research units. Social sensing data were scraped from the Dazhong Dianping Web API, including coordinates, ratings, and the number of reviews. GF-2 satellite imagery was preprocessed to generate orthophotos of the study area. GF-6 data underwent radiometric calibration and atmospheric correction to calculate NDVI data. The dataset details are summarized in Table 1.

2.3.2. Comprehensive Urban Vitality Model Dataset

The construction of the urban vitality indicator system is based on the comprehensive understanding of urban vitality derived from the existing literature. Urban vitality encompasses several dimensions, including economic, social, cultural, and environmental aspects [4,51]. This research has created a detailed indicator system for these four aspects and formulated an urban vitality model, grounded in the accuracy and consistency of diverse data sources. The dataset includes Dianping shop numbers, shop ratings, user reviews, Points of Interest (POIs), Baidu heat maps, and NDVI data. Integrating these diverse data sources with different spatial and temporal granularities helps to comprehensively and accurately quantify urban vitality [52]. The specifics of the dataset are presented in

Table 2. Description of data for constructing the urban vitality model.

Data Name	Source	Quantity and Type	Data Content
Dianping Store Count	https://www.dianping.com/ (Accessed on 15 January 2024)	141,350 locations	Reflects industry living density
Dianping User Reviews	https://www.dianping.com/ (Accessed on 16 January 2024)	7,783,935 reviews	Reflects consumer behavior
Dianping Store Ratings	https://www.dianping.com/ (Accessed on 17 January 2024)	4093 total, 3,507,296 ratings	Reflects store service quality
Company and Cultural Facilities (POI)	https://map.baidu.com/, https://ditu.amap.com/ (Accessed on 17 October 2023)	48,681 company POI points 15,240 cultural facilities POI points	Reflects business environment and urban layout
Baidu Heatmap	https://huiyan.baidu.com/ (Accessed on 4 November 2023)	875,559 hotspots, vector map	Reflects population flow and activity
Vegetation Index	https://www.cpeos.org.cn/ (Accessed on 29 April 2024)	Raster TIFF format	Reflects the lushness of surface vegetation

.

2.3.3. Built Environment Dataset

The neighborhoods in central Guangzhou were comprehensively analyzed from six dimensions: location, spatial form, functional form, demographic characteristics, accessibility, and land use [18]. Thirteen indicators were chosen to represent the characteristics of the urban infrastructure. These indicators are detailed in

Table 3. Description of built environment indicators.

	Influencing Factors	Indicator	Positive/Negative	Meaning
Internal Attributes	Location	Street Location (DTZ)	Negative	Reflects the accessibility of the block to the city center
	Spatial Form	Spatial Compactness (SC)	Positive	Indicates the intricacy of the spatial layout within the block
		Fractal Dimension (FD)	Positive	Reflects the complexity of the block’s form
	Functional Form	POI Mix Degree (ME)	Positive	Reflects the mixing degree of various functional POI densities
		POI Density (POID)	Positive	Indicates the concentration of different Points of Interest (POIs) within the area
	Population Characteristics	Population Density (PD)	Positive	Reflects the population density within the block
External Environment	Accessibility	Square (DSQ)	Negative	Reflects the accessibility of squares within the block
		Park (DTP)	Negative	Reflects the accessibility of parks within the block
		Subway Station (DSB)	Negative	Reflects the accessibility of subway stations within the block
	Building Function	Housing Price Level (APH)	Positive	Indicates the housing quality within the area
		Building Density (BD)	Positive	Reflects the block’s vacancy rate and building density
		Floor Area Ratio (FAR)	Positive	Indicates the level of development within the area
		Building Height (BH)	Positive	Indicates the mean height of buildings within the area

.

2.4. Research Methods

2.4.1. Construction of Urban Vitality Indicators

• Metrics for Measuring Economic Vitality

In China, the Dianping platform offers detailed and objective user reviews on various commercial facilities. These reviews significantly influence the choices made by online consumers and reflect the degree of consumer engagement at these facilities [53,54,55,56]. Additionally, related studies have shown that the clustering of companies and enterprises helps promote economic activities [57]. Therefore, this study combines the number and ratings of Dianping shops, user review counts from Dianping, and POI (enterprise) data collected I n September 2023 to construct a comprehensive indicator for measuring urban economic vitality using the entropy method. This approach offers a deeper insight into economic activities in Guangzhou’s central urban area. The spatial distribution of economic vitality is illustrated in Figure 3a. The calculation process is as follows:

(1)

Indicator Standardization

The selected indicators typically have positive and negative effects. Equation (1) is applied to indicators with positive effects, while Equation (2) is used for those with negative effects.

$$X_{ij}={\displaystyle \frac{x_{ij}-min\left(x_j\right)}{max\left(x_j\right)-min\left(x_j\right)}}$$

(1)

$$X_{ij}={\displaystyle \frac{max\left(x_j\right)-x_{ij}}{max\left(x_j\right)-min\left(x_j\right)}}$$

(2)

where $x_{ij}$ represents the initial value of the $j$th indicator, and $X_{ij}$ represents the standardized value of the $j$th indicator. The terms $max\left(x_j\right)$ and $min\left(x_j\right)$ are the maximum and minimum values of the $j$th indicator, respectively.

