A Deep Graph Learning-Enhanced Assessment Method for Industry-Sustainability Coupling Degree in Smart Cities

Abstract

The construction of smart cities has been a common long-term goal around the world. In addition to fundamental infrastructures, it also remains important to assess healthy development status of cities with use of intelligent algorithms. Currently, machine learning has gradually been the prevalent technical means to develop digital assessment methods. However, the whole social system can be regarded as a kind of graph-level complex network, in which node entities and their internal relations are involved. To deal with this challenge, this paper takes graph-level feature into consideration, and proposes a deep graph learning-enhanced assessment method for industry-sustainability coupling degree in smart cities. Specifically, an improved graph neural network model is developed to output the industry space aggregation consequence, and a multi-variant regression model is utilized to output the sustainability status level consequence. Taking the Guangdong-Hong Kong-Macau Greater Bay Area (GBA) as an example, simulative experiments are carried out on the real-world data collected from realistic society. The obtained results can well prove that the proposed method is able to effectively assess the industry-sustainability coupling degree in smart cities.

1. Introduction

Industrial agglomeration (IA) and economic growth have become the focus of new geodynamic economics since the late 90s of the 20th century [1]. IA is a geographical phenomenon in the process of industrial development evolution, which refers to the phenomenon of industrial concentration composed by a certain number of enterprises in order to pursue profits, thus becoming the main driving force of regional economic development, and its essence is the economic scale caused by the spatial agglomeration of economic activities and production factors [2]. An agglomeration is indeed a procedure in which the same type of business gets focused in a specific geographic area, and the accompanying aspects of business keep flowing and merge [3]. IA not only affects the spatial distribution of industrial structures and enterprise activities but also causes differences in city positions [4]. The general theory of IA and regional economic growth holds that industries are agglomerated in the form of clusters, and the localized economy and urbanization economy are improved through the employment of enterprises within the industry and the diversity of industries. IA has increasingly been acknowledged as a significant driving factor for economic growth as theories on economic development continue to expand [5].

IA is not only a catalyst for greater specialization and division of labour, but it also increases competitiveness among businesses. The constructed IA will reduce losses within the industrial organization, transaction costs and social costs through economies of scope and economies of scale. At the same time, it is also conducive to knowledge spillover, technology diffusion, human resources training, etc. Secondly, IA has the potential to provide businesses with economies of scale and other benefits [6]. In order to remain competitive in the age of IA, businesses must raise the size of their output. The company’s profits will also improve as a result of increased efficiency. Figure 1 depicts the IA process.

IA is closely related to economic development. The eastern region of China is a gathering area of manufacturing, foreign investment and trade, as well as a region with high economic development and residents’ income. However, the degree of IA in western China is relatively low. The process of agglomeration can not only increase the correlation between upstream enterprises and parallel enterprises in the industrial chain, but also enhance the innovation and competitiveness of the local regional system.

The GBA encompasses an area of 56,000 square kilometres and is comprised of nine cities in Guangdong provinces. They are “Guangzhou”, “Shenzhen”, “Zhuhai”, “Foshan”, “Huizhou”, “Dongguan”, “Zhongshan”, “Jiangmen”, and “Zhaoqing”. Additionally, the Hong Kong SAR and the Macao SAR are included in the GBA, as shown in Figure 2. The Guangdong-Hong Kong-Macao Greater Bay Area is a new industrial agglomeration area upgraded on the basis of the Pearl River Delta city cluster. A key goal for sustainable development in GBA is to accelerate the construction of IA. In this paper, we focus on the internal coupling between industrial agglomeration and regional economic development.

In recent years, some scholars have applied neural networks and other algorithms to the analysis of graph structure data. In this paper, considering the linkage effect of different regional economic conditions and GBA regional economic sustainability, the regional industrial economy is taken as the node of the network, and the influence between different regions is the edge of the network. The graph depth learning algorithm is used to study the good evaluation ability of nonlinear time series. Contribution of this research is summarized as follows:

(1)

Based on the economic data of 11 cities in GBA region from 2011 to 2020, the impact of industrial spatial agglomeration on economic sustainable development is analyzed.

(2)

On the basis of considering map level characteristics, this paper proposes an evaluation method of industrial sustainable coupling degree of intelligent city based on depth map learning.

(3)

An improved graphical neural network model is developed to output the results of industry spatial aggregation, and a multivariable regression model is used to output the results of sustainability status level.

The remainder of this paper is organized as follows. In the next section, the related works will be shown in detail. In Section 3, a method to examine the industrial agglomeration’s consequences is analyzed. In Section 4, the simulation and discussion are carried out. Finally, some conclusions are drawn in Section 5.

2. Literature Review

Several researches have been published on industrial agglomeration. The enhanced entropy approach is used to produce a complete pollution index, and the spatial concentration is used to determine the pollution agglomeration level. “Location Quotient Index (LQI)” measures IA in a specific region. The model of “Geographically and Temporally Weighted Regression (GTWR)” [7] examines the impact of IA on pollution agglomeration. [8] empirically assesses the geographical spillover consequence of IA concerning haze pollution in order to propose a fresh concept for improving the system of regional collaborative air pollution management. “Elilsionand Glaeser (EG)” and “Total Factor Production (TFP)” growth are estimated by taking into account the unwanted outcome of the manufacturing firm datasource and using an entropy weight approach to evaluate agglomeration effects. The author also investigates the link involving both the agglomeration and TFP development using the smooth transition approach for the specified Chinese centers and industrialized sectors between 2003 and 2013 [9].

