Evolution Characteristics and Causes—An Analysis of Urban Catering Cluster Spatial Structure

Abstract

Studying the development characteristics of the urban catering industry holds significant importance for understanding the spatial patterns of cities. In this manuscript, according to the characteristics of the distribution of catering points and based on catering point of interest (POI) data of 106 cities in China in 2016 and 2022, we propose the Natural Nearest Neighbor Single Branch Model (NNSBM) to identify catering points by adaptive clustering, which improves the efficiency of identifying catering clusters. Subsequently, a catering spatial structure division model is constructed to classify the spatial structure of catering clusters into 3 major categories and 17 subcategories, and the evolution pattern of urban catering clusters is analyzed. In addition, based on the population density raster data, a bivariate spatial autocorrelation model is employed to analyze the complex relationship between the distribution of urban catering clusters and population density, revealing the distinctive characteristics of urban catering cluster evolution. The results showed that (1) In the initial stage of catering cluster formation, catering activities tend to gather first in a specific area of the city, giving rise to the main catering cluster. However, as the catering industry progresses, the phenomenon of “central fading” occurs within the main catering cluster. (2) The overall trend of the catering spatial structure of most cities showed an evolution toward low primacy–high concentration (Lp-Hc), and cities at different stages of catering capacity exhibited different evolution characteristics of catering clusters. (3) The influence of population density on catering distribution was staged, with a varying impact on cities with different types of catering spatial structures.

1. Introduction

At present, the catering industry has assumed a pivotal role in the urban life service sector, establishing a profound connection with the daily lives of urban inhabitants [1,2]. In China, with the rapid development of the national economy and the increasing affluence of people’s lives, the spatial layout of the catering industry has long been one of the basic units of the state’s multi-pronged strategy to promote industry-driven development [3]. Moreover, an important way to study urban dynamics is to study the changes in urban facilities. Among various urban facilities, restaurant layout is decentralized and has a short life cycle, which can fully reflect various local socio-economic attributes, and is more sensitive to recent short-term changes in urban policies [4]. Therefore, the study of the spatial distribution and evolution of the catering industry can reveal the development of the city and holds significant research value.

The prerequisite for supporting the establishment and rapid growth of cities is to maintain a high degree of dynamism in the agglomeration economy. The agglomeration economy refers to the economic activities that different industries engage in within a specific area [5,6], thus promoting a high degree of dependence of industries on economic activities [7], and is the main intrinsic motivation for the formation of industrial clusters. Industrial clusters are flexible production combinations consisting of a large number of specialized industries or enterprises and related support institutions located in a specific region, rooted in the local social and cultural environment of continuous innovation. Most analyses of industrial clusters are based on case studies [8,9], quantitative studies of industries, and the diversity of cross-industry cluster behaviors [10,11,12], while there is limited understanding of the size, shape, evolutionary patterns, and reasons for the formation of service clusters, such as the catering industry.

Catering clusters represent a unique manifestation of industrial clusters, embodying a form of soft infrastructure or social capital [13]. Specifically, they are a dense concentration of catering enterprises and their related supporting service businesses located within a specific region [14,15,16]. The factors that influence the formation of catering clusters are multifaceted, including historical and cultural drivers, policy and institutional drivers, social opinion drivers, and planning and strategic drivers, among others [17,18,19,20]. Furthermore, catering clusters come in different types and forms. The clustering of catering enterprises may seem to contradict classical economic theory, which holds that competing firms in close proximity to one another will create greater market competition and reduce profitability [21]. However, since the catering industry is not primarily technology-based, such clustering can provide multiple advantages in terms of supply and demand. For example, joint promotion and mutual support among enterprises within catering clusters can enhance the visibility and brand image of the entire cluster [22]. Moreover, research has shown that the spatial relationships of urban and community catering clusters [23,24], the agglomeration process of catering clusters [25], and the variations in cluster size of different catering clusters [13] all contribute to regional economic development, including the creation of employment opportunities and tax revenue [8,14,26]. Catering clusters that are not severely affected by competition can elevate the visibility and appeal of the entire region, enticing more diners to patronize restaurants and bolstering the growth of the overall catering industry.

The spatial distribution of the catering industry is influenced by several factors, including population density [27], regional economic conditions [28], geographical location, and transportation facilities [29]. Among them, population density has always been the most significant factor affecting catering distribution, as sufficient foot traffic and high customer satisfaction are essential for a restaurant’s long-term viability. However, the prevalence of third-party catering websites has had an impact on catering distribution, making traditional research methods [30] less accurate in reflecting clustering conditions. Nowadays, with the changes in dining habits brought about by the Internet and smart delivery services, access to multi-period catering data is made possible through online platforms and POI data based on location-based services.

Currently, scholars have explored various aspects of catering clusters using POI data, specifically the identification of catering clusters [23,31], the spatial distribution characteristics of catering clusters [16,32], the guidance of catering clusters for urban planning [33,34], the economic benefits of catering clusters [35,36], and the competition and cooperation of catering clusters [37,38] and the network relationships of catering clusters [39,40]. The emergence of POI data enables a clearer and more accurate analysis of the distribution of restaurant establishments, the development patterns of catering clusters, and the mechanisms of cluster evolution, whether viewed from a macro or micro perspective.