(2)

Calculating Indicator Weights

$$Q_{ij}={\displaystyle \frac{X_{ij}}{\sum _{j=1}^n X_{ij}}}$$

(3)

where $Q_{ij}$ represents the standardized weight of the $j$th indicator, and $n$ is the number of indicator samples.

$$M_{ij}=-h\sum _{j=1}^n Q_{ij}ln{Q}_{ij}$$

(4)

where $M_{ij}$ represents the information entropy, and $h$ is a constant.

$$Z_{ij}={\displaystyle \frac{1-M_{ij}}{\sum _{j=1}^n 1-M_{ij}}}={\displaystyle \frac{1-M_{ij}}{n-\sum _{j=1}^n M_{ij}}}$$

(5)

• Metrics for Measuring Social Vitality

Social vitality, a key component of urban vitality, is largely driven by human activities. Hence, this study employs Baidu heat map data to quantify population aggregation. These data are obtained by collecting and analyzing the location information of users who use Baidu-related mobile applications, such as Baidu Maps, Baidu Search, and Baidu Weather. The Baidu heat index is calculated and displayed in different colors to show the spatial distribution of users within an area. This method has been widely used to measure population aggregation characteristics [58]. In this study, data from Baidu heat maps were selected for the period from September 24 to 25, 2023, between 10:00 and 20:00. The IDW interpolation method was used to obtain the heat index data for each time period, with the average heat index representing the social vitality of each neighborhood. Figure 3b illustrates the spatial distribution of social vitality. The calculation formula is as follows [59]:

$$x={\displaystyle \frac{\sum _{i=1}^n Z_i{w}_i}{\sum _{i=1}^n w_i}}$$

(6)

$$W_i={d^{-\beta }}_{x,y,i}$$

(7)

where $x$ is the point to be estimated, $Z_i$ is the control value of the $i$th sample point, and $w_i$ is the weight, defining the importance of a single control point $Z_i$ in the interpolation process. $d_{x,y,i}$ is the distance between $Z_{xy}$ and $Z_i$, and $\beta$ is the power parameter. The equation can be written as:

$$X_{yz}={\displaystyle \frac{\sum _{i=1}^n Z_i{d}_{x.y.i}^{-\beta }}{\sum _{i=1}^n d_{x.y.i}^{-\beta }}}$$

(8)

• Metrics for Measuring Cultural Vitality

Cultural centers in neighborhoods reflect residents’ material needs in the context of rapid social and cultural development and possess specific spatial characteristics. These centers draw cultural enthusiasts and host various activities, offering spaces for cultural exchange [60,61]. In this study, the density of education and cultural POIs in 2023 is used as an indicator to measure cultural vitality. This indicator offers a clear and quantifiable measure of the distribution of cultural facilities within the city. A high density of educational and cultural points of interest suggests that the area likely hosts more cultural activities and events. Accordingly, this study uses the POI points from the education and cultural category to conduct a kernel density analysis, obtaining a cultural vitality index for each neighborhood to represent cultural vitality. Figure 3c illustrates the spatial pattern of cultural vitality. The function for kernel density estimation is as follows [62]:

$$f_n(x)={\displaystyle \frac{1}{n\pi r^2}}\sum _{i=1}^n K{\left[\left(1-{\displaystyle \frac{{\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2}{r^2}}\right)\right]}^2$$

(9)

here, $K$ represents the kernel function, $(x-x_i{)}^2+(y-y_i{)}^2$ denotes the squared Euclidean distance from $(x_j,y_j)$ to $(x,y)$, $r$ refers to the kernel density bandwidth or search radius, and $n$ indicates the count of sample points within this radius. Choosing the search radius is crucial as it significantly affects the analysis results: a smaller radius will highlight more high-value or low-value areas, suitable for reflecting local aggregation characteristics, while a larger radius will produce smoother kernel density contours, suitable for indicating global-scale aggregation areas. Based on relevant research and the characteristics of the data in this study, a search radius of 500 m was chosen for the kernel density estimation.

• Metrics for Measuring Ecological Vitality

Ecological vitality is essential in influencing urban vitality. Higher environmental quality boosts people’s willingness to participate in outdoor activities and attracts more engagement in social activities [6]. The NDVI serves as a primary measure of vegetation cover and health [63,64]. This study uses NDVI values from GF-6 remote sensing imagery data from April 2024 to measure urban ecological environment vitality at a micro level [18]. The calculation formula is as follows:

$$EV={\displaystyle \frac{{\sum }_{i=1}^{n}NDV{I}_i}{n}}$$

(10)

where $NDV{I}_i$ represents the Normalized Difference Vegetation Index of the $i$th pixel in each neighborhood, $n$ s the number of pixels within the neighborhood, and $EV$ is the average Normalized Difference Vegetation Index of each neighborhood. Higher $EV$ values indicate stronger ecological vitality, while lower $EV$ values indicate weaker ecological vitality. Figure 3d illustrates the spatial distribution of ecological vitality.

• Method for Calculating Comprehensive Urban Vitality

To maintain consistency in measuring vitality across various dimensions, we performed min-max normalization on economic, social, cultural, and environmental vitality (Equations (1) and (2)). Furthermore, the comprehensive vitality values for each neighborhood in Guangzhou’s central urban area were determined using the entropy method. The weights of the four dimensions are shown in

Table 4. Weights of vitality indicators.

Vitality Dimension	Data Type	Weight
Economic Vitality	Block Store Comprehensive Rating	0.015
	Block Store Total Review Count	0.024
	Enterprise Company Density	0.079
	Dianping Store Density	0.154
Social Vitality	Baidu Heatmap	0.247
Cultural Vitality	Cultural Facility POI Density	0.425
Ecological Vitality	NDVI	0.056

. Figure 3e shows the spatial distribution of comprehensive vitality.

