Modeling of the ecological economic activity based on machine learning

Abstract

The eco-economic activity modeling is an effective method to analyze the eco-economic system. From the existing models, it can be seen that the disadvantages of eco-economic activity modeling are that the model evaluation accuracy is not high, and the system stability is poor. In order to improve the evaluation effect of the ecological economic activity, based on the machine learning algorithm, this study establishes a PNN evaluation model based on the probabilistic neural network classification principle. Moreover, in this study, a certain number of learning samples are generated by random interpolation of evaluation index standards, and then Matlab software is used to simulate the training and test of the model, and the feasibility and effectiveness of the model are verified by statistical indicators. In addition, this study combines the actual case to analyze the performance of the model and analyze the test results by statistical analysis methods. The research results show that the model proposed in this study has certain effects and high stability.

Keywords

Machine learning ecological economy economic activity simulation analysis

1 Introduction

Cities are the focus of global development and the political, economic, and cultural center of human participation in social activities. The development of cities is an important symbol of the development and progress of social civilization and plays a huge role in promoting the development of human society. The rapid development of the social economy has caused a large number of people to gather in cities and brought a wealth of material spiritual civilization, thereby continuously accelerating the process of urbanization. However, cities have gradually become a gathering point of contradictions in this accelerated process. Humans have consumed a lot of resources and changed the geological and geomorphological environment and climate conditions in the development and construction of cities. Due to the fragility, irreversibility and limited resources of the city itself, the growing urban population and the large amount of resource consumption under the limited environmental capacity have caused many cities to suffer from “urban diseases", such as traffic congestion, housing and land tension, environmental pollution, lack of resources, urban heat islands, etc., which has caused unprecedented challenges to the urbanization process [1]. Under such a grim reality background, people began to think about the future development model of cities and are committed to seeking a resource-saving and environment-friendly development approach to achieve the benign and coordinated development of the economy, society and ecological environment. Therefore, the concept of ecological city came into being. The Third Plenary Session of the Eighteenth Central Committee of the Party emphasized: “ Focusing on building a beautiful China and deepening the reform of the ecological civilization system, accelerating the establishment of an ecological civilization system, and improving the national land space development, resource conservation, and ecological environmental protection institutional mechanisms to promote the formation of a new pattern of modernization of the harmonious development of man and nature “[2].

As a new development model, eco-city construction is a development path for the transformation, green development, characteristic development and integrated development of the Yangtze River Economic Belt. Moreover, it is an important way and an effective way to realize the development of new realms and the formation of a new pattern of development in the cities along the Yangtze River Economic Belt in the course of comprehensively deepening reforms. At present, the research on the construction of ecological cities has become a research hotspot in various countries. However, the research on the construction of ecological cities in China is still in its infancy, and there is no systematic theory of ecological city construction research. Moreover, it pays too much attention to the theoretical level, and it is not strong in guiding the construction of ecological cities. Therefore, the substantive ecological city has not yet been established in China [3].

It is necessary to establish a scientific, practical and feasible evaluation index system for eco-city construction that can reflect the connotation of eco-city to reasonably measure the current status of the construction of ecological cities in the Yangtze River Economic Belt, find problems and solve problems in a timely manner, improve the construction and management of ecological cities along the economic belt, and promote the ecological construction of cities. Moreover, it is necessary to deeply analyze the connotation of the eco-city and its importance in practical application according to the development status of the eco-city in the Yangtze River Economic Belt. Then, we need to reasonably select index screening methods to build a set of evaluation index system for eco-city construction. Moreover, we need to use a scientific and objective comprehensive evaluation method for horizontal and vertical comparison to obtain the ecological degree of major cities in the Yangtze River Economic Belt, and to analyze the development trend of the ecological city construction in the Yangtze River Economic Zone, the problems existing in the process and propose countermeasures and suggestions to provide a certain theoretical basis for the construction of the ecological city in the Yangtze River Economic Belt.