Pei et al. and Mody et al. mentions that the method by which IA affects natural habitats is extensive and complicated, and it has been a popular focus of study in recent years [10,11]. The author’s goal is to provide policymakers with some useful advice on industrial growth by quantifying the impact of regional distribution on energy efficiency improvements in the research sector [12]. China’s environmental efficiency was measured using the Meta-constraints Efficiency model, and then a panel model was utilised to examine the consequence of industrial clustering on environmental efficacy. The research indicated that IAs get a noticeable influence about surrounding area’s geography [13]. Garg et al. examined the influence of IA on environmental performance in Chinese prefectural-cities [14]. IA as a diverse influence on sulphur dioxide and soot pollution intensity. The data suggest a non-linear relationship among agglomeration and SO₂ emission intensity, but not soot [15].

Ahmed et al. uses a spatial Durbin model to examine how pollution and ecological efficiency are affected by industrial agglomeration [16]. The impacts of combining industry and services to reduce pollution and promote environmental sustainability are also examined [17]. The dependent variable is the industry’s overall factor efficiency in terms of metric tonnes of energy used. In-depth analyses of the industry are also carried out at various degrees of IA based on linear panel examination of the relation between IA and energy efficacy [18]. IA’s effect on energy conservation was tested using nonlinear threshold regression, and a “double threshold regression analysis” was built wherein the cutoff of textile IA values represented a cutoff variable [19]. The Dynamic Spatial Durbin Approach is used to evaluate the relationship involving diverse IA, technology advancements, and carbon output across China’s 30 counties during 1998–2017. An important theoretical and practical takeaway is that industrial agglomerations may be reformed spatially to preserve economic development while increasing long-term carbon productivity [20,21]. Over the last 40 years, China’s industrial firms have become more and more consolidated. The industrial agglomeration either increases or decreases CO₂ emissions, depending on your perspective. Industrial Emissions of CO₂ per capita are analyzed in 187 township Chinese cities between 2005 and 2013 employing ten various fossil fuels [22].

The green development efficiency of 34 cities in Northeast China using panel data from 2003 to 2016 and concludes whether industrial agglomeration helps or hinders green development efficiency [23]. Using panel data from key cities in China’s Bohai Sea economic region (BSER), this study examines the effects of industrial agglomerations (IAs) on haze pollution (HP) in accordance with contemporary sustainable development trends and policies aimed at efficiently addressing air pollution concerns. Path features, geographical heterogeneity impacts, and development patterns of three main IA on the HP are carefully examined [24]. Industrial agglomeration impacts on LUE vary significantly amongst two-digit industrial sectors [25]. Studying environmental regulation’s impact on environmental pollution in China’s 30 provinces from 2003 to 2016 using Bayesian posterior probabilities, optimum model structure selection, and panel data from China’s 112 types of spatial econometric model structure is the focus of this article [26]. Using China’s provincial-level energy-intensive sectors from 2004 to 2017 as a case study, this article investigates the influence of industrial agglomeration on energy efficiency and its process [27]. The goal of this article is to provide policymakers with some useful advice on industrial growth by quantifying the impact of regional distribution on energy efficiency improvements in the paper sector. Among the key findings is that the paper sector in eastern China clearly exhibits agglomeration characteristics [28].

Machine learning technology is widely used in economic analysis because of its structural advantages and high efficiency of information processing. Kliestik et al. explored data-driven machine learning and neural network algorithms in industrial environments [29]. Combes et al. described the flexibility and prediction ability of machine learning, and analyzed the important factors affecting regional economic development by discussing the urban economic situation [30]. Wu et al. designed the economic model predictive control (EMPC) system based on the control Lyapunov obstacle function (CLBF) to optimize the process economy, and based on the prediction model using the recurrent neural network (RNN) model set to ensure stability and operation safety at the same time [31]. Huang et al. proposed a new unconstrained transformation method of OHLC data and combined it with various economic forecasting models [32]. We could see from the foregoing analysis that there is a wide range of views on the economical consequence of IA. A closer look at the consequence of IA for growth in the economy is encouraged by this development. To see if changes in industrial structure alter the correlation among both IA and economic expansion in a particular region. In this paper, considering the linkage effect of different regional economic conditions and GBA regional economic sustainability, the regional industrial economy is taken as the node of the network, and the influence between different regions is the edge of the network. The graph depth learning algorithm is used to study the good evaluation ability of nonlinear time series.

3. Methodology

This section focuses on how IA affects regional economic sustainability. In fact, the development of industrial agglomeration has changed the economic operation mode. Economic externalities can be effectively brought into play through industrial agglomeration. At the same time, the innovation ability of the regions along the line will be enhanced through the competitive incentive effect, so as to improve the sustainability of economic development. For this investigation, 2011–2020 was selected because of the restricted amount of data available and the stability of the statistical quality. It was based on data of China’s statistical yearbooks, China Industrial Statistics Yearbook, China Environmental Statistics Yearbook. Some of the attributes of the dataset is descripted, as show in

Table 1. Attributes of the dataset.