2.4.2. Method for Analyzing Nonlinear Relationships and Synergistic Effects

This research utilizes the XGBoost model to investigate the nonlinear effects and threshold impacts on neighborhood vitality within Guangzhou’s central urban areas. The method reduces prediction errors and enhances model accuracy through steps such as initial prediction, residual calculation, new regression construction, and model updating [65]. Referring to the work of Luo et al. [45], the XGBoost objective function before iteration consists of the loss function and the regularization function, as indicated by the following formula:

$$f_{OBJ}^{(t)}=\sum _{i=1}^n l(y_i,{\widehat{y}}_i^{(t)})+\sum _{k=1}^k \mathsf{\Omega }(f_k)$$

(11)

where $\sum _{i=1}^n l(y_i,{\widehat{y}}_i^{(t)})$ represents the loss function, indicating the goodness of fit; $\sum _{k=1}^k \Omega (f_k)$ represents the regularization term.

When solving for the extremum of the loss function, we apply Newton’s method, using a second-order Taylor expansion. This approach accelerates gradient convergence and enhances the prediction accuracy of the urban vitality model. The regularization term defines the model’s complexity by penalizing the number of leaf nodes, thereby preventing overfitting. The formula is as follows:

$$\mathsf{\Omega }(f)=\gamma T+{\displaystyle \frac{1}{2}}\lambda {\left|\omega \right|}^2=\gamma T+{\displaystyle \frac{1}{2}}\lambda \sum _{j=1}^T {\omega }_j^2$$

(12)

where: $\gamma$ is the regularization term for the entire tree’s leaf nodes, controlling their number and reducing each tree’s weight, thus providing more learning space for the next tree; $T$ is the count of leaf nodes in each tree; $\lambda$ controls the complexity of the leaf nodes; and $\omega$ is the vector of leaf nodes.

For optimization, Equation (11) is expanded using a second-order Taylor series as follows:

$$f_{OBJ}^{(t)}\approx \sum _{i=1}^n [g_i{f}_t(x_i)+{\displaystyle \frac{1}{2}}{h}_i{f}_t^2(x_i)]+\mathsf{\Omega }(f)$$

(13)

$$G{g}_i={\displaystyle \frac{\partial l(y_i,{\widehat{y}}_i^{t-1})}{\partial {\widehat{y}}_i^{t-1}}},h_i={\displaystyle \frac{{\partial }^{2}l(y_i,{\widehat{y}}_i^{t-1})}{(\partial {\widehat{y}}_i^{t-1}{)}^2}}$$

(14)

where $g_i$ and $h_i$ are the first and second derivatives of the loss function, respectively; $f_t\left(x_i\right)$ is the prediction of the $t$-th decision tree for the $i$-th sample.

Further expand and combine the regularization term as follows:

$$\begin{array}{l}{f}_{OBJ}^{\left(t\right)}\approx {\displaystyle \sum _{i=1}^n} \left[g_i{f}_t(x_i)+{\displaystyle \frac{1}{2}}{h}_i{f}_t^2(x_i)\right]+\gamma T+\\ {\displaystyle \frac{1}{2}}\lambda {\displaystyle \sum _{j=1}^T} {\omega }_j^2={\displaystyle \sum _{j=1}^T} [\left({\displaystyle \sum _{i\in I_j}} g_i\right){\omega }_j+{\displaystyle \frac{1}{2}}({\displaystyle \sum _{i\in I_j}} h_i+\\ \lambda ){\omega }_j^2]+\gamma T\end{array}$$

(15)

In summary, during each iteration of the XGBoost algorithm, a decision tree is generated based on the current model’s prediction residuals. This iterative process continues, with each tree addressing the errors from the previous iteration, until the residuals are minimized to a very low level. The dataset, which includes urban built environment indicators and comprehensive city vitality values, was split randomly into training and testing sets in an 8:2 ratio. Model performance was assessed using MSE and R². To determine the best parameters and enhance the model’s generalization capability, a grid search along with 5-fold cross-validation was used for hyperparameter tuning, resulting in the best parameter set (

Table 5. Model-specified parameters.

Hyperparameter	Description	Optimal Hyperparameter
max_depth	Specifies the maximum depth of each tree	5
learning_rate	Determines the contribution of each tree in the model	0.1
colsample_bytree	Specifies the subsample ratio of columns when constructing each tree	0.8
subsample	Subsampling ratio of the training instance	0.9
min_child_weight	Minimum sum of instance weight (hessian) needed in a child	1
n_estimators	Number of trees to be constructed	200

). For a thorough evaluation of the model, metrics such as MAE, MSE, RMSE, and R² were calculated (Table 6).