In conclusion, there have been some studies on the evolutionary characteristics of catering clusters [16,41], but they have paid little attention to the underlying mechanisms of their formation and lacked a comprehensive framework for understanding their evolutionary process. Furthermore, the advent of the Internet and smart delivery services have significantly transformed dining habits, leading to a more intricate relationship between the spatial distribution of the catering industry and population density. By integrating online ICT catering website data with GIS, it is possible to conduct more detailed and prospective research and analysis on the formation, influencing factors, and evolutionary patterns of catering clusters.

The main contributions of this study are as follows:

(1)

A novel approach was adopted to identify urban catering clusters, known as the Natural Nearest Neighbor Single Branch Model (NNSBM), which is a soft clustering model. By considering the inherent characteristics of data objects, the density and cluster density of each data point were dynamically measured, resulting in an adaptive clustering method that leads to improved accuracy in identifying catering points.

(2)

Our research introduced a novel catering division spatial structure model and measurement method that enabled the identification of four distinct types of urban catering spatial structures based on two fundamental dimensions: primacy and concentration. The proposed model enabled us to explore the evolutionary characteristics of catering spatial structures in 106 Chinese cities and establish a comprehensive and clear framework system for the evolution of urban catering clusters.

(3)

Statistical and economic indicators were introduced to quantitatively evaluate the correlation between population density and catering distribution. Moreover, the degree of influence of population density on catering distribution was analyzed by a bivariate spatial autocorrelation model, and the significance of the two variables was visualized through LISA clustering plots to further systematically dissect the influence of population density on the evolutionary pattern of catering clusters.

2. Related Work

2.1. Industrial Agglomeration Effect

Research on industrial agglomeration effects mainly involves two aspects: industrial location selection and agglomeration economics. Industrial location selection aims to explain the reasons and influencing factors behind enterprises choosing specific geographical locations. Early classical location theories focused on the impact of costs, market proximity, and transportation convenience on industrial efficiency, such as Weber’s industrial location theory [42] and Bobek’s central place theory [43]. In the 1980s, the rise of new economic geography shifted the focus toward spatial agglomeration of economic activities and regional disparities, emphasizing the interactions between firms and externalities. Scholars like Anas and Arnott [44] analyzed factors influencing urban spatial economies, and Dasgupta and Stiglitz [45] researched the impact of market structure on international trade. Over time, location selection theories have evolved into comprehensive frameworks that consider various factors. In addition to economic factors, non-economic factors such as social, cultural, political, and institutional aspects have been considered regarding their influence on enterprise location selection [46,47]. Agglomeration economics, on the other hand, examines the concentration of industries and economic activities in specific regions. In recent years, evolutionary economic geography has gained prominence, emphasizing the impact of historical path dependence and institutional factors on industrial agglomeration in local economic development. Scholars like Henning [48] and Kogler [49] have focused on the role of local characteristics, innovation, and social capital in economic evolution and agglomeration.

2.2. Cluster Identification Methods

Currently, methods for identifying the morphological characteristics of industrial clusters can be broadly categorized into three types. The first type of approach is the hierarchical-based method, which involves data aggregating or splitting. Aggregation is a bottom-up process that initially treats data as individual clusters and then merges clusters that are close in distance until the desired number of clusters is reached, as demonstrated by CHAMELEON [50]. On the other hand, splitting is a top-down approach that starts with all data in one cluster and gradually divides them into smaller clusters, as exemplified by DIANA [51]. The second type of approach is a density-based method, where the minimum number of points and radius are determined within a specified region to form each cluster, and then clustering is performed accordingly, as seen in DBSCAN [52]. The third type of approach is a grid-based method, which quantizes the data space by dividing it into a finite number of grid cells, with all clustering processes occurring within these grids, as exemplified by STING [53].

3. Methodology

The overall methodology of this study is depicted in Figure 1. Firstly, data acquisition and preprocessing are conducted. Next, a novel clustering model is developed to identify patterns in the POI data. Subsequently, the identified results are utilized to delineate the spatial structure and establish an analysis framework for the evolution of catering clusters. Lastly, a bivariate spatial autocorrelation model is employed to examine the influence of population density on the distribution of catering establishments.

3.1. Data Sources and Processing

This manuscript incorporates a variety of data, and the main research data are catering point data, China administrative boundary data, and population density data. Among them, the catering point data are mainly from AMAP, the Chinese administrative boundary data are from the website of Standard Map Service of the Ministry of Natural Resources, and the population density data are from online network data. Figure 2 shows the data composition and processing flow of this study. The first step is data collection. We collected catering point data and population density data for 2016 and 2022. In the second step, data preprocessing is performed to create a database for easy management. In the third step, data checking is required. We reduce the error of POI data by two methods. The first method is to use several large online data platforms, such as Baidu Maps, Meituan, Renren, etc., while procuring catering data for careful checking and overlaying to screen out the anomalies and determine their locations through telephone inquiries or field research. The second method is to correct the fields, rules, and changes in the POI data. In the fourth step, data classification is performed to summarize the catering point data and crop the population density data in each city. In the fifth step, map matching is needed. The POI data are calibrated on a map to determine the coordinate system and paired with the population density data for a location to ensure accurate data location. According to the 2020 Chinese census data and the Circular on Adjusting the Standard of City Size Classification, the 106 large cities in China were divided into different categories, as shown in

Table 1. Classification of city size levels in China.