2 Related work

The literature [6] believes that eco-city is an ideal urban model. Under this model, humanities and nature, social economy and technology are fully integrated, and material resources, natural energy and industrial information are used efficiently. At the same time, it maximizes human creativity and productivity, maximizes the protection of the quality of the natural environment and the physical and mental health of the residents, and is an efficient, harmonious, ecologically virtuous circle of ideal human settlements. The literature [7] summarizes the principles of eco-city in detail. The literature [8] discusses the significance and principles of building an ecological city and proposes how to build Berkeley into an ecological city. The literature [9] put forward the concept of “eco-city” and believes that eco-city is actually a synthesis of various theories to reform and solve social and urban problems. With the convening of the 5th International Conference on Eco-Cities and other research conferences on eco-city construction in the same period, the theoretical concept of eco-city construction has become popular, which expands the impact of eco-city construction and greatly promotes the popularization and development of eco-city construction practice research worldwide. As for the evaluation index system of the sustainable development of eco-city construction, there have been relatively mature and comprehensive studies abroad, whose scope involves economic, social, resource and environmental aspects. At the same time, the research also focuses on solving key issues in urban development, which is an important reference for the study of eco-city indicator systems. Specifically, by searching a large number of foreign documents, it is concluded that the current evaluation index system on sustainable construction and development of ecological cities mainly includes six categories [10]: (1) Human occupation of net primary productivity (HANPP); (2) Life footprint (EF) and ecological carrying capacity (EC); (3) Environmental vulnerability index (EVI); (4) Environmental sustainability index (ESI) (5) Environmental performance index (EPI); (6) Ecosystem Health Index (EHI). The literature [11] puts forward the concept of loading capacity indicators and parameters and the evaluation index group of the eco-city about “results, behavior, capacity", and believes that in the construction planning of eco-city, the capacity index group should be satisfied first. Under the framework of the “Press-State-Response (PSR)” conceptual model, the Economic Cooperation and Development Organization has designed a set of indicator systems with environmental sustainability indicators at the core. This type of indicator system does not appear in the form of the title of “ecological city", but its influence is very extensive. The United Nations Commission on Sustainable Development has established a complete set of indicators for sustainable development by referring to the 134 indicators in the Work Program on Indicators of Sustainable Development (ISD) based on the above conceptual model. Subsequently, Peter Newman improved it and obtained a total of 44 indicators involving five major items including economy, population, transportation, environmental quality, and livability [12]. In addition, the representative eco-city evaluation index system abroad is constructed by the “Eco-city Project” funded by the European Union. The indicator system includes social economy, urban structure, urban transportation, energy and material flow. Moreover, a number of sub-indicators are set under each evaluation criterion, and the scores of the evaluation indicators are divided into five levels from A (best) to E (worst). When summarizing the characteristics of the eco-city evaluation index system, the literature [13] believes that the foreign eco-city evaluation index system mainly relies on planning and planning (projects), focusing on construction practice and the formulation and realization of specific targets in several key aspects. Generally speaking, the evaluation index system of eco-city construction in foreign countries is more concrete, and it focuses on specific aspects.

The literature [14] regards the city as a “economy-society-nature” complex ecosystem, and applies sensitivity models and system control theory to analyze the eco-city system from the aspects of structure and function. The literature [15] proposes and evaluates the evaluation index system of urban ecosystem from three aspects: economic development, social life and ecological environment. The literature [16] builds an evaluation index system for ecological cities from three aspects: social ecosystem, economic ecosystem, and natural ecosystem. The index system of eco-city construction proposed in the literature [17] divides the criterion layer into three major categories of 64 single indicators. Moreover, it starts from the hierarchical index system of social ecological civilization degree, economic ecological efficiency and natural ecological harmony degree to combine specific quantitative indicators and highly comprehensive goals. The literature [18] builds 60 indicators from three subsystems related to economic ecology, social ecology and environmental ecology, and evaluates the capacity of ecological city construction in Sichuan based on the principle of principal component analysis.

Relevant scholars have also done a lot of research in the selection of evaluation indicators for the construction of ecological cities, which mainly includes subjective judgment methods such as Delphi method, AHP method, Vague set method, mathematical statistical screening methods such as correlation coefficient method, principal component analysis method, stepwise regression method, and includes knowledge mining screening methods such as gray correlation analysis, rough set analysis, neural network analysis [19]. With the development of eco-city construction theory and practice, the index screening method of the evaluation index system has gradually become the focus of research.

3 Parzen window function

The traditional Bayes classifier needs to estimate the prior probability P (ω_i) and the class conditional probability density P(x|ω_i) through training samples. However, it is usually impossible to accurately estimate P(x|ω_i) by the parameter method. Therefore, it is generally chosen to use non-parametric estimation methods to estimate it. Among them, Parzen window function is one of the non-parameter estimation methods. Then, the estimate of P(x|ω_i) obtained by the Parzen window function is as follows [20]: $\begin{matrix} f_{A} (x) = \frac{1}{{(2 π)}^{d / 2} σ^{d} m} \times \\ \sum_{i = 1}^{m} exp [- \frac{{(x - x_{Ai})}^{T} (x - x_{Ai})}{2 σ^{2}}] \end{matrix}$ (1)

In the above formula, the dimension of the training sample is d. Among them, m samples belong to class A, and x_Ai represents the i-th training sample of class A, and σ represents the smoothing parameter.

The principle of the Parzen window function is as follows: The probability that a certain vector X falls into the region Rn is assumed to be: $P = \int_{Rn} p (x^{'}) {dx}^{'}$ (2)

From this, we can estimate the probability density function p (x) according to the probability P. If it is assumed that n samples x₁, x₂, ⋯ , x_n are all extracted by independent distribution of p (x), then it can be seen that the probability of k samples falling into the region Rn will obey the binomial theorem: $P_{k} = (\begin{matrix} n \\ k \end{matrix}) P^{k} {(1 - p)}^{n - k}$ (3)

E [k] = nP is the expectation of k, and the binomial distribution of k exhibits very obvious peaks above and below the mean. Therefore, k/n is an estimate of the probability p. If we assume that p (x) is continuous and the region Rn is small enough, then: $\int_{Rn} p (x^{'}) {dx}^{'} \approx p (x) V$ (4)

In the above formula, x is a point, and V is the volume contained in the region Rn. Through formulas (3) and (4), the estimated formula for p (x) can be obtained as: $p (x) \approx \frac{k / n}{V}$ (5)

When we want to estimate the probability of the sample point x, we need to determine a small area Rn that can surround x. That is, a d-dimensional hypercube is created as Rn, where the side lengths h and k are the dimensions of the feature space. Then, the volume V of Rn can be expressed as: $V = h^{d}$ (6)