While the XGBoost model excels over traditional linear regression models in accuracy and generalization, it lacks the interpretability of linear models. To elucidate the complex impact of built environment factors on urban vitality, this study uses the SHAP interpretation method. SHAP, grounded in classical cooperative game theory, calculates Shapley values to explain predictions [66]. The specific calculation method is as follows:

$${\mathrm{S}\mathrm{H}\mathrm{A}\mathrm{P}}_j=\sum _{S\subseteq \{V_1,V_2,\cdots ,V_p\}\setminus \left\{V_j\right\}} {\displaystyle \frac{\left|S\right|!(p-|S|-1)!}{p!}}[f_x(S\cup \{V_j\})-f_x(S)]$$

(16)

$$y_i=y_{\mathrm{base}}+\sum _{j=1}^k \mathrm{SHAP}(x_{ij})$$

(17)

where ${\mathrm{S}\mathrm{H}\mathrm{A}\mathrm{P}}_{\mathrm{j}}$ represents the $\mathrm{S}\mathrm{H}\mathrm{A}\mathrm{P}$ value of sample $\mathrm{i}$ for feature $\mathrm{j}$; $\mathrm{S}$ is the subset of features used by the model; ${\mathrm{V}}_{\mathrm{p}}$ is the set of all model features; $\mathrm{P}$ is the number of features; ${\mathrm{f}}_{\mathrm{x}}\left(\mathrm{S}\right)$ is the model’s prediction for the subset of features; ${\mathrm{y}}_{\mathrm{i}}$ is the prediction result for sample $\mathrm{i}$; ${\mathrm{y}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}$ is the average prediction value of other samples; and $\mathrm{k}$ is the number of features. $\mathrm{S}\mathrm{H}\mathrm{A}\mathrm{P}$ values offer an additive attribution method, summing the attribution values of each input feature to explain the model’s prediction. The sign of $\mathrm{S}\mathrm{H}\mathrm{A}\mathrm{P}$(${\mathrm{x}}_{\mathrm{i}\mathrm{j}}$) reveals the specific influence of various urban characteristics on the prediction outcome. In the urban vitality prediction model, the SHAP algorithm determines the marginal contribution of each built environment factor, thereby enhancing the interpretability of the machine learning model.

3. Results

3.1. Spatial Characteristics of Urban Vitality

Using the entropy weight method (Equation (5)) to determine the weights for economic, social, cultural, and environmental vitality, we calculated the comprehensive vitality indicator. Next, we applied the natural break method to classify the overall vitality values, including economic, social, cultural, and environmental dimensions [32], resulting in the categorization of different neighborhood vitality levels in Guangzhou’s central urban area (Figure 3).

3.1.1. Spatial Distribution of Economic Vitality

Economic vitality in Guangzhou’s central urban area shows a clear pattern: high values in the center and lower values on the periphery (Figure 4). High economic vitality is concentrated in commercial activity centers such as Tianhe Sports Center, Zhonghuan Plaza, Grandview Mall, Zhujiang New Town CBD, and Chebei South Road shopping area in Tianhe District, as well as Beijing Road Commercial Area and Gongyuanqian Commercial Area in Yuexiu District. These adjacent high-value areas showcase dynamic commercial activities, financial services, and vibrant nightlife venues. Liwan District, as the historical and cultural core of Guangzhou, boasts rich cultural heritage and historical landmarks. Areas such as the Chen Clan Ancestral Hall and Shangxiajiu Pedestrian Street in Liwan District have high economic vitality, with the combination of culture and commerce effectively enhancing the economic vitality of these neighborhoods.

3.1.2. Spatial Distribution of Social Vitality

Unlike economic vitality, areas of high social vitality are more dispersed (Figure 5). They are not limited to central districts like Tianhe, Yuexiu, and Haizhu but are also found in Baiyun and Liwan districts. High social vitality areas include the Tianhe Road Commercial Area, Zhongshan Fourth Road, and the vicinity of Jiahe Wanggang. The Tianhe Road Commercial Area and Zhongshan Fourth Road, as commercial and entertainment hubs of Guangzhou, host numerous shopping centers, theaters, dining, and entertainment facilities. These factors collectively attract large crowds, significantly enhancing the social vitality of these areas. Additionally, peripheral areas such as Jiahe Wanggang in Baiyun District also exhibit high social vitality.

3.1.3. Spatial Distribution of Cultural Vitality

The geographical pattern of cultural vitality in Guangzhou’s central urban area exhibits a clear multi-center pattern (Figure 6). High cultural vitality is found in key locations such as the Wushan University District and Huashui Road in Tianhe, Sun Yat-sen University’s South Campus in Haizhu, Wende Road in Yuexiu, and the area surrounding Guangzhou Zoo. In Liwan, the Fangcun area, known for its rich history and cultural heritage, stands out as a center of cultural vitality. Together, these areas create a diverse and widely distributed urban landscape of cultural vitality in Guangzhou.

3.1.4. Spatial Distribution of Ecological Vitality

The spatial distribution of ecological vitality exhibits a non-homogeneous pattern, with high-value areas mainly located on the outskirts of Guangzhou’s central urban area and in several natural landscapes and parks (Figure 7). Specifically, high ecological vitality areas include Baiyun Mountain Scenic Area and Maofengshan Forest Park in Baiyun District; Huolushan Forest Park and Tianhe Park in Tianhe District; Ersha Island and Yuexiu Park in Yuexiu District; Haizhu National Wetland Park and Yingzhou Ecological Park in Haizhu District; and Guanggang Park in Liwan District. These areas, with their abundant natural resources and excellent environmental protection, serve as centers of ecological vitality. In contrast, although ecological vitality is unevenly distributed in the central urban neighborhoods, these areas still maintain a relatively good level.