City	Time	IA	Manufacturing IA	Service IA	Score Normalization	Standardization of IA	Standardization of MIA	Standardization of SIA
Guangzhou	2011	0.09712	0.038095	0.053096	0.138722	0.100864	0.149371	0.060807
	2012	0.098617	0.038239	0.054243	0.196497	0.102689	0.149989	0.062203
	2013	0.107801	0.035602	0.057975	0.18042	0.113883	0.1387	0.066745
	2014	0.113957	0.038405	0.059006	0.204024	0.121387	0.150699	0.067999
	2015	0.120453	0.038816	0.061684	0.256003	0.129305	0.152456	0.071259
	2016	0.126802	0.038971	0.064772	0.240379	0.137044	0.153122	0.075015
	2017	0.13372	0.038775	0.068467	0.300928	0.145476	0.152282	0.079512
	2018	0.141556	0.037257	0.100552	0.248271	0.155028	0.145784	0.118558
	2019	0.144369	0.036109	0.10432	0.328784	0.158458	0.140871	0.123143
	2020	0.15078	0.035463	0.118736	0.285443	0.166272	0.138103	0.140686
Shenzhen	2011	0.330384	0.179049	0.178363	0.308675	0.385196	0.75281	0.213248
	2012	0.326581	0.171363	0.181682	0.330916	0.38056	0.719909	0.217287
	2013	0.394975	0.198041	0.20803	0.360025	0.463927	0.834119	0.249351
	2014	0.417475	0.195826	0.210404	0.36009	0.491353	0.824638	0.25224
	2015	0.438999	0.191924	0.21676	0.379165	0.517589	0.80793	0.259975
	2016	0.459738	0.190215	0.226543	0.403876	0.542869	0.800613	0.27188
	2017	0.479588	0.190546	0.23231	0.424685	0.567065	0.802034	0.278898
	2018	0.498635	0.229281	0.327857	0.364349	0.590281	0.967863	0.395172
	2019	0.496218	0.227126	0.327042	0.404915	0.587335	0.958634	0.39418
	2020	0.503815	0.236788	0.361157	0.451278	0.596594	1	0.435696
Zhuhai	2011	0.061036	0.027634	0.030599	0.26488	0.056881	0.104589	0.03343
	2012	0.059071	0.027987	0.028474	0.254754	0.054485	0.106098	0.030844
	2013	0.0697	0.030958	0.02634	0.301444	0.067442	0.118819	0.028246
	2014	0.073019	0.031638	0.027076	0.342903	0.071488	0.121727	0.029143
	2015	0.075509	0.031103	0.026694	0.34679	0.074522	0.11944	0.028677
	2016	0.079743	0.031094	0.027718	0.428849	0.079683	0.1194	0.029923
	2017	0.084722	0.031065	0.029176	0.416563	0.085752	0.119276	0.031698
	2018	0.090568	0.037603	0.051724	0.268508	0.092878	0.147267	0.059137
	2019	0.088757	0.036738	0.050652	0.377766	0.090671	0.143561	0.057832
	2020	0.097984	0.038319	0.0594	0.306541	0.101918	0.150329	0.068479
Foshan	2011	0.10945	0.066645	0.039112	0.103553	0.115893	0.271597	0.043789
	2012	0.108979	0.065776	0.039325	0.108962	0.11532	0.267877	0.044049
	2013	0.117239	0.065454	0.04017	0.119603	0.125388	0.266498	0.045076
	2014	0.119656	0.065541	0.04108	0.150056	0.128334	0.266871	0.046184
	2015	0.122393	0.064551	0.042164	0.152388	0.13167	0.262633	0.047503
	2016	0.125114	0.064261	0.042453	0.134355	0.134987	0.261392	0.047855
	2017	0.127699	0.063021	0.04306	0.162624	0.138137	0.256084	0.048593
	2018	0.130767	0.067316	0.063006	0.131825	0.141877	0.274472	0.072867
	2019	0.13097	0.067019	0.063167	0.175866	0.142125	0.273197	0.073063
	2020	0.130707	0.06765	0.069834	0.136625	0.141805	0.275898	0.081176
Huizhou	2011	0.023322	0.011654	0.007219	0.129068	0.01091	0.036176	0.004977
	2012	0.023521	0.011752	0.007355	0.137483	0.011153	0.036596	0.005143
	2013	0.024957	0.012056	0.00771	0.128628	0.012903	0.037894	0.005576
	2014	0.02563	0.01238	0.007771	0.226378	0.013724	0.039282	0.005649
	2015	0.026036	0.012247	0.008039	0.170311	0.014218	0.038716	0.005976
	2016	0.026675	0.012498	0.008205	0.168583	0.014997	0.03979	0.006177
	2017	0.027311	0.012608	0.008434	0.128452	0.015772	0.040258	0.006457
	2018	0.027879	0.012913	0.01107	0.218139	0.016464	0.041565	0.009664
	2019	0.027663	0.012669	0.011159	0.088651	0.016202	0.040518	0.009773
	2020	0.028315	0.012776	0.012112	0.058978	0.016996	0.04098	0.010933
Dongguan	2011	0.226572	0.177094	0.056544	0.146721	0.258657	0.744441	0.065002
	2012	0.22846	0.17857	0.057057	0.118221	0.260958	0.75076	0.065627
	2013	0.23433	0.179053	0.057253	0.166232	0.268113	0.752827	0.065865
	2014	0.244889	0.168313	0.079611	0.208998	0.280983	0.706849	0.093074