City Scale Level	City Name
Megacities (7)	Shanghai, Beijing, Shenzhen, Chongqing, Guangzhou, Chengdu, Tianjin.
Megacity (14)	Wuhan, Dongguan, Xi’an, Hangzhou, Foshan, Nanjing, Shenyang, Qingdao, Jinan, Changsha, Harbin, Zhengzhou, Kunming, Dalian
Type I Large City (14)	Nanning, Shijiazhuang, Xiamen, Taiyuan, Suzhou, Guiyang, Hefei, Urumqi, Ningbo, Wuxi, Fuzhou, Changchun, Nanchang, Changzhou.
Type II Large City (71)	Lanzhou, Zhongshan, Huizhou, Shantou, Linyi, Zibo, Wenzhou, Hohhot, Shaoxing, Tangshan, Haikou, Liuzhou, Xuzhou, Yantai, Luoyang, Handan, Zhuhai, Baotou, Baoding, Weifang, Datong, Jiangmen, Ganzhou, Xining, Nantong, Yinchuan, Yangzhou, Zunyi, Xiangyang, Anshan, Kunshan, Putian, Mianyang, Yancheng, Quanzhou, Xianyang, Taizhou, Wuhu, Zhuzhou, Huai’an, Jining, Jilin, Daqing, Guilin, Qinhuangdao, Zhanjiang, Yichang, Qiqihar, Fushun, Shangrao, Nanchong, Yiwu, Xingtai, Tai’an, Kaifeng, Zhangjiakou, Xinxiang, Liaocheng, Huainan, Shiyan, Yibin, Zaozhuang, Yueyang, Cixi, Hengyang, Changzhi, Lianyungang, Jinzhou, Chifeng, Jinjiang, Luzhou.

.

3.2. Model

3.2.1. Natural Nearest Neighbor Single Branch Model

We propose a soft clustering model, the Natural Nearest Neighbor Single Branch Model (NNSBM), for clustering identification of catering point data. Most clustering algorithms require parameter adjustments when processing different types of data. The data studied in this paper include catering point data from 106 major cities. Traditional clustering methods require frequent parameter adjustments, and there is no standard parameter tuning rule for clustering catering points, leading to inaccurate cluster results. To address this issue, we propose a dynamic threshold approach that measures the density of each data point and cluster based on its data object characteristics, and then performs contraction and expansion operations to differentiate between the core area and the boundary area. This approach enables the threshold value to be dynamically adjusted, rather than using a fixed value, to accurately identify the clusters of catering points.

To better explain the theoretical basis of our proposed Natural Nearest Neighbor Single Branch Model (NNSBM), we provide the following definitions. Our model is designed to adjust its parameters dynamically based on the characteristics of the dataset, thus effectively capturing the distribution patterns of the data.

Definition 1.

Nearest neighbor ${NT}_r\left(x_i\right)$ refers to the $r$ nearest neighbors of sample point $x_i$, where$r$ is automatically generated by the natural nearest neighbor search algorithm.

Definition 2.

Inverse nearest neighbor ${INN}_r\left(x_i\right)$ refers to the $r$ inverse nearest neighbor of sample point $x_i$.

$${INN}_r\left(x_i\right)=\left\{x_j\in X|x_i\in {NT}_r\left(x_j\right),i\ne j\right\}$$

(1)

Definition 3.

Natural nearest neighbor $NNN\left(x_i\right)$ refers to the natural nearest neighbor of a sample point $x_i$.

$$NNN\left(x_i\right)=\left\{x_j\in X|x_i\in {NT}_r\left(x_j\right),x_j\in {INN}_r\left(x_i\right)\right\}$$

(2)

Definition 4.

Natural Neighbor Feature Value ${nne}_k$ refers to the number of searches performed during the natural convergence of sample states, which is denoted as:

$${nne}_k=\left\{r|\forall x\exists y\left(y\ne x\cap x\in {NT}_r\left(y\right)\right)\right\}$$

(3)

By iteratively searching r times to obtain the natural nearest neighbors of all objects, it is an adaptive and scale-free neighbor, and when it reaches natural stability, the distribution of each data object is determined accordingly. The specific steps are shown in Figure 3.

3.2.2. Bivariate Spatial Autocorrelation Model

The bivariate spatial autocorrelation model can reveal the spatial distribution correlations and dependencies between restaurants and variables [4,54]. The formula for bivariate global spatial autocorrelation is:

$$B-Moran\mathrm{’}sI=\frac{\sum _{i=1}^n\sum _{j=1}^n{W}_{ij}\left(x_i-\overline{x}\right)\left(y_j-\overline{y}\right)}{S^2\sum _{i=1}^n\sum _{j=1}^n{W}_{ij}}$$

(4)

where $n$ is the total number of hexagonal grids, $W_{ij}$ is the spatial weight matrix, ${\mathrm{a}\mathrm{n}\mathrm{d} x}_i$ and $y_j$ are the values of the independent variable $x$ and the dependent variable $y$ at the $i$ and $j$ grid, respectively. The dependent variable $y$ represents the density of restaurants, and the independent variable $x$ represents the variables that affect catering distribution. $S^2$ is the variance of all samples. The formula for bivariate local spatial autocorrelation is:

$$I_i=Z_i\sum _{j=1}^n{W}_{ij}{Z}_j$$

(5)

where $I_i$ is the local spatial autocorrelation of hexagon $i$, and $Z_i$ and $Z_j$ are the standardized values of the variance for hexagon $i$ and hexagon $j$, respectively. Z-Score standardization is applied to the indicator data to eliminate the dimensional influence in bivariate spatial autocorrelation analysis.

