Classification of Shrinking Cities in China Based on Self-Organizing Feature Map

Abstract

Since the 1980s, China has been experiencing shrinking cities as part of a massive urbanization process. In recent years, the Matthew effect of factor accumulation has led to an increasingly substantial divergence in population concentration and sparseness in China. The pattern of shrinking Chinese cities has become increasingly severe. Accurate classification of shrinking cities is important for formulating policies and achieving the rational development of shrinking cities. In this study, the data of the 6th and 7th population censuses are used to investigate the shrinking Chinese cities, and prefecture-level cities are utilized as the scale of administrative units. The resident population in 130 cities decreased during the last decade. The population, economy, society, and space indicators are selected to cluster the shrinking cities through the self-organizing feature map neural network. Results show that China’s shrinking cities can be divided into four categories: (1) Sixty-two cities are characterized by a high degree of transfer dependence on the economy due to a chronic lack of population. (2) Twenty-eight cities are characterized by high urban expansion but with population loss. (3) Fourteen cities are characterized by obvious transportation and location advantages and with relatively slight population loss. (4) Twenty-six cities have good industrial development prospects but with serious urban pollution and “siphoning” effects from other cities. The shrinking cities are mainly concentrated in the western, central, and northeastern regions of China, which are represented by the old industrial and resource-depleted cities. The shrinking cities in the eastern region are fewer and less severe, which is mainly related to the high population concentration and developed economy in the region. This study provides solutions from different perspectives for four types of shrinking cities and serves as an empirical reference for policymakers and urban planners.

1. Introduction

The shrinkage of the urban population has a long history [1]. In 1988, German scholars Häußermann and W. Siebel first introduced the term “shrinking cities” [2] to describe cities that were hollowed out due to massive population loss. After the Industrial Revolution, some Western cities grew explosively [3], and the number and size of towns showed a rapid growth, unprecedented in human history [4]. However, beginning in the mid-20th century, the overlapping effects of a series of problems, such as deindustrialization, suburbanization, aging, resource depletion, and social transformation, led to a general decline in the population of these cities [5,6]. A total of 450 cities and towns with a population of more than 1 million have lost a tenth of their population globally [7]. Urban shrinkage accompanied by adverse development effects, such as housing vacancies [8], economic downturn [4,9], and inefficient land use [10], has widely emerged after cities experienced a historical transition from boom to bust. Since the beginning of the new century, the trend of urban shrinkage spreading worldwide has become increasingly evident due to the overall slowdown of global economic growth and the emergence of local financial crises [11].

Relevant scholars have conducted corresponding studies on the definition [12], causes [13], classification [14], problems faced [15], and countermeasures for the governance [12] of shrinking cities [16]. In Western countries, shrinking cities have been systematically analyzed with the help of basic data established by government-led surveys, such as census property tax and community survey housing surveys [17,18,19]. Shrinking city types have been classified into three main categories. The “perforated” shrinking cities are represented by the old industrial city of Leipzig in the former German Democratic Republic region, where its population shrinkage occurred mainly in various parts of the city, in vacant and abandoned buildings [14,20]. The Rust Belt cities of the Northeastern United States, such as Detroit, Cleveland, Youngstown, and Flint, represent the “pie-shaped” shrinking cities with hollowed-out urban centers, where the inner city population has moved out in large numbers, and the suburban population has remained relatively stable or even grown [21,22]. The Paris region of France represents a shrinking peripheral city, which is the opposite of a “pie-shaped” shrinkage, with a thriving core and a declining periphery [23,24]. Specific measures at the operational level, such as public participation [25], community planning [26], and welfare governance [27], are also proposed for the common problems faced by shrinking cities globally, such as the lack of development resources, urban decay, and declining quality of life.

In the process of large-scale urbanization, shrinking cities come into existence in China [28]. China’s population density and urbanization pattern have undergone drastic structural changes since 2000 [29]. According to Long Ying et al., the population size or density in 180 out of 654 cities at and above the county level has decreased [1], which is evident in Northeast China. Shrinking local cities successively show up in some developed areas, such as the Pearl River Delta, the Beijing–Tianjin–Hebei region, and the Yangtze River Delta [30]. However, unlike the mainstream characteristics of shrinking cities in Western countries, such as the United States and Germany, which show a continuous decrease in population size and relative stagnation in spatial expansion, shrinking cities in China more widely present the paradoxical phenomenon of population loss and spatial expansion, exacerbating the waste of land resources [31]. Zhang Xueliang et al. [32] classified shrinking cities into global, local, and edge types with the help of census data between 2000 and 2010. Meng Xiangfeng et al. identified five types of shrinking cities, perforative, global, local, pie-shaped, and edge type, by using physical cities as the research object and utilizing the resident population data of a 200 m grid of Baidu Huiyan. Zhou Kai et al. [33] summarized five morphological type characteristics of regional decline, central area decline, subcenter decline, residential land vacancy, and industrial land abandonment at two levels, namely, restricted shrinking (broad sense) and urban shrinking (narrow sense). Strategies for spatial form optimization are explored from urban shrinkage in the perspective of territorial spatial planning.

In accordance with existing studies, most scholars take prefecture-level and county-level cities as research objects when identifying the spatial scale of China’s shrinking cities. They lack the unification of administrative levels or only observe shrinking samples in local areas, which cannot reflect the full view of shrinkage in China [6] and hinders the identified shrinking cities to be governed and planned through classification. Scholars have mainly relied on census data and household population data to conduct research, lacking a comprehensive consideration of population, economy, space, and society conditions, resulting in a lack of support for analysis of the characteristics of shrinking cities and exploration of relative mechanisms. Self-organizing feature map (SOFM) as a neural network clustering method has powerful processing capabilities for the research of data discovery. It is an effective method for solving data classification problems characterized by high complexity, nonlinearity, and large data structures. SOFM performs category partitioning by the competitive learning of input signals [34,35,36,37]. It is currently widely used in clustering partitioning in geography and ecology [38,39]. This study takes prefecture-level cities as the spatial research scale, identifies shrinking cities in China during 2010–2020 based on demographic data and SOFM research methods, and combines four indices and multiple elements of population, economy, space, and society for cluster analysis. It realizes the classification of shrinking cities and analyzes the characteristics of different categories of shrinking cities by combining the classification results. This study is expected to provide new ideas for the study of shrinking cities and serve as a scientific basis for improving the urban land use structure, urban livability, and optimizing the spatial pattern of national land.