	2015	0.244083	0.166547	0.078734	0.196987	0.280001	0.699289	0.092006
	2016	0.245624	0.16672	0.078825	0.153828	0.28188	0.70003	0.092118
	2017	0.249043	0.168255	0.079597	0.14651	0.286047	0.7066	0.093057
	2018	0.251994	0.165947	0.098756	0.115471	0.289644	0.69672	0.116373
	2019	0.253913	0.167254	0.099559	0.148288	0.291983	0.702318	0.117349
	2020	0.253115	0.167432	0.105533	0.182539	0.291011	0.703077	0.124619
Zhongshan	2011	0.109661	0.075664	0.031233	0.19474	0.116151	0.31021	0.034201
	2012	0.110721	0.075993	0.031996	0.211752	0.117443	0.311619	0.03513
	2013	0.116091	0.076851	0.031965	0.197955	0.123988	0.31529	0.035092
	2014	0.118884	0.076777	0.032793	0.250085	0.127393	0.314972	0.036099
	2015	0.119778	0.07556	0.03347	0.179482	0.128483	0.309765	0.036924
	2016	0.122723	0.075956	0.034308	0.190292	0.132072	0.311458	0.037944
	2017	0.12369	0.074579	0.035301	0.175578	0.133251	0.305563	0.039152
	2018	0.125622	0.072886	0.051577	0.192359	0.135606	0.298317	0.058958
	2019	0.12486	0.071995	0.051598	0.172199	0.134677	0.2945	0.058984
	2020	0.123186	0.071129	0.057456	0.190885	0.132637	0.290793	0.066113
Jiangmen	2011	0.026176	0.011502	0.006907	0.002795	0.014388	0.035526	0.004598
	2012	0.025791	0.010953	0.00706	0	0.013919	0.033174	0.004785
	2013	0.026715	0.010438	0.006883	0.05249	0.015046	0.030971	0.004569
	2014	0.026863	0.010065	0.006943	0.074052	0.015227	0.029371	0.004642
	2015	0.027218	0.010035	0.00713	0.067301	0.015659	0.029243	0.00487
	2016	0.027965	0.010044	0.007202	0.06315	0.016569	0.029281	0.004957
	2017	0.028468	0.010165	0.007224	0.054572	0.017183	0.0298	0.004984
	2018	0.029061	0.009071	0.012141	0.083491	0.017905	0.025117	0.010968
	2019	0.028237	0.009062	0.011315	0.068121	0.016901	0.025077	0.009962
	2020	0.028057	0.008834	0.012698	0.031088	0.016682	0.024101	0.011645
Zhaoqing	2011	0.01441	0.003496	0.003129	0.119847	4.65 × 10−5	0.00125	0
	2012	0.014371	0.003477	0.003164	0.117004	0	0.001167	4.35 × 10−5
	2013	0.014736	0.003488	0.003231	0.093962	0.000445	0.001214	0.000125
	2014	0.014936	0.003615	0.003342	0.134519	0.000689	0.001758	0.00026
	2015	0.015069	0.003674	0.003451	0.129408	0.000851	0.002011	0.000392
	2016	0.015275	0.003809	0.003821	0.064575	0.001101	0.002588	0.000842
	2017	0.015415	0.003822	0.003864	0.015933	0.001272	0.002647	0.000895
	2018	0.015723	0.003204	0.005569	0.074488	0.001647	0	0.00297
	2019	0.015436	0.003305	0.005224	0.065997	0.001297	0.000433	0.00255
	2020	0.01585	0.003219	0.005795	0.00872	0.001802	6.34 × 10−5	0.003245
Hongkong	2011	0.304188	0.012512	0.294856	0.951656	0.353265	0.039848	0.355013
	2012	0.308528	0.012512	0.299236	0.94617	0.358554	0.039848	0.360343
	2013	0.313461	0.011006	0.30534	0.927724	0.364568	0.0334	0.36777
	2014	0.316158	0.011872	0.307415	0.934997	0.367856	0.037109	0.370295
	2015	0.316124	0.011128	0.307933	1	0.367813	0.033924	0.370926
	2016	0.316512	0.011223	0.308255	0.975945	0.368287	0.034328	0.371318
	2017	0.320039	0.010186	0.312577	0.967802	0.372585	0.02989	0.376577
	2018	0.321255	0.009828	0.314067	0.844349	0.374068	0.028356	0.37839
	2019	0.318752	0.009592	0.311719	0.8736	0.371016	0.027347	0.375534
	2020	0.315395	0.009601	0.308332	0.834604	0.366924	0.027387	0.371411
Macau	2011	0.739865	0.041918	0.719226	0.572903	0.884322	0.16574	0.871441
	2012	0.764456	0.033868	0.748288	0.643826	0.914297	0.131276	0.906807
	2013	0.784549	0.02927	0.770902	0.519804	0.938789	0.111593	0.934328
	2014	0.824552	0.024129	0.813786	0.51287	0.987549	0.089582	0.986515
	2015	0.834767	0.022444	0.824868	0.658393	1	0.082366	1
	2016	0.823168	0.024932	0.812023	0.67909	0.985862	0.093022	0.984368
	2017	0.803398	0.020884	0.793903	0.654927	0.961764	0.075691	0.962318
	2018	0.775385	0.019266	0.766386	0.552479	0.927619	0.068763	0.928832
	2019	0.778739	0.018968	0.769911	0.612271	0.931707	0.067486	0.933122
	2020	0.788872	0.019266	0.779994	0.76398	0.944058	0.068763	0.945392