3.1.5. Spatial Distribution of Ecological Vitality

In Guangzhou’s central urban area, the overall spatial pattern of comprehensive vitality shows a balanced distribution (Figure 8). Notable high vitality areas include Zhujiang New Town and Tianhe Sports Center in Tianhe District, the Beijing Road Commercial Area in Yuexiu District, and the Sun Yat-sen University Guangzhou South Campus and Jiangnanxi area in Haizhu District. These areas have become key sources of urban vitality due to their dense commercial facilities, abundant cultural institutions, and concentration of educational resources. Major transportation arteries such as Huangpu Avenue and Huacheng Avenue further enhance the comprehensive vitality of these areas by promoting the efficient movement of people and resources. In contrast, the peripheral areas of the central urban region, including northwest Baiyun District, western Liwan District, and eastern Haizhu District, exhibit relatively weaker vitality.

3.2. The Comprehensive Impact of the Built Environment on Urban Vitality

3.2.1. XGBoost Model Validation

The XGBoost model was executed using Python, with the SHAP method applied to enhance model interpretability. Indicators of the built environment were used as input variables, while the comprehensive urban vitality index functioned as the output variable. The model’s effectiveness is demonstrated through the P-T curve, as shown in Figure 9. When actual values are high, the predictions become unstable due to insufficient learning from underrepresented areas in the training data [36]. To guarantee the model’s reliability and stability, K-fold cross-validation was performed to validate its predictive capability. Additionally, the regression results were contrasted with those from the OLS linear regression model. Performance and comparison results are detailed in Table 6.

Table 6. Model performance.

	MSE	RMSE	MAE	R-Squared
XGBoost	0.0053	0.0724	0.0487	0.6057
OLS	0.0071	0.0843	/	0.497

Table 6. Model performance.

	MSE	RMSE	MAE	R-Squared
XGBoost	0.0053	0.0724	0.0487	0.6057
OLS	0.0071	0.0843	/	0.497

3.2.2. Relative Importance of Built Environment Indicators

Figure 10 (left) emphasizes the significance of various variables among the built environment indicators. These variables are arranged from top to bottom according to their significance. The right side of Figure 10 shows how each built-environment variable contributes to urban vitality. Within the built environment indicator system, the prominent importance of the functional form dimension (POID and ME) suggests that multifunctional and dense economic and social attributes are key factors in enhancing urban vitality. In the location dimension, the importance of street location, with a value of 0.039, is higher than that of other indicators. Additionally, the right side of the figure indicates that the distance from a neighborhood to Zhujiang New Town (DTZ) negatively impacts urban vitality. This implies that the closer a neighborhood is to the CBD, the more positively it affects vitality; proximity to Zhujiang New Town typically correlates with higher levels of economic and social activities. In the accessibility dimension, the combined importance of the distances to the square (DSQ), park (DTP), and subway station (DSB) is 0.031, highlighting the significant impact of proximity to parks, squares, and subway stations on vitality. Good accessibility facilitates residents’ access to public spaces and transportation facilities, thereby promoting the development of economic, cultural, and social activities. Conversely, the lower importance of demographic characteristics (PD), building functions (FAR, APH, BD, and BH), and spatial form dimensions (FD, SC) indicates that these urban structural elements have a relatively limited impact on urban vitality.

3.2.3. The Nonlinear Relationship between the Built Environment and Urban Vitality

The SHAP dependence diagram in Figure 11 demonstrates the complex influences of various factors on street vitality. The X-axis represents different indicator values, while the Y-axis indicates each indicator’s partial impact on overall vitality. Specifically, the proximity of neighborhoods to Zhujiang New Town (DTZ) and subway stations (DSB) significantly affects vitality, with closer distances having more positive effects. The diversity (ME) and density (POID) of POIs also have a clear impact on vitality; higher POI diversity suggests richer neighborhood amenities, contributing more positively to comprehensive vitality. Initially, POI density exhibits a weak negative impact on vitality, but as density increases, it strongly contributes positively to vitality. The relative location of neighborhoods in public spaces is equally important. The distance from neighborhoods to squares (DSQ) shows a shift to a weak and slightly negative contribution to vitality when it exceeds the threshold of 0.14. Conversely, the proximity to parks (DTP) consistently exerts a positive influence on vitality, with this effect diminishing as the distance increases. The relationship between average housing prices (APR) and comprehensive urban vitality shows a clear threshold effect. Below the threshold (feature value less than 0.16), the impact is negative but weak; beyond this threshold, housing prices positively influence vitality. Population density (PD) consistently contributes positively to urban vitality, reflecting that higher population density promotes more economic and social activities. Due to the spatial complexity of neighborhoods, fractal dimension (FD) exhibits a threshold effect. Above a certain level (feature value greater than 0.16), higher fractal dimensions positively influence vitality. Both spatial compactness (SC) and building density (BD) also show threshold effects. Spatial compactness contributes positively to vitality after reaching a threshold of 0.07, while building density (BD) shows a similar effect after reaching a threshold value of 0.05. However, its contribution stabilizes at higher values, indicating diminishing returns. This suggests that more cohesive and efficiently organized neighborhood structures can enhance vitality. Floor area ratio (FAR) boosts vitality at lower values but diminishes it once the value exceeds 0.41. Additionally, the building height (BH) has no significant impact on vitality.