2. Data and Research Methods

2.1. Data Sources

2.1.1. Census Data

The value of population censuses as an essential means to map regional population changes is immeasurable. Since the country’s founding, China has conducted seven nationwide population censuses, collecting and obtaining a large amount of demographic data information in different periods and providing demographic data and research and judgment basis for national construction and the improvement of macro control policies [40]. In this study, we summarize the information on the zoning changes experienced by the population of 293 prefecture-level cities between 2010 and 2020 using the data from the sixth census (2010) and the seventh census (2020). We define those cities with a negative rate of change in resident population between the two censuses as shrinking cities.

2.1.2. Categorical Indicator Data

Narrow and broad urban shrinkage are entirely different. The former refers to the decline in population size and is the “nucleus” of urban shrinkage; the latter is the extrapolation of urban shrinkage, characterizing the population, economy, space, and society decay and destruction of the city. Shrinking cities differ in terms of shrinkage, distribution area, and type of shrinkage [30]. Therefore, the more indicators there are, emphasizing multidimensional processes and effects [41], the more reasonable the classification results will be when considering the category of shrinking cities. Referring to the existing literature, population shrinkage is the most fundamental sign of urban shrinkage. The average annual population and urban population density are selected as the measurement indicators. Economic shrinkage implies the lack of dynamics and vitality of urban development. The secondary and tertiary industries, as a percentage of regional gross domestic product (GDP) and per capita regional GDP, and the registered unemployment rate are selected as the measurement indicators. Spatial shrinkage is the external manifestation of urban shrinkage, and the urban expansion rate in the last decade and VIIRS-DNB nighttime lighting data are selected as the indicators of measurement. The social environment is the potential factor of urban shrinkage, and the road area per capita, housing area per capita, greening coverage of the built-up area, and annual average PM2.5 (which refers to the particulate matter in the ambient air with an aerodynamic equivalent diameter less than or equal to 2.5 μm) index are selected as indicators. The period of the flow indicators is 2009–2019, and the stock indicators are chosen for 2019, due to the statistical time problem of the sixth census and the seventh census. The entropy value method is used to calculate the weight of each hand after the standardization of the 12 indicators, and the specific hands and their interpretations are in

Table 1. Construction of indicator system.

Indicator Layer	Indicator Breakdown Layer	Unit	Weights	Indicator Calculation or Source
Population	The average annual population of the city	10,000 people	0.12	China Statistical Yearbook
	The population density in urban areas	people/km2	0.17	Urban resident population/urban area
Economy	Share of secondary industry in regional GDP	%	0.05	China Statistical Yearbook
	Share of tertiary sector in regional GDP	%	0.03	China Statistical Yearbook
	Per capita gross regional product	CNY 10,000	0.10	China Statistical Yearbook
	Registered unemployment rate	%	0.03	China Statistical Yearbook
Space	Urban built-up area expansion rate	%	0.03	(Built-up area in 2019-Built-up area in 2009)/Built-up area in 2009
	Night lighting data (Average radiation pixel value)	nanowatts/ cm2/sr	0.27	National Oceanic and Atmospheric Administration (https://www.noaa.gov/) (accessed on 20 January 2022)
Society	Road area per capita	m2/person	0.06	China Statistical Yearbook
	Greening coverage rate of built-up area	%	0.02	China Statistical Yearbook
	Annual average PM2.5	μm	0.05	China Statistical Yearbook
	Housing living area per capita	m2	0.08	China Statistical Yearbook

and

Table 2. Description of indicator construction.

Indicator Breakdown Layer	Description	Positive Indicator	Negative Indicator
Average annual population of the city	A comprehensive reflection of the annual population size, and an objective and realistic reflection of the attractiveness of the city. A decrease in population size often signals a decrease in the attractiveness of the city and an increase in the risk of urban shrinkage.	✕
Population density in urban area	It reflects the degree of population agglomeration. A decrease in population density denotes that urban agglomeration economies are less likely to occur, and urban shrinkage is more likely to occur.	✕
Share of secondary industry in regional GDP	China’s market economy is still only at the initial stage of development, whether it is the processing of products for the primary industry or the development and growth of the tertiary industry. The secondary industry is needed as the backbone of the economy.	✕
Share of tertiary sector in regional GDP	The development of tertiary industry is a sign of urbanization development, and the growth of the proportion of tertiary industry heralds the increase in industrial vitality and the reduction of urban shrinkage risk in the city.	✕
Per capita gross regional product	An important indicator to reflect the level of economic development of a city and the living standard of its people.	✕
Registered unemployment rate	An increase in unemployment often signals greater uncertainty about the expected earnings of the labor force, and the negative effects on socioeconomic development are obvious.		✕
Urban built-up area expansion rate in the last decade	It reflects the actual change in a city’s urbanized area and the scale of urban construction land.	✕
Nighttime lighting data (average radiant pixel values)	It reflects the level of urbanization of a city, monitors the urbanization process, extracts the extent and changes of built-up areas, and shows the economic vitality of a city side-by-side.	✕
Road area per capita	It reflects the security capacity of urban infrastructure, but the increase in road area per capita will inhibit the comprehensive development level of shrinking cities.		✕
Greening coverage rate of built-up area	It reflects the living environment of city residents. A good living environment is also an urban pull that reduces the risk of urban shrinkage.	✕
Annual average PM2.5	It reflects the urban living environment. Rising PM2.5 concentrations often cause harm to human health and contribute to the deterioration of local environmental quality, thereby reducing the attractiveness of cities and increase the risk of urban shrinkage.		✕
Housing living area per capita	It reflects the living conditions of urban residents. A good living environment is an urban pull that reduces the risk of urban shrinkage.	✕

.