. The depreciation rate for industrial fixed assets was established at 11.0, based on Shan’s research, which calculated the stock of fixed assets. Based on the year 2000 pricing comparison, the industrial added value was eliminated from the price change factors.

In the selection of data time nodes, the adverse impact of the global financial crisis caused by the United States in 2008 on China’s industrial development and a series of adverse effects brought by the public financial event on China’s economy, especially the two special administrative regions Hong Kong and Macao were severely impacted. This paper chooses to use the data after 2011 for empirical research, combined with the latest disclosure of the relevant city statistical yearbook, and the year is 2020.

The data sources used in this paper are as follows: The data of Hong Kong is from the Statistics Department of the Government of Hong Kong SPECIAL Administrative Region; the data of Macao is from the Economic Bureau of the Government of Macao Special Administrative Region and the Statistics and Census Bureau of Macao Special Administrative Region; the data of 9 cities in Guangdong Province are from the China Statistical Yearbook 2011–2020.

In terms of data processing, it should be noted that in the quantization process, 1% and 99% of data should be reduced according to the proportion. That is, the data exceeding the specified percentile value in a set of data should be replaced with the adjacent value retained by the specified percentile to eliminate the influence of outliers. Secondly, some index logarithms are processed by natural logarithm, that is, natural logarithm is taken and then regression is done to complete natural logarithm conversion. Finally, data subtraction is carried out to smooth out data fluctuations.

3.1. Degree of Industrial Space Agglomeration Measuring Methods

Bulleted lists look like this: The IA index was constructed using an index of industrial industry sales output value in order to gauge the degree of IA within a certain industry. The following is the formula:

$$\mathrm{IA}={\displaystyle \sum }_{l=1}^m|A_{jl}/A_j-A_l/A|$$

(1)

where j in $\frac{A_{jl}}{A_j}$ shows the regional industrial sector’s share of l industry sales output value; while $A_l/A$ indicates that the national industrial sector’s sales value of l industries account for the total industrial sales proportions. There is an arbitrary threshold IA of (0, 2).

The “Entropy Index (EI)” approach was used to analyze coupled and independent diversification. The EI of workers in major enterprises was developed to reflect independent diversification in 35 double-digit industrial sectors. It was shown that the EI of workers working in sub-industries was connected to their diversity. The formula for this is as follows:

$$urd={\displaystyle \sum }_{l=1}^M{B}_{l}In\left(\frac{1}{V_l}\right)$$

(2)

$$V_l={\displaystyle \sum }_{l=1}^{N_l}{B}_k$$

(3)

$$rd={\displaystyle \sum }_{l=1}^M{B}_l{S}_l$$

(4)

$$S_l={\displaystyle \sum }_{l=1}^{N_l}\frac{B_k}{B_l}In\left(\frac{1}{B_k/B_l}\right)$$

(5)

where l denotes large industry; j denotes suburb industries in large-scale business operations; N denotes the number of subdivision in large-scale business operations; $N_l$ suggests the l number of subdivisions in large-scale business operations; B suggests the employees proportion to the total number of employees in large-scale business operations. Increasing the rd threshold value may result in a greater degree of diversification. urd is a threshold at which diversity begins to grow.

3.2. Graph Neural Network (GNN) for Predicting Industrial Space Agglomeration’s Consequence

The advantage of Graph Neural Network is that it can directly process the graph structure, and at the same time, it can transmit information between nodes and neighbors and update parameters. This method has the ability of feature learning and reasoning in non-sequential sorting. GNN is used to forecast the outcomes of IA. The GNN network can not only handle the challenging issues that other neural network approaches cannot, but it can also make deep learning theory extensively applied in the domains of recommendation systems, graph clustering, and so on. The GNN network structure is the simplest when compared to the architectures of other networks. Most significant operations are completed by using Graph Convolution (GC) and Graph Pooling (GP), which make use of the whole connection and output layers to construct the entire network structure, as shown in Figure 3.

Data matrices are often given to the input layer of a GNN network structure for correlation processing as an input object. The GNN structure then uses operation modules such as GC, GP, and others to perform correlation processing. The output layer is where the impact prediction findings are sent once they’ve been computed. Graph combinators combine each data point’s feature with its neighbors and use the adjacency matrix to process data features. Nonlinear layers may link data feature points.

The graph volume kernel may be used to extract features and the pooling technique can be used to minimize the dimension of the extracted data features in order to achieve data mapping. As a result, the GP, or dimension reduction method, also known as multi-layer clustering, may be applied. It is possible to aggregate and represent the characteristics of distinct local parts by using larger dimensional features in order to make the features taken from any part relevant to other different parts. These algorithms are often used in CNN to determine the feature sizes of distinct portions and are stated in terms of the a peak or a median feature value of the data.

Data features are processed using GNN’s graph convolution technique and impact results are produced. The GP layer handles data in this field; hence it contains many feature points. GNN uses GC to produce numerous graph features and feature clustering to deliver graph feature data of different dimensions. GP operations on graph features should be carried out as quickly as possible, and the GP and higher layers should be connected in an ordered manner. They contain discontinuous feature points formed by GP on graph features that don’t affect pooling, as shown in Figure 4.