3.3. Identification of Catering Clusters

The most critical aspect of identifying catering clusters is to better and more accurately characterize the degree of closeness between each data object and its surrounding data objects. We found that better decision-making results can be obtained by shrinking and expanding the data during the clustering process. The catering point data used in this study are relatively large, and directly using the Natural Nearest Neighbor Single Branch Model (NNSBM) proposed in this paper to identify clusters will result in adaptive data redundancy, meaning bad separability of the entire data space. Therefore, in the contraction and expansion process of the single linkage clustering, a simple classification of data was performed in this paper. The specific process for identifying catering clusters is shown in Figure 4.

In Figure 4, $S_c\left(x_e\right)$ represents the structural operator, $S_c\left(C_i\right)$ represents the average natural nearest neighbor count of cluster $C_i$, and $S_c\left(v\right)$ represents the natural nearest neighbor count of data object v. Firstly, the characteristics of the catering point data were studied, and it was found that small clusters generally do not form around discrete data objects far from the cluster center. The further away from the center, the more discrete the data, and the number of neighbors for a discrete point is usually smaller than that for a cluster center. To address this issue, we set a parameter $\rho =1.3$. Furthermore, during the single-branch clustering process, data are classified to avoid generating too many adaptive parameters that lead to redundancy. The data are divided into two categories, denoted as class I and class II. Data points that have more neighbors within their natural neighborhood belonging to the same cluster than the average number of data objects in the cluster multiplied by a factor of $\rho$ are classified as class II and assigned to the core area of the corresponding cluster. Conversely, data points that do not meet this criterion are classified as class I and partitioned into the boundary domain of the corresponding cluster. This classification is a generalization operation, which generates a single-linkage clustering result based on the hard clustering result. Then, we introduce the structure generation functions $S_1$ and $S_2$, the former for contraction and the latter for expansion. Here, $v$ is any data object in $V$, and $S_1$ and $S_2$ are reflexive. Finally, the core domain $Co\left(C_i\right)$ and boundary domain $Fr\left(C_i\right)$ of the cluster $C_i$ can be obtained.

In order to evaluate the effectiveness of the proposed algorithm in this section, we compare it with DBSCAN, which is most commonly used to identify industrial clusters. Comparison experiments are conducted with DBSCAN on two standard UCI datasets. The messages related to the two sets of test data are shown in

Table 2. Basic information of the experimental dataset.

Dataset	Sample Size	Sample Dimension	Number of Categories
Banknote	1372	4	2
Hill Valley	1212	100	2

.

The performance of clustering results is evaluated using macro $F1$ and micro $F1$, which are denoted by subscripts $a$ and $i$, respectively; e.g., NNSBM_a is the macro $F1$ metric of NNSBM. Figure 4a,b show the presentation of the results of NNSBM and DBSCAN on the dataset of Banknote and Hill Valley, respectively. It can be clearly seen that as the structural operator $q$, which determines the cluster size, keeps increasing, the results of DBSCAN’s macro $F1$ and micro $F1$ in the two datasets are always in a straight line. On the contrary, the results of our proposed NNSBM in the two datasets are moving in a positive direction, and the performance indexes of macro $F1$ and micro $F1$ are getting bigger and bigger, which proves that there are constantly data that have been correctly categorized in the process. This comparative evaluation experiment directly reflects the effectiveness of our algorithms constructed in this manuscript.

3.4. Catering Spatial Division Structure Model and Measurement Method

The presence of a significant concentration of catering establishments within a given area gives rise to the formation of catering clusters, which can be further classified into main catering cluster (the cluster with the highest density) and secondary catering clusters (clusters with relatively lower densities) based on their scale. Based on the above definition, we propose a catering spatial structure division model and measurement method, in which we define two dimensions to describe the characteristics of catering clusters: Primacy and Concentration. “Primacy” is characterized by the proportion of the catering point scale included in the main catering cluster to the catering point scale included in the entire catering cluster (including the main and secondary clusters), as shown in Formula (6). “Concentration” is characterized by the proportion of the catering point scale in the catering cluster to the total scale of all catering points in the region, as shown in Formula (7).

$$PR=\frac{x_{max}}{{\sum }_{i=1}^n{x}_i}$$

(6)

$$CO=\frac{{\sum }_{i=1}^n{x}_i}{total}$$

(7)

where $PR$ and $CO$ represent the primacy and concentration of the spatial structure of catering establishments in the region, respectively. Here, $x_i$ represents the number of catering establishments included in cluster $i$, $x_{max}$ represents the number of catering establishments included in the main cluster, n represents the total number of clusters, and the total represents the total number of catering establishments in the region. Obviously, the values of $PR$ and $CO$ are between 0 and 1, with higher values indicating higher primacy and concentration of catering clusters in the region. This is illustrated in Figure 5.