3.2.4. The Synergistic Effects of the Built Environment on Urban Vitality

In the SHAP model, each explanatory variable’s effect encompasses both its primary and interaction effects with other variables [16]. We further analyzed the interactions between the five most influential indicators on comprehensive vitality (DTZ, POID, DSB, DSQ, and ME) and other variables by determining the mean absolute Shapley interaction values for each pair of variables [36]. We then identified the variables with the most significant interactions (POID and DTZ). Figure 12 visualizes these local interactions for each pair of indicators. Each plot illustrates a pair of indicators, demonstrating how changes in one variable influence the impact on vitality of another. The X-axis represents a specific built environment indicator, the color indicates the magnitude of the indicator with the strongest interaction effect on vitality, and the Y-axis shows the positive or negative contribution of the interaction between the two indicators on vitality.

The results indicate that neighborhoods near Zhujiang New Town (DTZ) and with high POI density (POID) significantly enhance comprehensive vitality. However, as the distance increases while the POI density remains high, their synergistic effect on vitality becomes weak or negative. Additionally, when POI density is low, the synergistic effect is insignificant regardless of the neighborhood’s distance to Zhujiang New Town. When neighborhoods are close to both squares (DSQ) and Zhujiang New Town, there is a clear positive synergy. However, when neighborhoods are close to squares but far from Zhujiang New Town, there is a significant negative contribution. As the distance to squares exceeds the threshold (feature value of 0.12), the positive interaction effect diminishes or flattens regardless of the distance to Zhujiang New Town (indicated by various colors). Especially when neighborhoods are close to the CBD but far from squares, they negatively contribute to vitality. This could be due to the negative impact of over-reliance on the CBD. When POI density (POID) is low, the combined effect of POI density and proximity to Zhujiang New Town (DTZ) adversely affects vitality. Conversely, when POI density is high, neighborhoods near the CBD enhance comprehensive vitality; however, this positive influence weakens and eventually turns negative as the distance increases. The interaction between POI diversity (ME) and POI density shows a high threshold effect (0.74); below this threshold, the interaction is dominated by POI density. Low POI density positively affects vitality, while high POI density negatively affects it. This could be explained by the imbalanced resource allocation leading to the repetitive clustering of basic service facilities, reducing neighborhood vitality. Above this threshold, the synergistic effect becomes more pronounced, with high POI diversity and density providing the strongest positive contribution to vitality. The contribution weakens as density decreases. When neighborhoods are closer to metro stations (DSB), the interaction between POI density and proximity to metro stations significantly impacts vitality. Higher POI density results in higher vitality for neighborhoods close to metro stations, while lower POI density results in lower vitality. Once the distance reaches a certain value (0.04), even high POI density only weakly contributes to neighborhood vitality, indicating that the advantage of high POI concentration largely depends on the convenience of transportation.

4. Discussion

4.1. Comparative Analysis of the Spatial Distribution of Urban Vitality

The division of streets within administrative management units often only measures vitality from a town or street perspective [18,67], whereas the neighborhood scale provides more detailed information on vitality distribution, supporting refined urban management. In Guangzhou’s central urban area, economic vitality is highly concentrated in core commercial districts that integrate shopping, dining, entertainment, office, and residential functions, such as Tianhe Sports Center, Zhujiang New Town, and Gongyuanqian. These areas not only offer convenience to consumers but also create diverse economic activities, attracting significant foot traffic and capital flow [8]. Good urban design and superior transportation conditions are key factors in maintaining their high economic vitality [32,36]. The dispersed distribution of social crowd gatherings reflects a diverse pattern of interactions and crowd gatherings within Guangzhou’s central urban area.. Neighborhoods like Tianhe Road and Zhongshan Fourth Road naturally attract high social vitality due to their commercial, entertainment, and historical values. Peripheral areas such as Jiahe Wanggang also exhibit high social vitality due to the concentration of migrant workers [20,68]. These areas become new sources of vitality by providing essential infrastructure and community services. Cultural vitality in Guangzhou’s central urban area exhibits a multi-center pattern, indicating balanced development of cultural resources and activities across key locations [20]. High cultural vitality is evident not only in traditional central areas but also in districts with dense educational institutions, historical and cultural backgrounds, and recreational facilities, such as Wushan, Wende Road, and the South Campus of Sun Yat-sen University. This dispersed layout of cultural vitality promotes broader cultural participation and social interaction, enhancing the city’s overall cultural appeal and community vitality. The non-homogeneous distribution of ecological vitality in Guangzhou reveals the diversity and stratification of the city’s ecological structure. Ecological vitality is concentrated in the city’s outskirts and natural landscape areas, highlighting the uniqueness of these regions in ecological resource conservation and utilization. The successful management of major urban parks and nature reserves demonstrates a positive urban ecological policy [8]. Through strategic greening projects and ecological improvement measures, the city center also maintains a relatively stable ecological environment. The comprehensive vitality of Guangzhou’s central urban area demonstrates the functional differences between the center and the periphery [69]. Central areas such as Zhujiang New Town and Tianhe Sports Center in Tianhe District, the Beijing Road Commercial Area in Yuexiu District, and the South Campus of Sun Yat-sen University and Jiangnanxi in Haizhu District show high vitality. The prominence of these areas is primarily due to the high concentration of commercial, cultural, and educational resources, as well as excellent transportation networks. These factors collectively promote the high concentration and flow of population and resources, forming core areas of vitality. In contrast, peripheral areas like northwest Baiyun District and western Liwan District, though relatively low in vitality, still maintain essential urban functions, ensuring the basic living needs of residents.