When utilizing a GNN model to analyze data features, the primary goal is to optimize the network model’s convolution kernel parameters, and to get the optimal value by repeated rigorous training. As a result, polynomial expansion is used in conjunction with convolution kernel operations in this research. As network model training is reinforced, optimizing convolution kernel parameters becomes optimizing polynomial coefficients. As a result, the polynomial coefficients may be optimized depending on the results of past model training. The following is an expression of the loss function used in this study as a standard for training and evaluating network model parameters.

Denote $G=\left(N,E\right)$ as a graph model. Where N represents vertex set, and E represents edge set. $ne\left[n\right]$ represents the adjacent vertex of vertex n, co[n] represents the edge of associated vertex n. Parameter function f_w is denoted as the local transformation function, which describes the dependence of vertex n and its neighborhood. g_w is defined as a local output function.

$$q_y=f_w\left(l_n,l_{co\left[n\right]},x_{ne\left[n\right]},l_{ne\left[n\right]}\right)$$

(6)

$$O_n=g_w\left(x_n,l_n\right)$$

(7)

where $l_n$, $l_{co\left[n\right]}$, $x_{ne\left[n\right]}$, $l_{ne\left[n\right]}$ respectively represent the attributes of vertex n, the attributes of associated edges, the states and attributes of adjacent vertices. The definition of neighborhood can be set freely according to the actual situation. The parameters of transformation function and output function may depend on different given vertex n. For non-positional graphs

$$x_n={\displaystyle \sum }_{u\in ne\left[n\right]}{h}_w\left(l_n,l_{\left(n,u\right)},x_u,l_u\right)$$

(8)

Therefore, the iterative calculation process of state and output value is as follows:

$$x_n\left(t+1\right)=f_w\left(l_n,l_{co\left[n\right]},x_{ne\left[n\right]},l_{ne\left[n\right]}\right)$$

(9)

Functions $f_w$ and $g_w$ can be implemented using feedforward neural networks.

$$k=-\frac{1}{n}{\displaystyle \sum }_y{x}_{y}In e_y$$

(10)

As seen above, there is a correlation between the predicted data x and the amount of samples in an input dataset x after it has been processed by the GNN model. When there is a substantial discrepancy between the impact result and the actual value, the loss function may be utilized to rapidly tune the GNN parameters. Backward and forward processing are two of the primary aspects of the GNN network model technique employed in this study. The GNN network model is used to process the data characteristics. With this method, the data structure characteristics are first processed using the Fourier transform before being sent into the data convolution process for further processing. The convolution layer’s processing function may be summarized as follows:

$$z^2=\lambda \left(x_y,j+f\right)=\lambda \left({\displaystyle \sum }_l^{i}g{\omega }_{l,j}{z}_y,j+f\right)$$

(11)

where the activation function is denoted by λ which is employed by convolution, z² denotes the output result of the data feature after convolution, x_y, j represents the output feature after convolution operation, f and constant parameter of convolution. For GP operations, it is necessary to cluster the input data’s feature points and then turn them into one-dimensional data features using the GP layer of the GNN model. Convolution processing is used to feed one-dimensional graph characteristics back into subsequent layers, completing the extraction of graph features from a network model’s data. The GNN model’s input object is a spliced and integrated one-dimensional graphic feature vector, which reduces all graphic characteristics and transforms them into one-dimensional vectors. Splicing and integrating graph feature vectors in GNN model’s complete connection layer are expressed as follows

$$z^{js}=\lambda \left(q^{js}{z}^{2c}+f^{js}\right)$$

(12)

The complete connection layer’s activation function is $\lambda ()$, $z^{2c}$ is the pooling layer’s data feature processing result, $q^{js}$ is the layer’s constant parameter, and $f^{js}$ is the spliced and integrated data feature output. The activation function modifies the necessary model parameters, and the GNN model processing yields the output results. Figure 5 depicts the representation of the algorithm’s onward movement.

The optimum model parameters and weights for GNN’s reverse processing technique are primarily derived via network model learning, training, and optimization. Using a forward processing approach, the loss function is obtained in a GNN model, and the error value is then calculated using the loss function, which is then sent back from the lower layer to the top layer. It is then utilized to improve the GC settings using a gradient approach, as seen above. Preprocessing the input data is done using a network model that takes the gathered data samples as inputs. Using a visual feature adjacency matrix, the model’s output may be brought closer to the prediction objective than ever before. By using graph convolution, the graph aspects of the GC process are examined. Clustering is used to classify features in the graph pool layer using the cluster algorithm.

The GNN network model is validated using the experimental test results, and the output results are obtained using the forward processing technique. In order to ensure that the GNN network model is continuously optimized, it trains a large number of sample data and utilizes the new model to process the data samples of the test set repeatedly until the optimum prediction results are produced. Using the GNN reverse processing technique and network training criteria, the model output may be as near to the actual data samples as possible. It is necessary for the network model to be trained and learned again if it fails to meet the predetermined standard of error. If the network model doesn’t match these conditions, it won’t be trained and its final trained model will be utilized for data processing. Figure 6 shows GNN training.