2.2. Research Method

This study explores the current shrinking cities in China, the status of shrinkage, and classifies the types of shrinkage. We collected data from two population censuses, namely the sixth and seventh censuses, and extracted the population change rate of prefecture-level cities between them to identify the shrinking cities and their spatial distribution in China. The entropy value method is used to confirm the weights after reviewing the relevant information and collecting the identification indexes for the classification of shrinking cities. The shrinking cities are inputted in the SOFM neural network with the index weights already set for classification. The specific technical route is shown in Figure 1.

2.2.1. Identification of Shrinking Cities

$$S_i=\frac{X_{2020}-X_{2010}}{X_{2010}}\times 100\%$$

where $S_i$ represents the population shrinkage degree of city i, $X_{2020}$ represents the resident population of city i in 2020, and $X_{2010}$ represents the resident population of city i in 2010. $S_i$ greater than 0 denotes that the population of city i has increased in 10 years and is considered a growth-oriented city. The larger the $S_{i }$ value, the faster the population growth. $S_i$ equal to 0 indicates that the population inflow and outflow of city i in 10 years are balanced, neither growing nor shrinking, and is considered a stable city. $S_i$ less than 0 denotes the population loss of city i in 10 years and is considered a shrinking city. The smaller the $S_i$ value, the more serious the population loss.

2.2.2. Entropy Value Method

The reasonable determination of indicator weights is the key to scientific assessment. The commonly used assignment methods are mainly the subjective assignment and objective assignment methods. The subjective assignment method is controversial because it includes the subjective consciousness of decision makers. The entropy value method in the objective assignment method can effectively solve the problem of overlapping information between multiple variables and is widely used in research [30]. Therefore, this study adopts the entropy value method to determine the weight of each indicator, and the specific steps are as follows.

In the shrinking cities evaluation system, it is assumed that m cities need to be evaluated with n indicators, and X_ij is the specific value of the nth indicator of the mth city. X is the evaluation result, and the following matrix is established.

$$X=\left(\begin{array}{ccc}{x}_{11}& \dots & x_{1n}\\ ⋮& \ddots & ⋮\\ x_{m1}& \dots & x_{mn}\end{array}\right)$$

(1)

$$X={\left|x_{ij}\right|}_{m\times n}\left(0\le i\le m,0\le j\le n\right)$$

(2)

The urban shrinkage measurement index system constructed in this study includes positive and negative indicators, and the magnitudes of different indicators are different from each other. The evaluation indexes must be standardized before the measurement to eliminate the influence of the index magnitudes.

Let $X_{ij}$ be the value of the jth indicator of the ith evaluation unit. The indexes are standardized by using the extreme difference method as follows:

$X_{ij}$ is normalized when it is a positive indicator:

$$X_{ij}^{\prime }=\frac{X_{ij}-min{X}_j}{max{X}_j-min{X}_j}$$

(3)

$X_{ij}$ is normalized when it is a negative indicator:

$$X_{ij}^{\prime }=\frac{max{X}_j-X_{ij}}{max{X}_j-min{X}_j}$$

(4)

Create a weighting matrix, calculate the weight of the value of the jth indicator of the ith evaluation unit:

$$Y_{ij}=X_{ij}^{\prime }/{\displaystyle \sum }_{i=1}^m{X}_{ij}^{\prime }$$

(5)

Calculation of indicator information entropy:

$$e_j=-k{{\displaystyle \sum }}_{i=1}^m\left(Y_{ij}\times \ln \left(Y_{ij}\right)\right), k=\frac{1}{ln\left(m\right)}$$

(6)

Regarding computational information redundancy, the higher the $d_j$ value, the higher the weight:

$$d_j=1-e_j$$

(7)

Calculate the weight of the evaluation indicators, where the greater the weight of the indicator of the jth item, the more important it is to the evaluation:

$$W_j=d_j/{\displaystyle \sum }_{j=1}^n{d}_j$$

(8)

2.2.3. SOFM Network Model and Learning Algorithm

• SOFM Network Model

An artificial neural network is an analog of the human nervous system, which has only neurons as its most basic processing units despite its magnitude, structural complexity, and outstanding functions. The parts of the artificial neural system are realized by the extensive interconnection of a large number of neurons in parallel operations of the magnificent scale.

SOFM is a type of artificial neural network that learns by network training in an unsupervised manner. It discovers and extracts the intrinsic features from a large amount of input data through the self-organization of the network structure and forms a topological map of input data distribution on the weight vector space of network output nodes, reflecting a specific distribution pattern of input. SOFM can automatically cluster the input patterns. The so-called clustering is a process of dividing the data set into several subsets. Each subset is called a class such that the data objects within the same class have a high degree of similarity, and the differences between data objects of different classes are as large as possible.

The network adjusts the network weights by self-organizing feature mapping so that the neural network converges to a representation morphology. In this morphology, a neuron only matches or is particularly sensitive to a certain input pattern. The neurons are divided into different regions after the network is trained, and each area has different response characteristics to the input model.

The structure of the artificial 2D self-organizing mapping network is shown in Figure 2, which consists of an input layer and an output layer with total connectivity between the input and output layers. The input layer is a 1D sequence of $\mathrm{m}$ neurons. The output layer is also called the competition layer, a 2D planar array. The input pattern is an n-dimensional vector, $x_i=\left(x_{1i},x_{2i},\dots ,x_{ni}\right)$, the connection weight between input unit i and output unit j is $w_{ij}$, and $w_j=\left(w_{1j},w_{2j},\dots ,w_{nj}\right)$ is the weight vector corresponding to the jth output unit.

2.

SOFM Learning Algorithm

The training steps of the self-organizing feature mapping network are as follows.

(1) Initialize the network. Initialize the network weights $w$.