Here, it is important to point out that two issues should be noted regarding the model we proposed for the spatial division of catering clusters. Firstly, the determination of the thresholds for Primacy and Concentration must be based on the specific circumstances of the study area. Moreover, it is important to note that these two dimensions are not necessarily correlated. Areas with high Primacy may not have high Concentration and areas with low Primacy may not necessarily have low Concentration. Secondly, it is worth noting that a catering cluster is a unique type of spatial arrangement of restaurants, consisting of both concentrated and dispersed catering distributions, with the concentrated catering areas appearing continuously within a certain spatial range and achieving a specific density of catering distribution. Areas with a smaller number of restaurants may not have established a large-scale catering agglomeration area, and therefore, the above division method may not be suitable for characterizing their catering cluster types.

3.5. Study on the Relationship between Catering Clusters and Population Density

To uncover the intricate spatial structure and evolution patterns of catering clusters, it is essential to elucidate the fundamental reasons behind their formation. In the Introduction section, we highlighted that the formation of urban catering clusters is influenced by various factors [27,28,29]. One of the main factors is population density. Areas with higher population densities tend to have more competitive markets and more prosperous business activities, which are more conducive to the concentration of catering establishments. We found that the linkage between population distribution and catering cluster level can reflect the degree of correlation between population density and catering distribution. The use of the appropriate scale of the fishing net can be more effective to correspond the population density raster grid data and catering point data, and the degree of correlation can be derived from the significance analysis of the two variables, as illustrated in Figure 6.

4. Results

4.1. Evolution Characteristics of Urban Catering Cluster Spatial Structure

According to the statistical characteristics of primacy and concentration in the spatial structure of China’s catering clusters, the overall trend of primacy is decreasing while that of concentration is increasing, as shown in

Table 3. Statistical characteristics of Primacy and Concentration in urban catering cluster structure.

Indicators	Primacy		Concentration
	2016	2022	2016	2022
Minimum value	0.274	0.172	0.154	0.120
Maximum value	1.000	1.000	0.945	0.967
Average	0.794	0.680	0.514	0.706
Median	1.000	0.667	0.728	0.785

. For instance, the average value of primacy decreased from 0.826 in 2016 to 0.680 in 2022, and the median value decreased from 1 to 0.667. The average value of concentration increased from 0.734 in 2016 to 0.806 in 2022, and the median value increased from 0.728 to 0.785. This trend indicates that (1) China’s urban catering points are expanding continuously from the center to the periphery, and many new secondary catering clusters with a certain scale are forming outside the main catering clusters. (2) China’s catering points are continuously concentrating within the agglomeration areas, and the proportion of scattered catering points in the total catering scale of the city is continuously decreasing.

4.2. Evolution Patterns of Urban Catering Clusters

Utilizing the measuring method elucidated in Section 3.4, a methodology for appraising the spatial structure of urban catering clusters was established by employing the mean primacy (0.737) and concentration (0.610) of all cities in 2016 and 2022 as benchmarks. The identification results and urban catering cluster analysis are presented in Figure 7 and Figure 8. It is apparent that the number of cities exhibiting a low primacy–high concentration (Lp-Hc) structure (fourth quadrant) has risen significantly, indicating the overarching trend of China’s catering cluster spatial structure evolution. Through further analysis and summarization of the evolution patterns of 106 cities in China, the spatial structure of China’s catering cluster can be subcategorized into 17 subtypes under three primary classifications, as shown in

Table 4. Different evolutionary patterns of urban catering cluster spatial structure.

Patterns	Urban Catering Spatial Structure		Number of Cities	City Name
	2016	2022
Stable	Hp-Lc	Hp-Lc	5	Zibo, Weifang, Taizhou, Shangrao, Shaoxing
	Hp-Hc	Hp-Hc	5	Qingdao, Jinan, Shenyang, Chongqing, Lanzhou
	Lp-Lc	Lp-Lc	4	Changzhi, Yibin, Xinxiang, Mianyang
	Lp-Hc	Lp-Hc	8	Shanghai, Tianjin, Chengdu, Xi’an, Nanjing, Foshan, Changsha, Nanchong
Evolved	Hp-Lc	Lp-Hc	21	Nanning, Fuzhou, Changchun, Changzhou, Suzhou, Guiyang, Hefei, Ningbo, Huizhou, Shantou, Zhongshan, Xiamen, Zhengzhou, Dalian, Kunming, Wuxi, Taiyuan, Wenzhou, Tangshan, Quanzhou, Xianyang
	Hp-Hc	Lp-Hc	7	Shijiazhuang, Nanchang, Urumqi, Harbin, Dongguan, Haikou, Jilin
	Hp-Lc	Hp-Hc	7	Liuzhou, Linyi, Hohhot, Baotou, Yueyang, Cixi, Hengyang
	Lp-Lc	Lp-Hc	5	Handan, Luoyang, Xuzhou, Baoding, Jining
	Lp-Hc	Hp-Hc	4	Beijing, Shenzhen, Guangzhou, Hangzhou
	Lp-Lc	Hp-Hc	3	Zhuhai, Yantai, Datong
	Hp-Hc	Hp-Lc	2	Tai’an, Jiangmen
	Hp-Lc	Lp-Lc	3	Anshan, Zhuzhou, Huai’an,
	Lp-Hc	Hp-Lc	5	Wuhan, Ganzhou, Daqing, Huainan, Shiyan
Newly added	—	Hp-Lc	10	Xining, Nantong, Yancheng, Zunyi, Wuhu, Putian, Guilin, Liaocheng, Qiqihar, Fushun
	—	Lp-Lc	8	Zhangjiakou, Kaifeng, Luzhou, Jinzhou, Chifeng, Jinjiang, Zaozhuang, Lianyungang
	—	Lp-Hc	5	Yiwu, Xingtai, Qinhuangdao, Zhanjiang, Yichang
	—	Hp-Hc	4	Yinchuan, Yangzhou, Xiangyang, Kunshan

.