3.3. Panel Tobit Regression Model (PTRM)

The GNN model was utilized to compute industrial economic growth, and the Stata 15.0 program was used to assess the influence of IA on the PTRM. To further understand how IA affects GBA’s economic development, the random effect PTRM was used after the LR test revealed a significant p-value. Existing study on the impact of IA on economic development has yet to achieve consensus, thus the linear and nonlinear connections between them were independently studied. The following is an example of a regression model:

$$xjt=\propto +{\beta }_{jt}+\gamma y_{jt}+{\epsilon }_{jt}$$

(13)

where $xjt$ is the explained variable, which reflects industrial economic development for j provinces over t, ${\beta }_{jt}$ is the explanatory variable’s function form, $\propto$ and $jt$ are intercept and random disturbance factors, and $\gamma y_{jt}$is a control variable.

In addition to the location of industrial agglomerations, current research suggests that regional development, energy structure, openness to the outside world, technical advancement, environmental regulatory rigor, and the degree of marketization all impact economic growth.

3.4. Coupling Coordination Model Establishment

To be more precise, the “Coupling Degree (CD)”, “Coordination Degree (COD)”, and “Coupling coordination degree (CCOD)” in coupling coordination must be calculated.

The interaction degree between two subsystems is referred to as the “coupling degree”. It’s a common way to measure the power of a group’s combined efforts. The coupling degree mode structured as follows:

$$C=2{\left[\frac{V_1\times V_2}{\left(V_1+V_2\right)\times \left(V_1+V_2\right)}\right]}^{\frac{1}{l}}$$

(14)

where C stands for the CD, l for the adjustment coefficient, and the usual number of subsystems is 2. V₁ and V₂ represent the two subsystems’ performance levels, and the closer V₁ or V₂ is to 1, the better the two subsystems’ performance is. In every case, the CCD falls somewhere in the range of zero to one. Whereas a lower C value indicates a tighter connection, a larger C value indicates an open space between the two systems. There are four types of coordination status: low coupling (C = 0), antagonism (C = 0.3–0.5), running-in (0.5–0.8), and highly coupling (0.8–1).

When evaluating a system’s coupling, it’s crucial to keep in mind the COD, which measures how the performance levels of the two subsystems interact and affect each other. It is possible to express the COD in this way:

$$T={\displaystyle \sum }_{n=1}^m{\beta }_n{V}_n$$

(15)

where T stands for both the COD existing and the stage of development of the system. It is possible for it to indicate the degree to which the indicators contribute to the level of coupling and coordination within the system. ${\beta }_n$ stands for the coefficient whose value has not yet been established. We found that urban–industrial land use efficiency and highway network accessibility contribute equally to the total system. Urban–industrial land and the highway network are mutually advantageous, but none is a driving element for the other, hence ${\beta }_n$ = 0.5 when n = 2.

Although the CD may represent the interaction connection between two subsystems, it is difficult to show how the significant development interacts. CCOD, as stated as follows: Previous researches have advocated its inclusion because of this.

$$E=\sqrt{C\times T}$$

(16)

The value [0, 1] is the range for the CCOD is E. The CD and CCOD between the systems is a useful measuring metric since it shows how tightly the systems are intertwined. This was done based on earlier research, which resulted in eleven layers of coupling coordination. The CCOD levels and their accompanying requirements is show in

Table 2. CCOD levels and their accompanying requirements.

Coupling Coordination Type	Coupling Coordination Level	Value
High	0.80 ≤ E ≤ 0.89	Good
	0.90 ≤ E < 1.00	High quality
Good	0.60 ≤ E ≤ 0.69	Basic
	0.70 ≤ E ≤ 0.79	Moderate
Moderate	0.40 ≤ E ≤ 0.49	Imbalance
	0.50 ≤ E ≤ 0.59	Coordinate
Low	0.00 < E ≤ 0.09	Extreme imbalance
	0.10 ≤ E ≤ 0.19	Serious imbalance
	0.20 ≤ E ≤ 0.29	Moderate mbalance
	0.30 ≤ E ≤ 0.39	Mild imbalance

. The algorithm pseudo code provided is shown in Algorithm 1.

Algorithm 1. The proposed algorithm pseudo code

The Deep Graph Learning-Enhanced Assessment Method

1. Initialize w

2.  Build a graph model according to Equations (6)–(10). 3.  x = Forward(w); 4.  repeat 5.     $\frac{\partial e_w}{\partial w}=\mathrm{Backward}\left(x,w\right)$ 6.    $w=w-\lambda ·\frac{\partial e_w}{\partial w}$

7.    x = Forward(w) 8.    until (a stopping criterion); 9.   return w;

10.  End

11. Forward(w)

12.  Initialize x(0), t-0;

13.  Repeat

14.   $x\left(t+1\right)=F_w\left(x\left(t\right),l\right);$

15.   $t=t+1$;

16.  Until $\Vert x\left(t\right)-x\left(t-1\right)\Vert \le {\epsilon }_f$

17.  return x(t)

18. End

19. Backward(x, w)

20.  $o=G_w\left(x,l_N\right)$

21.  $A=\frac{\partial F_w}{\partial x}\left(x,l\right)$

22.   $b=\frac{\partial e_w}{\partial o}·\frac{\partial G_w}{\partial x}\left(x,l_N\right)$

23.  Initialize z(0), t = 0;

24.  Repeat

25.   $z\left(t\right)=z\left(t+1\right)·A+b$

26.   $t=t-1$

27.  Until $〚z\left(t-1\right)-z\left(t\right)〛\le {\epsilon }_b$

28.  Return $\frac{\partial e_w}{\partial w}$

29. End

4. Results and Discussion

This strategy is tested using the Origin Pro and MATLAB software. Simulation environment: Windows 10, Intel i7-8565U, 8GB RAM. The number of hidden layer nodes is the only parameter that needs to be specified when using the classer. We compare the accuracy of convolutional neural network (CNN), recurrent neural network (RNN), deep trust network (DBN) and the algorithm in this paper under different hidden layer nodes.