(2) Calculate the distance. Calculate the distance $d_j$ between the input vector $X=\left(x_1,x_2,x_3,\dots ,x_n\right)$ and the competing layer neuron j.

$$d_j=\left|{\displaystyle \sum }_{i=1}^m{\left(x_i-w_{ij}\right)}^2\right|\hspace{1em}\hspace{1em}j=1,2,3,\dots ,n$$

(3) Select neurons. The competing layer neuron $c$ with the smallest distance from the input vector $X$ is taken as the optimal matching output neuron.

(4) Adjust the weights. Adjust the node $c$ and the node weight coefficients contained within its domain $N_C\left(t\right)$:

$$N_C\left(t\right)=\left(t/find \left(norm po{s}_t, po{s}_c\right)\right)<r,$$

$$t=1,2,3,\dots ,n,$$

$$w_{ij}=w_{ij}+\eta \left(X_i-w_{ij}\right),$$

where $po{s}_c$ and $po{s}_t$ are the positions of neurons c and t, respectively; $norm$ calculates the Euclidean distance between two neurons; r is the domain radius; η is the learning rate; r and η decrease linearly with the increase in the number of evolutions.

(5) Determine whether the algorithm is completed; if not, return to step (2).

3. Results

3.1. Identification Results and Spatial Distribution of Shrinking Cities

On the basis of the data from the 6th and 7th censuses, we identified 130 shrinking cities, accounting for 44.37% of China’s current prefecture-level cities. Analysis of the data revealed that the total resident population of the 130 cities at the time of the 6th census was 451 million, accounting for 32.93% of the total population at the time of the 6th census. The total resident population at the time of the 7th census was 260 million, accounting for 18.41% of the total population at the time of the 7th census, with a population change rate S of −42.35% during the decade. Severe population loss occurred. The per capita gross regional product in 2019 was CNY 44,490, lower than the domestic per capita gross regional product of CNY 70,900. The average expansion rate of urban built-up areas in the past 10 years was 57.70%. In 2019, the annual average PM2.5 was 37.88 μm, higher than the national level of 36 μm in the same period.

As shown in Figure 3, the shrinking cities are mainly concentrated in the east of China’s Heihe Tengchong line, which is consistent with the current situation that China’s population distribution is more in the east and less in the west. The shrinking cities are mainly concentrated in densely populated areas. According to the four major divisions of China’s economy (northeast, central, western, and eastern regions), shrinking cities are mainly concentrated in the western, central, and northeast regions, accounting for 33.08%, 32.30%, and 23.08% of the entire shrinking cities, respectively. By contrast, shrinking cities in the eastern region account for 11.54% of the shrinking cities. The top three cities with the highest number of shrinking cities are Heilongjiang Province, Sichuan Province, and Liaoning Province, with 12, 12, and 10 shrinking cities, respectively. The 32 prefecture-level cities in the northeast region (Heilongjiang Province, Jilin Province, Liaoning Province), except Fuxin City in Liaoning Province and Changchun City in Jilin Province, have not shrunk, and the other 30 prefecture-level cities are shrinking cities. The population change rate S is −39.90% during this decade, and the regional recession is severe.

3.2. Classification and Characterization of Shrinking Cities

China is a vast and complex country, tracing the causes and characterizing shrinking cities at the national level with a single indicator are difficult, and structural and industrial weaknesses can be easily ignored when designing policy measures to prevent urban shrinkage [42]. The use of SOFM neural network classification solves this problem, and the more the indicator factors in the input layer, the higher the accuracy of its training. Competitive learning rules are used to measure the similarity of the training set in the massive data by self-organizing and adaptively changing the network parameters and structure, and the shrinking cities are classified so that the interclass differences are maximized. By contrast, the intra-class differences are minimized [43]. In this study, the SOFM network is established, the competitive layer is set to 2 × 2 = 4 neurons, and the Euclidean distance between neural units is selected. The initial learning rate of the classification stage is set to 0.9, the step size of the learning in the classification stage is set to 1000, and the results tend to stabilize without changing to reach the accuracy requirement after 200 iterations. The classification results are selected for four species in accordance with the actual research status, as shown in Figure 4.

3.2.1. First Category of Shrinking Cities

Sixty-two shrinking cities are found in this category, accounting for 47.69%. Most of them are concentrated in the western and northeastern regions of China, with 29 in the western region and 22 in the northeast region. Among them, Heilongjiang Province and Gansu Province account for the highest proportion, with 10 cities each, accounting for 32.26% of the shrinking cities in this category, as shown in Figure 5.

3.2.2. Second Category of Shrinking Cities

Twenty-eight shrinking cities are found in this category, accounting for 21.54%. Most of them are concentrated in the central and western regions of China, with 14 in the central region and 8 in the western region. Among them, Sichuan Province accounts for the highest proportion of 5, accounting for 17.86% of the shrinking cities in this category, as shown in Figure 6.

3.2.3. Third Category of Shrinking Cities

Fourteen shrinking cities are found in this category, accounting for 14.77%. Most of them are concentrated in the central region, accounting for 64.29% of the shrinking cities in this category. Shanxi Province has the most, with five, as shown in Figure 7.

3.2.4. Fourth Category of Shrinking Cities

Twenty-six shrinking cities are found in this category, accounting for 20.00%. Most of them are concentrated in the central and eastern regions of China, with 10 in the central region and 9 in the eastern region. Among them, Henan Province accounts for the highest proportion of five, accounting for 19.23% of the shrinking cities in this category, as shown in Figure 8.

3.2.5. Comparative Analysis of the Four Types of Cities

To better explore the characteristics of the four categories of cities, we analyzed the indicators of each category of shrinking cities in conjunction with research and data. Statistical methods commonly used to describe the data set are calculating the mean, quartiles, standard deviation, and standard score. SOFM achieves the maximum variation between classes and the minimum variation within classes at the classification stage because we use the mean to reflect the trend of concentration of an indicator in the same category of cities. Thus, we can compare and analyze the differences in this indicator between the different categories of shrinking cities.