4.2. Analysis of the Impact of Built Environment Factors on Urban Vitality

4.2.1. The Impact of Single Indicators on Urban Vitality

The built environment exerts a pervasive nonlinear influence on street vitality, consistent with the views of Tao and Liu et al. [70,71]. This study finds that urban vitality primarily depends on the proximity of neighborhoods to the city center, functional diversity, and accessibility to transportation and space, similar to the conclusions of Mouratidis et al. [72]. The distance from the CBD and the accessibility to transportation and space both negatively impact urban vitality. This implies that a neighborhood closer to the CBD and with convenient transportation is more vibrant [32]. Higher commercial density and richer service facilities can directly enhance the vitality of the area. The commercial resources, employment opportunities, and diverse social and cultural facilities around the CBD also promote increased urban vitality. Additionally, high accessibility to transportation and space further boosts this vitality by providing easier movement and encouraging people to explore and utilize the city’s core areas. At the same time, the increase in functional diversity also positively contributes to urban vitality, showing that people can more easily reach these diverse functions for their daily needs, consistent with earlier research findings [15]. On the other hand, fractal dimension and spatial compactness have relatively lower importance and exert a weak or even negative impact on urban vitality. This suggests that overly complex neighborhood morphology or excessively compact spaces may inhibit urban vitality and hinder the optimal utilization of urban resources. Furthermore, the relative importance of floor area ratio and building density is low, contrasting with some previous studies [13,19]. This may be because, at the neighborhood scale, the internal configuration and functionality have a greater influence on urban vitality. Even in neighborhoods with high floor area, insufficient service facilities can limit overall vitality. Similarly, high building density alone may not generate sustained vitality if the neighborhood is primarily single-function (residential). Additionally, urban villages represent a distinctive phenomenon in China, especially prominent in Guangzhou. These areas typically exhibit very high building density and floor area ratios, with densely packed self-built houses often maximizing the number of floors and rooms within limited space to accommodate more people [73]. Despite the high density and floor area ratio of buildings, they do not significantly contribute to the neighborhood’s vitality.

4.2.2. Synergistic and Threshold Effects of Variables on Urban Vitality

Furthermore, the combined effects of built environment elements on neighborhood vitality are particularly significant. Multiple variables exhibit threshold effects in their synergy, causing local impacts to switch between negative and positive. The rate at which local effects increase or decrease often shifts around these inflection points. Similar findings can be observed in related research in Shenzhen [58]. For example, when a neighborhood is closer to the CBD (feature value less than 0.1) and the POI density is higher (feature value greater than 0.5), their contribution to vitality accelerates. Inflection points can be categorized as upper limits and lower limits [16]. For the upper limit, when a neighborhood is very close to a metro station (feature value less than 0.1) and has a high POI density (feature value greater than 0.4), vitality shows a significant positive gain. Upon reaching a saturation value (around 0.1), the gain levels off or decreases to a lower level. This indicates that once the distance between a neighborhood and a metro station reaches a certain upper threshold, the positive contribution to urban vitality no longer increases; beyond this distance, the convenience of the metro station has a limited impact on vitality. For the lower limit, when a neighborhood is very close to Zhujiang New Town (feature value less than 0.1) and has a high POI density (feature value greater than 0.5), urban vitality is significantly positively affected. As the distance increases, regardless of POI density, this positive impact rapidly declines. After reaching a certain feature value (about 0.17), the impact of increasing distance on vitality becomes very small, almost stabilizing. This indicates the presence of a lower threshold; beyond this distance, the negative impact of increasing distance from Zhujiang New Town on urban vitality nearly ceases to intensify. These findings on nonlinear and threshold effects offer urban managers valuable guidance for effectively enhancing urban vitality within a practical range [16].

4.3. Theoretical and Practical Implications

The research emphasizes that governments and urban planners should optimize urban space allocation and enhance functional diversity. Specifically, they should increase the mixed use of commercial, recreational, and cultural facilities and enhance functional diversity and destination accessibility in densely populated neighborhoods and near transportation hubs. For areas such as Zhujiang New Town and Tianhe Sports Center in the Tianhe District, it is crucial to further increase the density of commercial and financial services and add corresponding cultural and entertainment facilities to maintain and enhance their economic and social vitality. Given that the comprehensive urban vitality of Guangzhou’s central urban area exhibits a high-center and low-periphery pattern, it is essential to improve infrastructure, increase public service facilities, and create community activity spaces in peripheral areas such as Jiahe Wanggang in the Baiyun District. This will attract more residents and enhance community social vitality. As the historical and cultural core, the Liwan District can strengthen the protection and promotion of cultural landmarks such as the Chen Clan Academy and Shangxiajiu Pedestrian Street and increase investments in cultural activities and creative industries to boost its overall vitality. Similarly, in the Longdong business district of the Tianhe District, the concentration of educational resources can be leveraged to promote the integration of education with commerce and culture, adding facilities such as bookstores, cafes, and cultural creative spaces to further enhance the area’s cultural and economic vitality. In addition, around the South Campus of Sun Yat-sen University in the Haizhu District, it is advisable to improve the surrounding residential environment and commercial facilities to attract more cultural and academic exchange activities, thereby enhancing the area’s cultural vitality. Implementing specific enhancement strategies in these key neighborhoods can create overall synergistic effects, thus comprehensively improving the urban vitality of Guangzhou’s central urban area. When formulating policies, the threshold effects of built environment indicators should be considered. For example, when the distance from a neighborhood to a park exceeds the threshold of 0.14, the indicator contributes weakly or even negatively to urban vitality. Conversely, a close distance to parks (feature value less than 0.8) continuously contributes positively to vitality, although this effect gradually diminishes as the distance increases. The complex, nonlinear influences and threshold effects of different indicators on urban vitality suggest that planners should conduct urban renewal within defined thresholds to ensure policy effectiveness and prevent resource wastage. Additionally, it is crucial to enhance the integration and analysis of multi-source data. Continuously collecting and analyzing multi-source urban data will allow for more precise monitoring of changes and trends in urban vitality, providing data support for urban planning and policy adjustments. By implementing these strategies, Guangzhou’s central urban area can enhance its urban vitality, promote more sustainable and people-centered urban development, and achieve higher-quality urban living spaces.