As shown in Figure 7, with the increase of the number of hidden layer nodes, the curve of recognition accuracy basically follows the trend of rising first and then falling, and reaches a relatively high recognition rate when the number of hidden layer nodes is 3000. This is because the feature expression ability of the hidden layer increases with the number of nodes. When the number of hidden layer nodes reaches about 3000, its expression ability reaches the optimal level. Increasing the number of hidden layer nodes will lead to performance degradation due to over fitting.

In the model proposed in this paper, there are two most important parameters: regularized least squares calculation parameters and hidden layer nodes. In order to analyze the sensitivity of these two parameters, two independent experiments were conducted. Figure 8 describes the trend of the system’s recognition accuracy with the regularized least squares calculation parameters when the number of hidden layer nodes is fixed. Figure 9 describes the change trend of the system’s recognition rate with the number of hidden layer nodes after fixing the value of regularized least squares calculation parameters.

It can be seen from Figure 8 that the curve trends corresponding to different parameters $\lambda$ are basically the same, because with the increase of the number of hidden layer nodes, the feature expression ability of the model also increases; When the number of hidden layer nodes is around 3000, the recognition efficiency is the highest; When the number of hidden layer nodes continues to increase, the over fitting phenomenon occurs, and the model performance starts to decline. According to the trajectory diagram, when a = 10,000, the identification performance of the system reaches the best. This can also be seen from Figure 9.

The proposed method’s behaviour is evaluated using metrics like a) Accuracy b) Recall and c) F1-score. Four elements will be considered in this evaluation: “True Positive”, “True Negative”, “False Positive”, and “False Negative” are all abbreviated as t_p, t_n, f_p and f_n respectively. Among, t_p denotes that the effect of IA on growth in the economy is positive, and it is really positive, t_n denotes that the effect of IA on growth in the economy is negative, and it is really negative, f_p denotes that the effect of IA on growth in the economy is negative, and it is really negative, yet it is a normal image, and f_n denotes that the effect of IA on growth in the economy appears to be positive, yet it is a negative.

Accuracy determines the impact are classified successfully. It decides how closely the outcomes match the initial outcome

$$Accuracy=\frac{t_p+t_n}{t_p+t_n+f_p+f_n}$$

(17)

The recall, also known as sensitivity, is the proportion of total significant samples collected.

$$Recall=\frac{t_p}{t_p+f_n}$$

(18)

The F1-Score is the balanced average of Precision and Recall. True positives and false negatives are included into this score.

$$F1-score=\frac{2\times precision\times recall}{precision+reccall}$$

(19)

Figure 10 compares the “accuracy”, “recall” and “f1-score” of existing with the proposed GNN. It depicts that the suggested method is superior to the existing methods. The three forms of agglomeration in GBA were assessed using Equations (1)–(5). Figure 11, Figure 12 and Figure 13 illustrate the specific outcomes. When looking at the whole GBA, it is clear that the temporal patterns of various forms of agglomeration have diverged between 2011 and 2020. The average of the eleven provinces in GBA shows a slightly increasing trend in IA. GBA’s degree of MIA and SIA shows a tendency of slightly increasing trend.

Figure 14a–c shows that the overall trend of the coupling coordination degree in GBA has decreased during 2020. Based on the findings, the following policy suggestions are made: first, IA cannot be overlooked in fostering economic development. It’s vital to create the IA region, grant industrial firms in the agglomeration area regulatory favours, build high-standard infrastructure, and attract more advanced industrial enterprises. Only with the qualities can the agglomeration area’s competitiveness be increased, and the industrial agglomeration effect is effectively used. IA needs free market development and government regulation. To attract additional capital and labour to the industrial sector, policies and the investment climate must be improved. At the same time, there should be an increase in investments made in research and development in the fields of science and technology in order to encourage an increase in the amount of scientific and technical innovation that occurs in the IA region. The input of both capital and labour, as well as advances in technical innovation, are essential driving factors for the development of the regional economy.

5. Conclusions

This research gathers data from eleven cities in GBA from 2011 to 2020 in order to better understand the agglomeration types and their impact on economic development in the area. It was suggested in this research that GNN and Panel Tobit Regression models would be used to analyze how the region’s economic growth was influenced by three primary agglomeration configurations. Economic development in GBA’s eleven cities is slightly increased by industry agglomeration, “U” curve in SIA, and has a slight increase on MIA, according to the study’s findings. In this paper, we use the depth map learning enhancement assessment method to assess the economic development of the city. This technology is not only applicable to GBA regions, but also widely used in other regions. This method focuses on the relationship between data and is good at linking between nodes. However, this method has no universal and effective graphic generation method for unstructured scenes. Therefore, in further research, we will focus on the measurement indicators and influencing factors of industrial upgrading. At the same time, it will also be committed to studying how the coordination of cross regional economic expansion contributes to the formation of IA.