The results show that the first category of shrinking cities is mostly old industrial cities and resource-depleted cities, and the local supporting industries are mostly equipment manufacturing, the petrochemical industry, and the steel industry. In terms of population, the average resident population change rate S of this category of cities is −11.98% during the 10-year period. Although the change rate is the lowest among the four categories of cities, the sixth and the seventh census data show that the resident population in this category of cities is remarkably lower than that of the other three categories of cities in the past 10 years, and a long-term lack of population attractiveness is observed. The average population density of urban areas is only 311 people/km², which is much lower than that of the other three categories of cities, and the long-term lack of population inevitably leads to high land costs, difficulties in maintaining the ecological environment, low industrial concentration, economic mobility, and overall competitiveness. Spatially, the 2019 night lighting data show that the average radiation image element value of this category of cities is only 0.21 nanowatts/cm²/sr, and the expansion rate of the built-up area of the city in the past 10 years is 44.56%, which is the lowest among the four categories of cities and reflects the lack of vitality and development of the city from the side. For the economic aspects, the average per capita gross regional product in terms of local finances in such cities is only CNY 36,800, the lowest among the four types of cities, and the average registered unemployment rate in 2019 is 0.72%, the most remarkable unemployment rate among the four types of cities. In terms of revenues and expenditures, transfer dependence is measured by the ratio of local fiscal expenditures to revenues, and the lower the revenues, the higher the expenditures, the higher the pressure of dependence, and the greater the land fiscal incentive [44]. The degree of this dependence is often inversely proportional to the level of economic development, that is, the higher the degree of dependence, the lower the economic self-sufficiency of the city. The per capita public budget expenditure of the city in this category is five times the public budget revenue, the highest among the four categories of cities. Combining the characteristics of their indicators, we define them as a high population shortage-low economic development city.

The second category of shrinking cities is dominated by agriculture, forestry, animal husbandry and fishery industries, that is, agricultural production. In terms of economy, the average registered unemployment rate of such cities in 2019 is 0.53%, and the average per capita gross regional product in terms of local finance is only CNY 41,600. In terms of income and expenditure, the per capita public budget expenditure of cities in this category is 3.55 times the public budget income, and the cities are less economically self-sufficient and only second to the high population shortage-low economic development city in terms of dependence on transfer payments. In terms of population, the average urban population density is 778 people/km², and the average resident population change rate S for this category of cities is −16.81% over the 10-year period, with the highest population loss among the four categories of cities. The average value of green coverage in the built-up area of this type of cities is 40.62%, and the annual average PM2.5 content is 42.22 μm, which is at a high level. With the improvement of the living standard of residents, people’s requirements for living environment gradually increase, and poor air quality becomes an important factor limiting people’s quality of life, which reduces the attractiveness to the population in the long run. Spatially, this category of cities has experienced a rapid expansion, with a built-up area expansion rate of 79.73% in the last 10 years, much higher than the other three categories of shrinking cities. In the rapid urbanization process, the industrial advantages of this type of cities are difficult to be reflected, the living environment of residents has deteriorated, and the cities have experienced unreasonable expansion and more serious urban shrinkage. Combining the characteristics of their indicators, we define them as a high urban expansion-low population retention city.

The third category of shrinking cities is dominated by petrochemical or equipment manufacturing industries. In accordance with the Notice on the Adjustment of City Size Classification Standards issued by the State Council in 2014, such cities have a population distribution between 1 million and 5 million, where all of them are large cities (3 million to 5 million are Type I large cities and 1 million to 3 million are Type II large cities). The average urban population density is 436 people/km², and the city’s annual average population is 2,824,300. The average resident population change rate S is −1.59%, the lowest change rate among the four categories, that is, the slightest population loss. Economically, the average 2019 registered unemployment rate for this category of cities is 0.56%, and the average per capita gross regional product in terms of local finance is 64,700 yuan, which is the highest among the four categories. In terms of income and expenditure, the per capita public budget expenditure of cities in this category is 2.37 times the public budget income, and the cities have a high degree of economic self-sufficiency and a low dependence on transfer payments. The 2019 night lighting data show that the average radiation image element value of this category of cities is 0.57 nanowatts/cm²/sr, and the expansion rate of the built-up area of the city in the past 10 years is 48.73%, and the expansion level of the city is more orderly. Such cities have also opened and built the most high-speed railways among the four categories of cities, and all other cities have completed the opening of high-speed railways before 2020, except for Luliang and Shuozhou Cities in Shanxi Province. Regarding social indicators, the average value of greening coverage in built-up areas in 2019 is 41.61%, and the annual average PM2.5 content is 40.52 μm. The road area per capita is 13.85 m²/person, and the housing area per capita is 28 m², which does not show its outstanding impact compared with the other three categories. Such cities need to consider the depletion of non-renewable resources in the process of industrial development, the restricted development of leading industries, and the narrow and thin succession of industries, and to control the current situation of shrinkage to avoid further shrinking of the city. Combining their indicator characteristics, we define them as low population loss-high traffic accessibility city.