If we want to determine whether the training sample x_k can fall within Rn, then we need to check each component value of the vector x - x_k. If each component value is smaller than h/2, the sample is within Rn. However, if each component value is larger than h/2, the sample is outside Rn. In order to calculate the number K of training samples falling within Rn, the window function can be defined as: $ϕ (u) = {\begin{matrix} 1, | u_{j} | ⩽ 1 / 2, j = 1, 2, \dots, d \\ 0, otherwise \end{matrix}$ (7)

If u = (x - x_k)/h, formula (7) becomes: $ϕ ((x - x_{k}) / h) = {\begin{matrix} \begin{matrix} 1, {| (x - x_{k}) |}_{j} ⩽ h / 2, \\ j = 1, 2, \dots, d \end{matrix} \\ 0, otherwise \end{matrix}$ (8)

Then, further, there are: $k = \sum_{k} ϕ (\frac{x - x_{k}}{h})$ (9)

By substituting formula (9) into formula (5), the following results are obtained: $p (x) \approx k / nV = \frac{1}{nV} \sum_{k} ϕ (\frac{x - x_{k}}{h})$ (10)

This is the Parzen window estimation method (Ma Yunyong, 2008).

If the training sample of class A is assumed to be x_Ak, and λ (n) is some function of n, then the Parzen window estimate of f_A (x) of PNN can be written as: $f_{A} (x) = \frac{1}{n λ (n)} \sum_{k} ϕ (\frac{x - x_{Ak}}{λ (n)})$ (11)

Next, according to the Parzen window estimation method, f_A (x) is estimated, and the progressive unbiasedness of ${\hat{f}}_{A} (x)$ is proved (Zhao Jiabai, 2007). Then, from formula (10), we can obtain: ${\hat{f}}_{A} (x) = \frac{1}{{nV}_{n}} \sum_{k} ϕ (\frac{x - x_{Ak}}{h_{n}})$ (12)

Prove: Know $\begin{matrix} E [f_{A, n} (x)] = E [\frac{1}{n λ (n)} \sum_{k} ϕ (\frac{x - x_{Ak}}{λ (n)})] \\ = \int_{- \infty}^{+ \infty} \frac{1}{λ (n)} ϕ (\frac{x - y}{λ (n)}) f_{A} (y) dy \end{matrix}$ (13)

Definition: $g_{n} (x) = \int_{- \infty}^{+ \infty} \frac{1}{λ (n)} ϕ (\frac{y}{λ (n)}) f_{A} (x - y) dy$ (14)

Then, $\begin{matrix} g_{n} (x) - f_{A} (x) \int_{- \infty}^{+ \infty} ϕ (y) \\ = \int_{- \infty}^{+ \infty} \frac{1}{λ (n)} ϕ (\frac{y}{λ (n)}) [f_{A} (x - y) - f_{A} (x)] dy \end{matrix}$ (15)

Then: $\begin{matrix} | g_{n} (x) - f_{A} (x) \int_{- \infty}^{+ \infty} ϕ (y) dy | ⩽ \\ max_{| y | ⩽ δ} [f_{A} (x - y) - f_{A} (x)] \int | z | ⩽ δ / λ (n) ϕ (z) dz \\ + \int | y | ⩾ δ \frac{y}{λ (n)} \frac{| f_{A} (x - y) |}{y} ϕ (\frac{y}{λ (n)}) dy + | f_{A} (x) | \\ \int | y | ⩾ δ \frac{1}{λ (n)} ϕ (\frac{y}{λ (n)}) dy ⩽ \\ max_{| y | ⩾ δ} [f_{A} (x - y) - f_{A} (x)] \int_{- \infty}^{+ \infty} | ϕ (z) | dz + \\ \frac{1}{δ} sup_{| z | ⩾ δ / λ (n)} | z ϕ (z) | \int_{- \infty}^{+ \infty} | f (y) | dy + | f_{A} (x) | \\ \int | z | ⩾ δ / λ (n) ϕ (z) dz \end{matrix}$ (16)

When n approaches ∞, δ approaches 0, and the right side of the above formula approaches 0, then the above formula can be written as: $\underset{n \to \infty}{Iim} g_{n} (x) = f_{A} (x) \int_{- \infty}^{+ \infty} ϕ (y) dy$ (17)

Therefore, there are: $\begin{matrix} \underset{n \to \infty}{Iim} E [f_{A} (x)] = f_{A} (x) \int_{- \infty}^{+ \infty} ϕ (y) dy \\ \underset{n \to \infty}{Iim} E [f_{A} (x)] = f_{A} (x) \end{matrix}$ (18)

4 Probabilistic neural network model

The basic principle of the PNN model is to use Parzen window function estimation to obtain the conditional probability density of the class under the Bayes theorem and Bayes decision rules based on minimum risk, so as to obtain the class unit with the largest output. According to the characteristics of the PNN network structure, we can classify it as a forward network interconnected in the layer, which is similar to the forward network structure in terms of overall structure. Its structure is shown in Fig. 1:

Fig. 1

PNN network structure.