The first category includes 22 cities whose cluster spatial structure remains unchanged, dominated by low primacy–high concentration (Lp-Hc) and high primacy–high concentration (Hp-Hc) structures, as shown in Figure 7d,f,g,j. The second category includes 57 cities where the spatial structure of clusters evolved, mainly from high primacy–low concentration (Hp-Lc) to low primacy–high concentration (Lp-Hc), as shown in Figure 7a–c,e,h,i. The third category includes 27 cities with new cluster spatial structures, for which no significant catering clusters were identified due to the smaller size of these cities compared to other cities’ catering clusters in 2016.

4.3. The Impact of Population Density on Different Evolution Patterns

The spatial structure of urban catering in China exhibits distinct evolutionary patterns that are closely tied to changes in population density. Utilizing a 100 m × 100 m grid as the fundamental unit, we demonstrated through a bivariate spatial autocorrelation model that population density positively influences the distribution of catering establishments, as depicted in Figure 9. Additionally, we employed statistical economic indicators to quantify the impact of population density on catering distribution. Descriptive statistics were conducted on data from 106 Chinese cities, and the results are presented in

Table 5. Correlation analysis of catering distribution and population density in cities with stable catering spatial structures.

Urban Catering Spatial Structure		City Name	Beta		Moran’s I		R2		Sig
2016	2022		2016	2022	2016	2022	2016	2022	2016	2022
Hp-Lc	Hp-Lc	Weifang	0.295	0.701	0.225	0.606	0.087	0.491	b	a
		Shangrao	0.419	0.781	0.321	0.688	0.132	0.578	a	a
		Taizhou	0.304	0.671	0.239	0.591	0.081	0.455	b	a
Hp-Hc	Hp-Hc	Qingdao	0.787	0.750	0.722	0.713	0.578	0.521	a	a
		Jinan	0.755	0.712	0.704	0.699	0.570	0.507	a	a
		Chongqing	0.791	0.782	0.754	0.749	0.582	0.526	a	a
Lp-Lc	Lp-Lc	Changzhi	0.187	0.541	0.154	0.496	0.067	0.352	b	a
		Xinxiang	0.257	0.632	0.201	0.572	0.071	0.402	b	a
		Yibin	0.157	0.563	0.132	0.489	0.054	0.478	c	a
Lp-Hc	Lp-Hc	Shanghai	0.714	0.734	0.703	0.732	0.510	0.519	a	a
		Chengdu	0.651	0.656	0.631	0.634	0.490	0.509	a	a
		Nanjing	0.711	0.716	0.675	0.681	0.529	0.542	a	a
		Changsha	0.789	0.777	0.725	0.711	0.632	0.592	a	a

^a p < 0.01, ^b p < 0.05, ^c p < 0.1.

,

Table 6. Correlation analysis of catering distribution and population density in cities with evolved spatial structures.

Urban Catering Spatial Structure		City Name	Beta		Moran’s I		R2		Sig
2016	2022		2016	2022	2016	2022	2016	2022	2016	2022
Hp-Lc	Lp-Hc	Zhengzhou	0.765	0.750	0.584	0.571	0.585	0.563	a	a
		Xiamen	0.627	0.590	0.553	0.501	0.392	0.348	a	a
		Suzhou	0.612	0.550	0.512	0.499	0.478	0.421	a	a
		Fuzhou	0.601	0.591	0.541	0.521	0.524	0.482	a	a
Hp-Hc	Lp-Hc	Nanchang	0.355	0.512	0.304	0.679	0.373	0.517	a	a
		Nanchang	0.321	0.492	0.307	0.616	0.361	0.517	a	a
		Urumqi	0.415	0.527	0.375	0.607	0.487	0.532	a	a
Hp-Lc	Hp-Hc	Hengyang	0.187	0.541	0.154	0.496	0.067	0.352	b	a
		Hengyang	0.172	0.512	0.187	0.459	0.041	0.311	c	a
		Baotou	0.257	0.632	0.201	0.572	0.071	0.402	b	a
Lp-Lc	Lp-Hc	Handan	0.395	0.701	0.325	0.606	0.080	0.539	b	a
		Baoding	0.401	0.782	0.371	0.625	0.103	0.602	b	a
Lp-Hc	Hp-Hc	Beijing,	0.729	0.791	0.719	0.780	0.531	0.625	a	a
		Hangzhou	0.699	0.763	0.643	0.758	0.524	0.599	a	a
		Guangzhou	0.743	0.796	0.675	0.681	0.551	0.602	a	a
Lp-Lc	Hp-Hc	Yantai	0.587	0.750	0.522	0.713	0.462	0.597	a	a
		Datong	0.441	0.692	0.401	0.631	0.389	0.512	b	a
Hp-Hc	Hp-Lc	Tai’an	0.295	0.701	0.225	0.606	0.087	0.491	b	a
		Jiangmen	0.219	0.671	0.191	0.614	0.091	0.461	b	a
Hp-Lc	Lp-Lc	Anshan	0.282	0.301	0.232	0.406	0.087	0.098	b	b
		Zhuzhou	0.191	0.371	0.173	0.491	0.041	0.101	c	b
Lp-Hc	Hp-Lc	Wuhan	0.534	0.719	0.492	0.667	0.285	0.517	a	a
		Ganzhou	0.432	0.642	0.356	0.599	0.243	0.500	a	a