4.4. Limitations and Future Research Directions

This research explores the geographical distribution of urban vitality in Guangzhou’s central urban area and investigates the nonlinear and synergistic effects of the built environment on urban vitality. However, there are several limitations. (1) The data sources used to assess different dimensions of urban vitality have limitations that could impact the accuracy of the evaluation results. Specifically, in assessing cultural vitality, this study relies solely on the density of cultural facilities without distinguishing the specific contributions of different levels of cultural facilities, which may lead to an overestimation or underestimation of cultural vitality in certain neighborhoods [18]. Secondly, the assessment of economic vitality depends on the number of shop reviews on Dianping, but due to the potential for fake reviews, this data source may overestimate the economic vitality of certain neighborhoods. Finally, when using Baidu heat map data to represent social vitality, the data primarily reflects the activity patterns of young and middle-aged people, with insufficient coverage of other age groups [16], potentially failing to fully capture the city’s social vitality. (2) This study focuses on the neighborhood scale in Guangzhou’s central urban area, analyzing the nonlinear relationships between the built environment and urban vitality. However, since the study does not include comparative analyses of different cities or scales, it has not yet revealed the regional characteristics of urban vitality in a broader geographical and scale context. (3) This study does not use time-series analysis to examine trends in urban vitality changes and their dynamic relationships with influencing factors, which may limit the comprehensive exploration of the evolution mechanisms of urban vitality. (4) Although this research employed the XGBoost-SHAP model to investigate the various impacts of built environment factors on urban vitality and analyzed the interactions among different indicators, we recognize that the influence of these indicators extends beyond pairwise interactions. It may also be affected by the simultaneous interaction of three or four factors, a complex multi-factor synergy not fully examined in this study. (5) This study identified significant spatial variations in how built environment indicators collectively influence urban vitality. However, because the research focused on the nonlinear relationships and synergistic interactions involving the built environment and urban vitality, the fundamental causes of this spatial dispersion were not examined due to methodological constraints.

Future research should prioritize the following areas:

• To enhance the measurement of urban vitality, data sources should be expanded to include mobile phone signaling data [74], social media check-ins [75], and street view images [76], refining the construction of the comprehensive urban vitality index.
• Comparative empirical studies from multi-scale and multi-regional perspectives should be conducted to explore the similarities and differences between built environment indicator systems and urban vitality at different scales. Comparative studies across different scales can help reveal how factors influencing urban vitality perform at various levels. Multi-scale comparisons will aid in developing a more comprehensive and flexible indicator system for a more precise assessment and enhancement of urban vitality [77]. Cross-city comparative studies can identify general patterns and regional characteristics of different cities [15].
• Future research can investigate the temporal variation characteristics of vitality to dynamically explore trends in urban vitality changes and the evolving relationships with influencing factors over time [6]. By collecting and analyzing data across multiple time points, long-term trends and periodic fluctuations in urban vitality can be identified, providing deeper insights into how urban vitality evolves over time and the impact of influencing factors at different temporal stages.
• Future research could consider employing other regression models to better reveal the complex impacts of multiple factors on urban vitality. Additionally, the application of new interpretative methods could provide a deeper understanding of the synergistic effects of multiple factors within the built environment on urban vitality.
• In future research, clustering models could be employed to conduct spatial clustering of SHAP values. When combined with fixed effects models, this method can provide deeper insights into the reasons behind the spatial variation in how built environment factors synergistically impact urban vitality.

5. Conclusions

The research results indicate that neighborhood vitality in Guangzhou’s central urban area shows significant spatial heterogeneity. By examining the nonlinear connections between the built environment and urban vitality, it was discovered that the indicators influencing urban vitality display distinct threshold effects. Among the factors impacting urban vitality, the distance from neighborhoods to Zhujiang New Town, POI density, accessibility to subway stations, distance to squares, and POI diversity have the greatest nonlinear impacts (in decreasing order). For example, the proximity of neighborhoods to Zhujiang New Town and subway stations significantly affects urban vitality; the closer the distance, the more positive the effect. Spatial compactness also contributes positively to vitality after reaching a threshold of 0.07. These factors exhibit significant synergistic effects with other built environment indicators. For instance, neighborhoods that are closer to Zhujiang New Town and have high POI density contribute significantly positively to urban vitality. However, as the distance from Zhujiang New Town increases, the positive contribution of high POI density to urban vitality gradually decreases. The synergistic effect of POI diversity (ME) and POI density (POID) also shows a high threshold effect (0.74). Below this threshold, the synergistic effect is primarily dominated by POI density, with low POI density positively influencing vitality and high POI density having a negative impact. Other indicators also exhibit varying degrees of synergistic effects on urban vitality.