Input layer: The number of neurons is the dimension of feature vector. Its role is to input the value of the training sample, that is, to pass the feature vector to the network;

Pattern layer: The number of neurons is equal to the number of training samples. Its role is to calculate the matching relationship between the input vector and each category in the training set. After inputting x, the input-output relationship between the neurons in the j-th layer corresponding to the i-th pattern is determined by formula (19):

$f_{ij} (x) = \frac{1}{{(2 π)}^{d / 2} σ^{d}} exp [- \frac{{(x - x_{ij})}^{T} (x - x_{ij})}{2 σ^{2}}]$ (19)

Summation layer: The number of neurons is the number of categories of the sample. The outputs of the neurons of the model layer belonging to the same class are added and then averaged: $f_{{iN}_{i}} (x) = \frac{1}{N_{i}} \sum_{j = 1}^{N_{i}} f_{ij} (x)$ (20)

Output layer: The number of neurons is 1, that is, the final output of a certain category.

The following describes the learning algorithm steps according to the 4-layer probabilistic neural network structure (He Shudi, 2014):

Step 1: Normalization. That is, the input sample matrix is normalized. We assume that the input matrix is: $X = [\begin{matrix} x_{11} & x_{12} & \dots & x_{1 n} \\ x_{21} & x_{22} & \dots & x_{2 n} \\ \dots & \dots & \dots & \dots \\ x_{m 1} & x_{m 2} & \dots & x_{mn} \end{matrix}] = [\begin{matrix} X_{1} \\ X_{2} \\ \dots \\ X_{m} \end{matrix}]$ (21)

In the above formula, x represents a total of m training samples X_i, (i = 1, 2, ⋯ , m), and X_i has n attributes. If we want to find the normalization coefficient, firstly, we need to calculate the matrix B: $B^{T} = [\begin{matrix} \frac{1}{\sqrt{\sum_{k = 1}^{n} x_{1 k}^{2}}} & \frac{1}{\sqrt{\sum_{k = 1}^{n} x_{2 k}^{2}}} & \dots & \frac{1}{\sqrt{\sum_{k = 1}^{n} x_{mk}^{2}}} \end{matrix}]$ (22)

In the following formula, C represents the normalized learning matrix, where “^*” means that the corresponding elements of the matrix are multiplied, that is: $C_{m \times n} = B_{m \times 1} {[11 \dots 1]}_{1 \times n}^{*} X_{m \times n}$ (23)

Step 2: The normalized X_i, (i = 1, 2, ⋯ , m) is passed into the PNN pattern layer. $\begin{matrix} C_{m \times n} = [\begin{matrix} \frac{x_{11}}{\sqrt{\sum_{k = 1}^{n} x_{1 k}^{2}}} & \frac{x_{12}}{\sqrt{\sum_{k = 1}^{n} x_{1 k}^{2}}} & \dots & \frac{x_{1 n}}{\sqrt{\sum_{k = 1}^{n} x_{1 k}^{2}}} \\ \frac{x_{21}}{\sqrt{\sum_{k = 1}^{n} x_{2 k}^{2}}} & \frac{x_{22}}{\sqrt{\sum_{k = 1}^{n} x_{2 k}^{2}}} & \dots & \frac{x_{2 n}}{\sqrt{\sum_{k = 1}^{n} x_{2 k}^{2}}} \\ \dots & \dots & \dots & \dots \\ \frac{x_{m 1}}{\sqrt{\sum_{k = 1}^{n} x_{mk}^{2}}} & \frac{x_{m 2}}{\sqrt{\sum_{k = 1}^{n} x_{mk}^{2}}} & \dots & \frac{x_{mn}}{\sqrt{\sum_{k = 1}^{n} x_{mk}^{2}}} \end{matrix}] \\ = [\begin{matrix} C_{11} & C_{12} & \dots & C_{1 n} \\ C_{21} & C_{22} & \dots & C_{2 n} \\ \dots & \dots & \dots & \dots \\ C_{m 1} & C_{m 2} & \dots & C_{mn} \end{matrix}] \end{matrix}$ (24)

Step 3: The pattern distance is calculated. That is, the distance between the sample matrix to be classified and the corresponding elements in the learning matrix is calculated. If it is assumed that a matrix composed of P n-dimensional vectors is called a sample matrix to be classified, it can be expressed as: $D = [\begin{matrix} d_{11} & d_{12} & \dots & d_{1 n} \\ d_{21} & d_{22} & \dots & d_{2 n} \\ \dots & \dots & \dots & \dots \\ d_{p 1} & d_{p 2} & \dots & d_{pn} \end{matrix}] = [\begin{matrix} D_{1} \\ D_{2} \\ \dots \\ D_{p} \end{matrix}]$ (25)

The Euclidean distance is calculated: That is, the Euclidean distance between the sample vector d_i and each normalized training sample c_j is calculated.

$\begin{matrix} E_{p \times m} = \\ [\begin{matrix} \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{1 k} - \\ c_{1 k} \end{matrix} |}^{2}} & \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{1 k} - \\ c_{2 k} \end{matrix} |}^{2}} & \dots & \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{1 k} \\ - c_{mk} \end{matrix} |}^{2}} \\ \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{2 k} - \\ c_{1 k} \end{matrix} |}^{2}} & \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{2 k} - \\ c_{2 k} \end{matrix} |}^{2}} & \dots & \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{2 k} \\ - c_{mk} \end{matrix} |}^{2}} \\ \dots & \dots & \dots & \dots \\ \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{pk} - \\ c_{1 k} \end{matrix} |}^{2}} & \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{pk} - \\ c_{2 k} \end{matrix} |}^{2}} & \dots & \sqrt{\sum_{k = 1}^{n} {| \begin{matrix} d_{pk} \\ - c_{mk} \end{matrix} |}^{2}} \end{matrix}] \\ = [\begin{matrix} E_{11} & E_{12} & \dots & E_{1 m} \\ E_{21} & E_{22} & \dots & E_{2 m} \\ \dots & \dots & \dots & \dots \\ E_{p 1} & E_{p 2} & \dots & E_{pm} \end{matrix}] \end{matrix}$ (26)

In the above formula, E_ij represents the distance between the i-th sample D_i to be classified and the j-th learning sample C_j.