^a p < 0.01, ^b p < 0.05, ^c p < 0.1.

and

Table 7. Correlation analysis of catering distribution and population density in newly added cities.

Urban Catering Spatial Structure	City Name	Beta	Moran’s I	R2	Sig
2022		2022	2022	2022	2022
Hp-Lc	Xining	0.284	0.241	0.083	b
	Nantong	0.310	0.299	0.068	b
	Yancheng	0.278	0.251	0.061	b
Lp-Lc	Luzhou	0.512	0.500	0.317	a
	Jinjiang	0.471	0.450	0.300	a
	Fushun	0.579	0.561	0.401	a
Lp-Hc	Kaifeng	0.531	0.506	0.447	a
	Yichang	0.507	0.481	0.412	a
Hp-Hc	Yinchuan	0.241	0.196	0.096	b
	Kunshan	0.181	0.191	0.071	b

^a p < 0.01, ^b p < 0.05.

. In these tables, the parameter “Bata” signifies the degree of influence of population density on catering distribution, while “Sig” denotes the p value of the significance test: “a” represents high significance, “b” denotes moderate significance, and “c” indicates significance. A significance level of less than 0.05 indicates a significant effect of population density on catering distribution. Moreover, the Bivariate Local Moran’s I statistic is employed to measure the degree of correlation between population density and catering distribution, while R2 indicates the explanatory power of population density in relation to catering distribution.

Table 5 reveals four categories of cities with unchanged spatial structures in the catering industry. Among them, cities that maintain Hp-Lc and Lp-Lc experience a substantial increase in the impact of population density on catering distribution. Cities that maintain Hp-Hc witness a slight decrease in this impact, yet their population density consistently exerts a significant positive effect on restaurant distribution. Cities that maintain Lp-Hc exhibit minimal changes in the influence of population density on restaurant distribution, indicating a relatively stable pattern.

Table 6 presents correlation results for cities that underwent an evolution in catering structure, comprising nine categories. In most cases, cities transitioning to Lp-Hc experienced a slight decrease in the influence of population density on restaurant distribution. For instance, Zhengzhou, Xiamen, and Nanchang saw a respective decline in explanatory power by 0.022, 0.044, and 0.056. Conversely, cities transitioning from Lp-Hc to Hp-Hc witnessed an increase in the impact of population density on catering distribution. Notably, Beijing and Guangzhou exhibited an explanatory power increase of 0.062 and 0.053, respectively. For results related to other evolutionary patterns, refer to Table 6.

Table 7 presents the correlation results for newly added cities. The results indicate that in cities where no restaurant clusters were identified in 2016, different restaurant patterns emerged by 2022. For example, in Xining City, a Hp-Lc pattern emerged in 2022, with a relatively low correlation between population density and catering distribution, but a positive correlation was still observed.

5. Discussion

The general approach for catering cluster identification is to use density-based clustering algorithms; for example, Fan and Guo [31] used DBSCAN for the consumer clustering examination of geo-tagged social network data. Unsupervised clustering algorithms have also been used for clustering catering clusters; for example, Tian and Luan [14] used GMM to realize spatial clustering, evaluated the spatio-temporal clustering of Shanghai catering clusters, and explored the practical application of catering clusters such as the positional pattern, shape of the clusters, and spatial clustering. However, density-based clustering or unsupervised clustering, appropriate parameters, and sub-models must be manually selected in advance. In contrast, our proposed soft clustering algorithm, Natural Nearest Neighbor Single Branch Model (NNSBM), is adaptive to recognize the target clusters, which greatly reduces the time of manual intervention and improves the recognition accuracy of the catering clusters. In addition, the spatial distribution and evolution of catering activities can reveal urban development at a finer-grained spatio-temporal scale. For example, Zhang and Min [55] used digital field hierarchical structure mapping and generalized symmetric structure mapping to identify the spatial morphology and evolutionary features of dining in mountainous cities. Wu and Pei [56] used count regression models to regress restaurant distribution, births, and deaths on different location factors. Different from the above, we proposed a measurement method of a catering spatial structure, based on which a clear evolutionary system was constructed, so that the evolutionary characteristics of catering clusters can be seen at a glance.