The fourth category of shrinking cities is dominated by light industries, such as electronic information industry or textile and garment. Socially, the average greening coverage of the built-up area of this category of cities is 41.88%, with a low level of greening. With an annual average PM2.5 content of 46.76 μm, the cities are more polluted than the other three categories of cities, and environmental issues have increasingly become a factor in people’s choice of where to live in recent years. No significant difference is observed in road area per capita and housing area per capita compared with the other three categories. In terms of population, the average population density in urban areas is 1229 people/km², the highest density among the four categories of cities, which is also in line with China’s demographic situation. This condition is because the eastern and central regions, especially Henan Province, which is a large population province, have always been the concentration areas of China’s population distribution. The average resident population change rate S for this category of cities is −12.39% over the 10-year period, and the population loss is relatively serious. Spatially, the expansion rate of this type of city is faster, and the expansion rate of the built-up area in the last 10 years is 70.15%. The 2019 night lighting data show that the average radiation image element value of this type of city is 1.57 nanowatts/cm²/sr, which indicates that the night brightness of the city is much higher than that of the other three types of cities. Therefore, the high expansion rate and high nighttime luminance of this type of shrinking cities is more reasonable than the high expansion rate and low nighttime luminance of the second category of shrinking cities, which indicates their relatively active economy. On the economic side, the average 2019 registered unemployment rate of such cities is 0.53%, the lowest among the four types of cities, and the low unemployment rate is the basis for stable social development. In terms of local finance, the average per capita gross regional product is CNY 50.5 thousand, second only to low population loss-high traffic accessibility city. In terms of income and expenditure, the per capita public budget expenditure of this type of cities is 2.43 times the public budget income, and the cities have a high degree of economic self-sufficiency and less reliance on transfer payments. The study finds that the development prospects of the leading industries in these shrinking cities are excellent, which is conducive to the optimization of the industrial structure, labor force employment, and a reduction in the unemployment rate. China has also strongly encouraged the development of information technology industry in recent years, and the policy inclination makes the shrinking status of this type of shrinking city the smallest. However, most of the cities in this category are concentrated in Chinese provinces with net population outflow. The agglomeration power of the capital cities of these provinces for population has not decreased, and the agglomeration pull of large cities in the province and the pull of large cities outside the province, such as Beijing, Shanghai, and Guangzhou, are the possible reasons for the shrinking of these cities [44]. The environmental quality of this type of cities should not be ignored because the PM2.5 index is much higher than the normal level, and the maintenance of ecological environment and improving the quality of life of residents should be focused on in the next development. Combining their indicator characteristics, we define them as a low environmental quality-high passive siphon city.The analysis data is detailed in Figure 9.

The contribution of each indicator in the backpropagation classification process is evaluated in accordance with the set economic, social, spatial, and population indicator layers. The contribution of population and spatial indicators for the high population shortage-low economic development city is as high as 100%, which shows the important influence of population and spatial factors on their classification results. The contribution of economic indicators exceeds 80%, and the contribution of social indicators is around 55%. The contribution of economic indicators for the high urban expansion-low population retention city is as high as 100%, which shows the important influence of economy on the classification results. The contribution of social indicators is close to 80%, and the contribution of population and spatial indicators is around 60%. The contribution of population indicators for low population loss-high traffic accessibility city is the highest when classified, exceeding 80%, which shows the important influence of population on their classification results. The contribution of economic and spatial indicators is around 60%, and that of social indicators is over 50%. The contribution of social indicators for the low environmental quality-high passive siphon city is as high as 100%, which shows the important influence of social factors on the classification results. The contribution of spatial, population, and economic indicators is around 50% to the classification results. The different contributions of each indicator layer to the classification of each type of city indicate that remarkable differences are observed between the various types of cities classified based on the SOFM neural network. See Figure 10, Figure 11, Figure 12 and Figure 13 for details.

4. Discussion

4.1. Comparative Analysis of Classification Results

As shown in

Table 3. Comparison of China’s shrinking city classification studies.

Researchers	Research Scope	Research Method	Research Results
Dongfeng Yang Long Ying Wenshi Yang, et al.	Beijing City Laboratory website published 180 shrinking cities in China from 2000–2010	Phenomenological observation and typological description of the urban shrinkage paradox by measuring the population loss index and spatial expansion index of the identified shrinking cities.	Heavy population loss, significant spatial expansion (47) Heavy population loss, spatial expansion insignificant (44) Light population loss, significant spatial expansion (43) Light population loss, spatial expansion insignificant (46)
Jianan Wen Yingchang Song Gao Ren	Shrinkage levels in 287 prefecture-level and above cities in China, 2011–2016	The 3D index systems of population, economy, and society are constructed, and the entropy value method is used to assign values to the indexes and calculate the comprehensive shrinkage levels of cities. The cities are classified into four types of levels based on the natural interruption point grading.	Highly shrinking cities (18) Mildly shrinking cities (103) Mild growth cities (148) High growth cities (18)
Xiangfeng Meng Shuang Ma Wenyi Xiang, et al.	We examine the shrinking level of physical cities in China during 2016–2018 using 3022 physical cities in China as the unit of analysis	Among 3022 physical cities, 177 physical cities with resident population change rate ≤ −15% were examined, and a 200 m × 200 m resident population density grid was created. The resident population change rate of grid cells was measured and evaluated, and 126 shrinking cities were selected as research samples in accordance with the shrinking city research sample screening method.	Global shrinking city (33) Local-type shrinking cities (25) Circle pie type shrinking city (18) Perforated shrinking city (47) Edge-type shrinking city (3)
Rui Chen	Urban shrinkage levels in 285 prefecture-level cities and 330 county-level cities in China, 2009–2019	The 3D indicator systems of population, economy and society are constructed, and the entropy value method is used to assign values to the indicators and calculate the comprehensive shrinkage levels of cities. The cities are classified into five categories of levels.	Highly shrinking cities (33) Moderately shrinking cities (66) Mildly shrinking cities (31) Slightly shrinking cities (34) No shrinking or growing cities (451)
Xinyi Wang Zihan Li Zhe Feng	Shrinkage levels of 293 prefecture-level cities in China, 2010–2020	A total of 130 shrinking cities are defined as those with a negative rate of change in resident population over a 10-year period using the census data. A 4D index system of demographic, economic, social, and spatial dimensions was constructed, and the SOFM neural network was used to classify the shrinking cities.	High population shortage low economic development cities (62) High urban expansion low population retention cities (28) Low population loss high traffic accessibility cities (14) Low environmental quality high passive siphon cities (26)

, this study presents several studies that classify shrinking cities at a China-wide scale during the 2000–2020 period. The number of shrinking cities and their classification vary greatly due to the different size ranges of cities and the different methods of quantifying the weights when assigning information weights to indicators or using the expert scoring method. A large number of studies have provided a rich theoretical basis for the construction of a complete theoretical system for shrinking cities in China later on. However, they show that China does not constitute a unified theoretical framework for urban shrinkage research and needs to form a more unified indicator system and design response strategies.