Step 4: The neurons of the model layer Gaussian function are activated. Usually, we choose the Gaussian function with standard deviation σ = 0.1. Then, the initial probability matrix obtained after processing at the model layer is:

$\begin{matrix} P = [\begin{matrix} e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{1 k} - c_{1 k} |}^{2}}}{2 σ^{2}}} & e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{1 k} - c_{2 k} |}^{2}}}{2 σ^{2}}} & \dots & e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{1 k} - c_{mk} |}^{2}}}{2 σ^{2}}} \\ e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{2 k} - c_{1 k} |}^{2}}}{2 σ^{2}}} & e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{2 k} - c_{2 k} |}^{2}}}{2 σ^{2}}} & \dots & e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{2 k} - c_{mk} |}^{2}}}{2 σ^{2}}} \\ \dots & \dots & \dots & \dots \\ e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{pk} - c_{1 k} |}^{2}}}{2 σ^{2}}} & e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{pk} - c_{2 k} |}^{2}}}{2 σ^{2}}} & \dots & e^{\frac{\sqrt{\sum_{k = 1}^{n} {| d_{pk} - c_{mk} |}^{2}}}{2 σ^{2}}} \end{matrix}] \end{matrix}$ (27)

Step 5: The probability sum of each decision category is calculated. We assume that there are m samples, and the samples are divided into c categories, and each category has k samples. After the calculation of the summation layer, we can obtain the sum of the initial probabilities that the samples to be classified belong to a certain category, that is: $\begin{matrix} S = \\ [\begin{matrix} \sum_{l = 1}^{k} p_{1 l} & \sum_{l = k + 1}^{2 k} p_{1 l} & \dots & \sum_{l = m - k + 1}^{m} p_{1 l} \\ \sum_{l = 1}^{k} p_{2 l} & \sum_{l = k + 1}^{2 k} p_{2 l} & \dots & \sum_{l = m - k + 1}^{m} p_{2 l} \\ \dots & \dots & \dots & \dots \\ \sum_{l = 1}^{k} p_{pl} & \sum_{l = k + 1}^{2 k} p_{pl} & \dots & \sum_{l = m - k + 1}^{m} p_{pl} \end{matrix}] \\ = {[\begin{matrix} s_{11} & s_{12} & \dots & s_{1 c} \\ s_{21} & s_{22} & \dots & s_{2 c} \\ \dots & \dots & \dots & \dots \\ s_{p 1} & s_{p 2} & \dots & s_{pc} \end{matrix}]}_{p \times c} \end{matrix}$ (28)

In the above formula, S_ij represents the initial probability sum of the ith sample to be classified as the jth category.

Step 6: The probability is calculated. That is: the probability that the i-th sample is determined to be in the j-th category is calculated: ${prob}_{ij} = \frac{s_{ij}}{\sum_{j = 1}^{c} s_{ij}}$ (29)

5 Model building

The main ideas of the improved neural network model are: first, this study introduce set pair analysis theory to comprehensively evaluate the initially constructed index system to obtain the initial evaluation results. Then, in this study, the digital results of the initial evaluation are converted into descriptive results, which are projected into a unified coordinate system through mapping theory to achieve quantitative assignment. Secondly, the original evaluation index is used as input, and the quantitative evaluation result is used as output to establish a neural network, through training, adjustment, testing and preservation of the network. Finally, this study uses the improved MIV algorithm to achieve the selection of variable indicators.

The improved GRNN neural network model has mainly been improved in two aspects: (1) This study introduces the initial evaluation of the analysis theory to obtain the output value. (2) The improved MIV calculation method is introduced. The traditional MIV calculation method is: by observing the function change caused by each independent variable increasing or decreasing by 10%, the changes are averaged, that is, the average impact value of MIV. However, this calculation method mainly has two deficiencies: First, the function change caused by increasing or decreasing 10% may be large, but the signs of the two changes are opposite, and there are cases where positive and negative may cancel out. In this way, the result obtained after averaging may be very small, so that it cannot reflect the true degree of influence and cause inaccurate judgment. Second, because the change of the independent variable itself is non-linear, when only the calculation interval of 10% is increased or decreased to find the MIV value, the density is too large, and the result is one-sided. Therefore, the “inter-cell, large-scale” test method is used to obtain more fair results. Therefore, the range of change should be reduced and the scope of the test should be expanded, such as testing ±20%, ±15%, ±10%, ±5%.

The process of neural network screening index is shown in Fig. 2.

Fig. 2

The process of neural network screening indicators.