As Chinese cities continue to develop, the catering industry has undergone significant advancements, resulting in the expansion of the catering clusters’ spatial structure (as illustrated in Figure 10a,b). Prior to the emergence of such clusters, catering activities were typically concentrated in certain areas of the city, leading to the main catering cluster. However, as the size of the main catering cluster fails to meet the catering demands of the administrative district, catering activities may relocate from the central area toward the periphery, causing the “central fading” phenomenon. Despite this, the “central fading” of catering activities does not necessarily guarantee the emergence of new catering clusters in the periphery, resulting in the intricate evolution of urban catering spatial structures. For example, if the catering distribution is relatively scarce and dispersed, the spatial structure may shift from Lp-Lc to Lp-Hc or Hp-Hc, as observed in Handan, Luoyang, Xuzhou, and Zhuhai. Conversely, if the distribution is more concentrated and the main catering cluster particularly prominent, the spatial structure may shift from Hp-Lc to Lp-Hc or Hp-Hc, as observed in Nanning, Fuzhou, and Liuzhou. Regardless of the transformation stage, the majority of cities maintain or evolve into the Lp-Hc spatial structure, as depicted in Figure 10c,d. As depicted in Figure 8, regardless of the type of evolution, the growth rate of the secondary catering clusters surpasses that of the main catering cluster. Lp-Hc is the ultimate spatial structure for the majority of cities during the evolution of catering clusters.

The model for the division of the catering spatial structure proposed in this manuscript is definitely a priori in nature. To capture the complex and varied changes in the evolution of catering spatial structures, this study classifies cities where such changes occur in nine representative categories, aiming to provide descriptive representations of each type of change. However, it should be noted that this classification does not imply an exact description of the intricate diversity in the evolution process. This is because the “center fading” process observed in catering activities contributes to the complexity and diversity of urban catering spatial structure evolution. The “center fading” process does not necessarily result in the formation of new catering activity clusters in peripheral areas, nor does it inevitably lead to the decline of established catering activity clusters that were formed in the central regions.

Concerning the impact of population density on catering distribution, firstly, it is essential to note that population density exerts a positive influence on catering distribution (Figure 10e,f). Secondly, the extent to which population density affects different catering spatial structures varies considerably. In the early stages of catering cluster formation, the impact of population density on catering clusters is not especially significant, and the correlation between the two is low (Figure 9d). Upon examining cities that have undergone spatial structure evolution (Table 5), as catering clusters enlarge, the impact of population density on catering distribution becomes considerably greater. Once catering clusters reach a specific size (Table 4), the relationship between population density and catering distribution begins to decline, and the influence weakens, as observed in Jinan and Qingdao. Nonetheless, as catering clusters continue to expand, the correlation between population density and catering distribution begins to rise again, and the impact increases, as evidenced in Beijing and Shanghai. In conclusion, the influence of population density on catering clusters is cyclical, and the correlation between the size of catering clusters and population density is closely interrelated.

Our research has certain limitations that should be acknowledged. Firstly, the NNSBM computational requirements are substantial, resulting in slow convergence speed. Despite pre-dividing the dataset, it remains challenging to determine the optimal number of sub-models in advance, necessitating manual selection. Secondly, the utilization of raster data for population density and the association of POI data with food and beverage points in grid format introduce a significant dependency on the grid size, potentially influencing the correlation results. Therefore, further refinement of the grid size is imperative to achieve a more precise representation.

Undoubtedly, the spatio-temporal evolution of the catering industry is impacted by various factors, including government policies and urban development. Therefore, our study only presents an initial analysis of the spatial structure and spatio-temporal evolution of the catering industry. Our proposed model for an urban catering spatial structure division and the spatio-temporal evolution measurement methods necessitate continual improvement with the expansion of data sources. Furthermore, comprehensive fundamental theories are required to further refine the determinants that influence the distribution of the catering industry.

6. Conclusions

The study of urban catering space is a crucial aspect of implementing the national strategy to revitalize and promote the catering industry. An analysis of the measurement methods and evolution characteristics of catering clusters is a fundamental step toward comprehending the laws governing the development of urban catering space and providing guidance for urban catering space planning practice. In this study, we proposed the Natural Nearest Neighbor Single Branch Model (NNSBM) and the Urban Catering Space Structure Division Model and Measurement Method to investigate the distribution of catering activities in 106 cities in China. We also employed bivariate spatial autocorrelation models to evaluate the impact of urban population density on catering distribution and conducted correlation analysis on urban catering clusters under different spatial structure models. The following conclusions were drawn:

(1)

As urban catering continues to advance, the overall spatial structure of most cities was observed to trend toward a state of low primacy–high concentration. Nevertheless, variations in the clustering and diffusion characteristics of catering activities exist among cities at different stages of development, resulting in differing patterns of evolution in their catering spatial structures.

(2)

As catering activities expand outwards from the main catering cluster toward peripheral areas, a phenomenon known as “central fading” may occur, potentially causing the decline of the primary cluster. However, with the progression of urban catering, the early primary cluster may attract additional catering points and reestablish its primacy in the urban catering structure.

(3)

The impact of population density on catering distribution is contingent on the stage of development. For cities with different types of catering spatial structures, population density has varying degrees of influence. Nevertheless, irrespective of the city type, population density exhibits a positive correlation with urban catering distribution.

In this study, we offer a comprehensive quantitative analysis of the identification and evolution of catering clusters in 106 Chinese cities, along with an examination of the correlation between urban population density and various catering structures. This research enhances our theoretical comprehension of the evolution of catering clusters and provides insights into the commercial geographic landscape of cities. Additionally, it contributes to a better understanding of the interplay between the catering industry and population distribution, thereby shedding light on the spatial pattern of urban development.