4.2. Exploring the Causes of Global Shrinking Cities

From a global perspective, industrial decline is one of the most common and widespread causes of shrinking cities, such as the famous “Rust Belt” region of the northeast in the United States and the high population shortage-low economic development city in China, which have completed their urbanization through industrialization. However, their industrial advantages are no longer reflected, and their development dynamics are insufficient due to their homogeneous industrial structure along with the effects of deindustrialization and geographic marginalization, so they have gradually lost their competitiveness in the global market [41,45]. Typically represented by the city of Youngstown, Ohio, and Northeastern China, the high prosperity of the secondary industry has allowed them to rise rapidly in the past decades, but the decline of the industry has brought a series of problems, such as vacant houses, environmental degradation, and a less attractive population.

Inefficient land use is also a more common cause of shrinking cities, and housing vacancies are often used in Western countries to characterize the spatially uneven development of shrinking cities. For example, in Germany, the reunification of the East and West German regions and the shift of manufacturing industries led to the migration of large numbers of people from the former East German region, which resulted in large numbers of vacant buildings [10,46]. Vacancy and decay in Southern U.S. cities, such as Las Vegas and Atlanta, were triggered by mortgage lenders suspending their scheduled mortgage payments to banks due to mortgage defaults [47,48]. The operators of real estate companies will be under pressure in recovering funds when a certain city has excessive vacant houses, which will slowly affect the normal operation of real estate companies. When real estate enterprises and local urban construction invest money back to slow down, the whole city will face a relative “capital shortage”, and result in the “land finance phenomenon”. However, China exhibits a unique urban shrinkage paradox phenomenon of population loss and urban expansion compared with the mainstream characteristics of sustained population decline and relatively stagnant spatial expansion in Western countries. For example, the growth rate of land urbanization and population urbanization is out of balance, and the expansion is disordered for China’s high urban expansion-low population retention city, often resulting in the waste of resources, growth of local economic pressure, and exacerbation of the urban shrinkage phenomenon.

The impact of modern transportation infrastructure is another cause of shrinking cities. Today’s world relies on transportation road networks to promote collaborative exchanges between cities and cities and countries; in particular, the opening of high-speed railways breaks the transportation barriers between less developed and developed cities and enhances intercity connections, allowing residents to enjoy the diverse product services and higher labor remuneration of metropolitan cities and retreat to such cities to avoid the high cost of living and the distress caused by the harsh environment [49], facilitating the inflow and outflow of population. For example, the construction of the Eurostar high-speed rail line has made Lyon, Nice, and Toulouse, France, along the route a concentration of industries and populations; remote areas on the periphery of the construction of the transportation road network and beyond the radiation impact of the transportation road network have become exporters of population and resources [50]. The high population shortage-low economic development city and the low population loss-high traffic accessibility city in China are dominated by secondary industries. The reasons for the milder shrinkage of low population loss-high traffic accessibility cities are mainly attributed to the obvious advantage in location over a high population shortage-low economic development city, the proximity to central cities or economically developed areas, and the increased intensity of economic activity in the area around the stations due to the commissioning of high-speed rail stations [51].

The passive siphoning of small- and medium-sized cities has led to urban shrinkage. As a result of globalization, important infrastructure and intangible assets are concentrated in “mega cities” (e.g., New York, London, Paris, Tokyo, and Beijing), making them magnets for population, technology, and capital, bringing about new global patterns of production, manufacturing, distribution, and consumption [11]. However, such “mega cities” are surrounded by small- and medium-sized cities with close economic and cultural ties to them. For example, in Estonia, investments are concentrated in the surrounding large cities, and the economic dynamism of lower-ranking towns in the town system diminishes after the economic transition [52]. Among the low environmental quality-high passive siphon cities in China, a typical case is the massive labor drain from neighboring towns, such as Huanggang in Hubei Province under the polarized development of the Wuhan City circle.

4.3. Response Strategy of China’s Shrinking Cities

China should learn from many successful cases in Western countries for the governance of shrinking cities. For example, in response to the problem of industrial decay, the United States proposed the “Youngstown 2010 Plan”, which broke away from the previous planning goals of shrinking cities that still tend to maintain growth [11] and indicated that urban development must be better aligned with the regional economy, create a higher quality of life, and promote public participation-oriented planning goals [53]. In response to the problem of vacant houses and inefficient land use, Germany proposed the “Stadtumbau Ost” to reduce the vacancy rate of urban housing through subsidized reduction and demolition activities and achieved good results [54]. Artistic design and spatial creation to revitalize the image of a decaying city and reshape its spirit are means to manage shrinking cities, such as the Echelm Park designed by the German IBA (Internationale Bauausstellung), which has transformed the decaying industrial site of the Echelm area into a country park of good quality [55,56]. In response to the declining attractiveness of cities, France proposed the concept of “residential attractiveness,” which advocates the introduction of middle- and high-income people to live in the city to achieve a benign multisocial mix, leading to local economic revitalization [22]. The planning and design of shrinking cities in developed countries is still mainly aimed at “rational streamlining,” with spatial transformation, green infrastructure construction, and welfare management as specific measures. At present, the governance of shrinking cities in China still lacks universality, and the horizontal comparison with shrinking governance in Western countries helps managers and policy makers to develop coping strategies. This study proposes the following recommendations for the four different categories of shrinking cities considering the literature and the current state of local research in China.

4.3.1. Implementing Economic Revitalization by Relying on Traditional Industries and Broadening Measures to Introduce and Cultivate Talents

First category of shrinking cities focus on the secondary industry. Development has been a bottleneck in recent years due to the gradual loss of resources, location, and transportation advantages in the development process of these cities, coupled with the continued lack of population attraction. First category of shrinking cities should focus on economic revitalization and talent introduction. They should realize the marketization of investment behavior, reduce the past behavior of mainly relying on government investment, implement the new path of “government investment + private investment + foreign investment,” and effectively attract private capital and foreign investment through the marketization of public resource allocation from “strong government” to “strong government” and “strong market” combination. The old industrial bases in the northeast and western regions have never lacked “strong government,“ but mainly lacked ”big market” and “strong market,” including the market mechanism, market environment, and market concept, which are the market system. Conducting talent introduction and promoting preferential measures in employment, housing, and social security will attract college students from universities in the province and college students from universities outside the province for local employment. Promoting technological innovation with institutional innovation will provide a strong institutional solid guarantee for revitalizing such cities.