In this paper, there are a large number of indicators for the evaluation of the construction level of ecological cities, and there is a relatively complex and close relationship between the indicators. Therefore, in order to obtain good evaluation results and reduce the amount of calculation, the relative closeness is used to replace the original centralized analysis connection degree to calculate the relative closeness of the major cities to the optimal and worst solutions, that is, the comprehensive index of ecological city construction in the Yangtze River Economic Belt. Moreover, the ranking of the ecological city construction status of the 12 major cities in the Yangtze River Economic Belt is determined by size, as shown in Table 1 and Fig. 3.

Table 1

The rank and grade of ecological city construction levels of major cities in the Yangtze River Economic Belt

Area	Relative closeness	Rank	grade
Shanghai	0.7365	1	□
Suzhou	0.6808	2	□
Ningbo	0.5637	3	□
Nanjing	0.5545	4	□
Wuxi	0.5465	5	□
Hangzhou	0.5339	6	□
Chengdu	0.5235	7	□
Wuhan	0.5220	8	□
Changsha	0.4957	9	□
Nanchang	0.4316	10	□
Hefei	0.4308	11	□
Chongqing	0.2922	12	□

Fig. 3

Statistical diagram of relative closeness.

It can be seen from Table 1 that there are significant differences in the ecological city construction levels of 12 major cities along the Yangtze River Economic Belt. Judging from the scores and rankings of the relative closeness of ecological city construction, Shanghai is a city with a high level of ecological development. Its relative closeness reaches 0.7365, which ranks first. Chongqing is the one with the least relative closeness. Its value is 0.2922, which show that it is a city with a low level of ecological development and is ranked last. Moreover, the gap between the two cities is large. This shows that there is a serious imbalance in the construction of ecological cities along the Yangtze River Economic Belt. The relative closeness of cities in the east of the Yangtze River Economic Belt is generally higher than that of cities in the central and west. The second echelon city Suzhou is a Grade II development city. Grade III cities include Ningbo, Nanjing, Wuxi, Hangzhou, Chengdu and Wuhan. As a city in the east-west junction, Wuhan has a relatively high level of eco-city construction. Other cities are basically located in the Yangtze River Delta urban agglomeration downstream of the Yangtze River Economic Belt. Cities with relatively backward development in the third echelon are basically located in the middle and upper reaches of the Yangtze River Economic Belt, such as Changsha, Nanchang, and Hefei, all of which are Class IV cities. It can be seen from this that the development of the ecological city in the Yangtze River Economic Zone is uneven across the Yangtze River dimension and shows a good development trend in the downstream and a poor development trend in the middle and upper downstream.

The Yangtze River Delta urban agglomeration is the “leader” for the development of ecological cities in the Yangtze River Economic Belt. The lower reaches of the Yangtze River are emerging industrial areas, and the area is dominated by processing industries, while the upper and middle areas are resource-based areas, and there are many old industrial bases in the area. If the construction of an ecological city in the Yangtze River Economic Belt is to be coordinated and steadily developed, a good solution lies in: 1) The traditional technologies of old industrial bases in the middle and upper reaches need to be transformed, and new and more dynamic industrial bases should be established to guide high-tech industries in backward areas in the middle and upper reaches; 2) It is necessary to moderately relax the suppression of resource prices so that it can be partially marketized, so that the upper and middle regions with resource advantages can more reasonably seek their own interests to develop the local economy; 3) It is necessary to use Wuhan as the “junction” between the east and the west of the Yangtze River Economic Belt to drive the construction and development of the eco-city in the middle reaches, and gradually promote the construction of the eco-city in the upper reaches. As the most central city in the Yangtze River Economic Belt, Wuhan has both new industrial zones and old industrial bases. Once an eco-city with a high degree of modernization is created, its impact on the overall development of the eco-city construction in the Yangtze River Economic Belt and the surrounding radiation is incalculable.

When constructing the evaluation results of the eco-city subsystem, in order to facilitate a more intuitive comparative analysis, the evaluation results are uniformly converted to the interval [0,100]. The calculation steps are the same as above, which is expanded by a factor of 100 on the basis of relative closeness.

The evaluation results of the economic development subsystem are shown in Table 2 and Fig. 4.

Table 2

Evaluation table of economic development subsystem

	Evaluation index
Shanghai	75.35
Suzhou	59.14
Ningbo	77.78
Nanjing	59.89
Wuxi	58.74
Hangzhou	64.16
Chengdu	29.30
Wuhan	40.21
Changsha	28.92
Nanchang	37.05
Hefei	42.88
Chongqing	25.60

Fig. 4

Economic development subsystem evaluation chart.

The next level indicators of the eco-city construction index system are economic development indicators, including economic development level, economic development structural benefits, and economic competitiveness, which can fully reflect all aspects of economic development. It can be seen from Fig. 3 that the highest level of economic development is in the Yangtze River Delta region. From the Yangtze River Delta urban agglomeration to the upper reaches of the Yangtze River, the level of economic development presents a decreasing development gradient. Among the Yangtze River Delta urban agglomerations in the lower Yangtze River, Suzhou, Shanghai, Ningbo, Wuxi, Nanjing and Hangzhou have relatively high scores and are ranked high. The Chengdu, Wuhan, Nanchang, Hefei, Changsha and Chongqing scored lower in the middle and upper reaches of the Yangtze River, ranking lower. Through further analysis, it can be seen that in the second-level indicators of the economic development subsystem, the economic competitiveness obtains a relatively high weight of 0.1781, and in the third-level indicators, the city’s land output rate and the economic outward degree are scored 0.071 and 0.0787. The index weight of the tertiary industry as a percentage of GDP is 0.0397, so Shanghai, Nanjing, Hangzhou and other Yangtze River Delta regions with a high degree of openness and rapid development of the tertiary industry score higher.

The analysis of the difference between social harmony and progress is shown in Table 3 and Fig. 5.

Table 3

Evaluation table of social harmony and progress subsystem

	Evaluation index
Shanghai	59.28
Suzhou	56.91
Ningbo	64.89
Nanjing	57.50
Wuxi	63.09
Hangzhou	47.38
Chengdu	49.00
Wuhan	53.25
Changsha	48.81
Nanchang	43.99
Hefei	53.12
Chongqing	37.88

Fig. 5

Evaluation diagram of the social harmony and progress subsystem.

The next level indicators of the eco-city construction indicator system are social harmony and progress indicators, including population density, per capita daily comprehensive water consumption, urban registered unemployment rate, social security coverage, number of hospital beds per 10,000 people, number of students in higher education, The amount of books collected per capita and the proportion of R & D expenditure in GDP fully reflect the population indicators, indicators for resource allocation and utilization, social security, quality of life, and science and education.

The reasons for further analysis are: 1) Most indicators of social harmony and progress in the construction of ecological cities use indicators per capita, and the unilateral factors of uneven population distribution will affect the evaluation results of the development level of ecological cities in major cities. Therefore, under the pressure of a smaller population than Shanghai, Suzhou and Hangzhou have a better quality of life, and resources in all aspects of resource allocation, social security, science and education are relatively balanced, so Suzhou and Hangzhou score relatively high; 2) The level of science and education is sufficient to affect the further development of the Yangtze River Economic Belt, because the abundant labor and intellectual resources are important forces for the Yangtze River Economic Belt to take off again. According to the weight distribution of the three-level evaluation indicators mentioned above, among the second-level indicators of the social progress and harmony subsystem, the level of science and education is relatively high with a weight of 0.1340. The comparison results of the comprehensive source data show that since there are relatively few universities and research institutes in Ningbo and a large number of colleges and university students in major cities such as Shanghai, Nanjing, Wuhan, and Chengdu, Ningbo has a relatively low scores, but Chengdu has a relatively high score.

The evaluation results of the ecological environment protection subsystem are shown in Table 4 and Fig. 6.

Table 4

Evaluation table of ecological environment protection subsystem

	Evaluation index
Shanghai	56.52
Suzhou	46.74
Ningbo	62.71
Nanjing	55.19
Wuxi	50.24
Hangzhou	57.41
Chengdu	52.04
Wuhan	53.18
Changsha	61.72
Nanchang	51.12
Hefei	50.56
Chongqing	39.14

Fig. 6

Evaluation diagram of the ecological environment protection subsystem.

The next level of the index system of eco-city construction is the index of ecological environmental protection, including energy consumption per 10,000 yuan of GDP, SO2 per unit of industrial output value, smoke (dust) dust, waste water discharge, and excellent rate of ambient air quality, urban sewage treatment rate, comprehensive utilization rate of solid waste, green space rate in built-up area, per capita park green area, etc., which can fully reflect the development level of environmental quality and safety, pollution control, urban greening and other aspects. It can be seen from Fig. 5 that the environmental protection subsystem mainly reflects the impact of industrial development on the environment in different places. It is different from the economic development, social harmony and progress subsystem, and there is no obvious difference between the upper, middle and lower reaches. Nanjing and Hangzhou, which have a higher degree of economic development and social harmony and progress, rank lower and their scores are 46.74 and 51.12, respectively, which reflect the impact of the industrial development of traditional industrial cities on the environment. Suzhou, which undertakes industrial transfer in Shanghai and achieves rapid industrial upgrading, achieves good evaluation results on the premise of maintaining rapid economic growth and social harmony and progress. Moreover, it ranked first with a score of 62.71.

There are the following reasons for the above results: 1) With the continuous advancement of industrialization and urbanization, the waste generated by energy and the deterioration of the atmosphere are increasing, and the environmental quality is facing great pressure. Based on this, all urban agglomerations in the Yangtze River Economic Belt should strengthen cooperation, rationally lay out industries, pay attention to the adjustment and upgrading of industrial structure, optimize ecological networks, and build ecological corridors that depend on the five major urban agglomerations along the Yangtze River Economic Belt; 2) The industrial structure of each region is different, which leads to different energy consumption. Therefore, according to the economic conditions and social policies of different cities, some measures must be taken to promote energy conservation and emission reduction according to local conditions. For example, by eliminating equipment with high pollution and high energy consumption, introducing advanced clean technologies, and developing a resource-economic cycle development model, the trend of deteriorating environmental quality can be effectively contained, and the self-protection ability of coordinated development of regional economy and environment can be improved.

It can be seen from the above analysis that the results of the analysis of this research model are consistent with the actual situation. Next, in order to verify the stability of the model in this study, the model performance is verified by training a large amount of data, and 1 is set as the best stable node, and 0 is an unstable node. A total of 300 sets of data are trained, and each set of data is 100,000 pieces. If a single error occurs in a single group, it is considered that there is a problem with the training and the training result of this group is 0. The result is shown in Fig. 7.