4.3.2. Adjusting the Usual Growth-Oriented Planning Mindset to Focus on Inner-City Urban Renewal and Transformation

Second category of shrinking cities have no obvious industrial advantages, are highly dependent on government finance, and have experienced severe environmental pollution and population loss in recent years, resulting in the paradox of urban shrinkage and urban expansion. Second category of shrinking cities should focus on implementing the development strategy of “tightening+shrinking” to optimize their industrial structure and improve their economic vitality. They should focus on the development concept of “strengthening the bottom-line constraints of resources and environment”, promoting ecological priority and green development as proposed in the overall territorial spatial plan, and guide the delineation of urban development boundaries. Proactively abandon the development concept of “must grow” and formulate a planning policy of “moderate shrinkage.” Rational streamlining to create ecologically pleasant and scenic cities is an important strategy to attract people back, especially young people [12].

4.3.3. Implementation of Sustainable Development Strategy from Multiple Angles, Relying on Transportation Road Network to Promote Industrial Upgrading

Third category of shrinking cities face the problems of nonrenewable resource consumption, the regional development of leading industries, and insufficient power for new initiatives. For such cities, the development should not focus excessively on the improvement of complex economic indices, such as GDP. Transformative development should be conducted under the concept of sustainable development. Most resource-based cities have caused different degrees of damage to the ecological and natural environment in the past development process, and the urban transformation under the concept of sustainable development should focus on the restoration of the ecological and natural environment. Thus, the sustainable development strategy can be implemented from multiple perspectives, such as economic construction, urban development, and livelihood problem solving [57]. At the same time, the high-speed rail becomes an engine of economic development by relying on its location and transportation advantages. This process improves the economic development model of the city and promotes industrial clustering [58,59].

4.3.4. Actively Adjusting Urban Form, Seeking Characteristic Development, and Enhancing the Attractiveness of Urban Elements

Fourth category of shrinking cities have excellent prospects for industrial development, and the degree of shrinkage is the slightest among the four types of cities. In maintaining the current economic development conditions, attention should be paid to the influence of the external pull produced by other cities for themselves. Such cities should take the initiative to find the city’s industrial positioning, cultivate and strengthen the particular industries, accelerate economic development with particular industries, ensure sustainable development in the region, and avoid the city losing their development advantages under the influence of external gravity. To take the initiative to improve the city’s functions, realize the joint development of urban multifunction, improve the quality of residents’ living environment, make the city kernel larger and stronger, and improve the competitiveness of the city. Take the initiative to utilize the advantages of location, strengthen the degree of connection with the neighboring large cities, effectively absorb and use the resources of large cities, jump out of the “shadow area” of the siphoning effect, and transform the siphoning effect into the diffusion effect to achieve the mutual promotion and development of the city to city and region to region [60].

4.4. Shortcomings and Prospects

The problem of urban shrinkage involves a wide range and many factors. Although this study selected some indicators to classify shrinking cities, it still has some limitations. We lack the analysis of whether some indicators that are difficult to quantify will have an impact on shrinking cities. For example, for the selection of economic indicators, we used the indicators to reflect market economic activities, but lacked some indicators of activities where no payment behavior occurs; at the level of social indicators, we focused on objective indicators, such as environmental quality and housing quality, but lacked subjective indicators, such as whether the corruption of officials in a particular city affects the willingness of city residents to live there. This study mainly uses prefecture-level cities as the administrative scale. The current situation of shrinking county-level cities and the hollowing out of villages and towns remain unclear. These conditions should be considered in the following study. This study mainly proposes policy recommendations for each type of city, but each city has its uniqueness and lacks individual microanalysis. Precise requests should be made for each city to be implemented in its development plan.

China has the largest population and the third largest territory in the world. Its natural environment and human landscape have built unique cities for thousands of years. We will further explore the process and mechanism of urban shrinkage in this land, explore it in smaller units, and lay down more profound knowledge.

5. Conclusions

In this study, the SOFM neural network is used to cluster the identified shrinking cities from 2010 to 2020, which solves the problem of a single analysis angle and incomplete analysis factors for shrinking cities in the past. A total of 130 shrinking cities were identified and divided into four categories through the competitive learning of SOFM.

• high population shortage-low economic development city: This category includes 62 cities, which are mainly distributed in the western and northeast regions. These cities show extremely low population density, severe population loss, and gradual loss of industry, location, and resource advantages. They are characterized by high financial dependence on the government, low urban vitality, and complex development. The shrinkage in this type of city is the most serious among the shrinking cities.
• high urban expansion-low population retention city: This category includes 28 cities, which are mainly distributed in the central and western regions. These cities are characterized by severe population loss, high financial dependence, and low industrial vitality. A paradox is observed between population loss and high urban expansion. The shrinkage is more serious.
• low population loss-high traffic accessibility city: This category includes 14 cities, which are mainly located in the central region. These cities show a slight population loss, a high degree of economic self-sufficiency, and a more orderly urban expansion. The high degree of the opening of high-speed rail and special transportation conditions may be the reason for their relatively mild shrinkage. They also face the problems of insufficient power for the development of leading industries and unsustainable growth of resource depletion.
• low environmental quality-high passive siphon city: This category includes 26 cities, which are mainly located in the central and eastern regions of China. They show high population density but more serious population loss and severe pollution. However, they are characterized by high economic activity, low unemployment rate, and good spatial expansion. The shrinkage of this type of city is the mildest among the four categories, but the further intensification of “siphoning” by the surrounding large cities should be considered.

This study identifies shrinking cities and classifies each type of shrinking city. It provides new ideas for the government to finely adjust urban development priorities, rationalize urban planning and design, and realize the coordinated development of people and land in the urbanization process of China. This study fills the gap of neural networks in the classification of shrinking cities, which helps enrich the research methods of shrinking cities and provides the Chinese experience for the study of shrinking cities in the world urbanization process.