Fig. 7

Statistical diagram of model stability.

Through the model stability statistics of Fig. 7, it can be seen that errors occur only in the training of 148 groups and 268 groups. By querying the training records, it is found that there are word errors. This shows that the stability of this research system exceeds 99.99%, and it can be applied to the system.

6 Conclusion

This paper first uses the BP neural network model and the DEA-Malmquist index method to measure the financial ecological environment and capital allocation efficiency in the Yangtze River Economic Zone. Then, this study makes an empirical analysis of the influencing factors of capital allocation efficiency in the Yangtze River Economic Zone and focuses on the role of the financial ecological environment in capital allocation efficiency. Moreover, this study elaborated the economic, social and environmental development status of the Yangtze River Economic Belt from the perspective of the concept, characteristics, ecological city construction research theory and related evaluation theory of the ecological city. Then, based on the previous research results and the development characteristics of the Yangtze River Economic Belt, this study initially establishes an evaluation index system for the construction of the ecological city in the Yangtze River Economic Belt. By analyzing the corresponding changes in the function value when the independent variable changes within a certain range, this study uses the magnitude of change to measure the degree of influence of indicators and to screen and optimize the newly established evaluation indicator system, so as to ensure the scientificity, representativeness, hierarchy and operability of the indicator system.

References

Nagy

and Pipek

, An economic prediction of the finer resolution level wavelet coefficients in electronic structure calculations[J], Phys Chem Chem Phys 17(47) (2015), 31558–31565.

and Huafeng

, Quantitative analysis of regional economic indicators prediction based on grey relevance degree and fuzzy mathematical model[J], Journal of Intelligent & Fuzzy Systems 37(2) (2019), 1–14.

, Dong

, Sui

, et al., Fleet economic life prediction: A probabilistic approach including load spectrum variation and structural property variation[J], Engineering Fracture Mechanics 163 (2016), 189–205.

Paredes

, Rodrigues

G.C.

, Alves

, et al., Partitioning evapotranspiration, yield prediction and economic returns of maize under various irrigation management strategies[J], Agricultural Water Management 135 (2014), 27–39.

Karanikić

, Mladenović

, Sokolov-Mladenović

, et al., Retraction Note: Prediction of economic growth by extreme learning approach based on science and technology transfer[J], Quality & Quantity 53(2) (2019), 1095–1096.

Van Giessen

, Wilcher

, Peters

, et al. Health economic evaluation of diagnostic and prognostic prediction models. a systematic review[J], Value in Health 17(7) (2014), A560.

Barde

, Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction[J], Computational Economics 45(2) (2015), 337–358.

Ferramosca

, Limon

and Camacho

E.F.

, Economic MPC for a Changing Economic Criterion for Linear Systems[J], Automatic Control IEEE Transactions on 59(10) (2014), 2657–2667.

Zhou

, Lai

K.K.

and Yen

, Bankruptcy prediction using SVM models with a new approach to combine features selection and parameter optimisation[J], International Journal of Systems Science 45(1–3) (2014), 241–253.

10.

Bhattacharya

, Mukhoti

and Konar

, Learning regularity in an economic time-series for structure prediction[J], Applied Soft Computing 76 (2019), 31–44.

11.

Geng

, Wei

, Zhang

, et al., Analysis and Prediction of the Coupling Coordination Relationship between Tourism and Air Environment: Yangtze River Economic Zone in China as Example[J], Discrete Dynamics in Nature and Society 2020(10) (2020), 1–15.

12.

H.L.

, Ng

K.T.W.

and Bolingbroke

, Time-lagged effects of weekly climatic and socio-economic factors on ANN municipal yard waste prediction models[J], Waste Management 84(FEB.) (2019), 129–140.

13.

Zhou

, Luo

, Jain

D.K.

, Lan

and Zhang

, Double-Domain Imaging and Adaption for Person Re-Identification, IEEE Access 7 (2019), 103336–103345.

14.

Zhao

and Sun

, Government subsidies-based profits distribution pattern analysis in closed-loop supply chain using game theory, Neural Computing and Applications 32(6) (2020), 1715–1724.

15.

Rajsic

, Weersink

, Navabi

, et al., Economics of genomic selection: the role of prediction accuracy and relative genotyping costs[J], Euphytica 210(2) (2016), 1–18.

16.

Jahedpari

, Rahwan

, Hashemi

, et al., Online Prediction via Continuous Artificial Prediction Markets[J], Intelligent Systems, IEEE 32(1) (2017), 61–68.

17.

Daksiya

, Su

H.T.

, Chang

Y.H.

, et al., Incorporating socio-economic effects and uncertain rainfall in flood mitigation decision using MCDA[J], Natural Hazards 87(1) (2017), 515–531.

18.

Liang

and Yang

, Urbanization, economic growth and environmental pollution: Evidence from China, Sustain Comput Informatics Syst 21 (2019), 1–9.

19.

Gordini

, A genetic algorithm approach for SMEs bankruptcy prediction: Empirical evidence from Italy[J], Expert Systems with Application 41(14) (2014), 6433–6445.

20.

Ferramosca

, González

A.H.

and Limon

, Offset-free multi-model economic model predictive control for changing economic criterion[J], Journal of Process Control 54 (2017), 1–13.