Regional Economic Data Extraction and Development Prediction Based on an Improved GWO Algorithm

Summary

The proposed model can effectively capture the characteristics of regional economic data, improve prediction accuracy, and provide a scientific basis for regional economic development decisions.

Abstract

With the increasing demand for high-quality regional economic development, accurately extracting hidden features of economic data and achieving reliable development trend prediction has become an important prerequisite for formulating scientific economic policies. To optimize the feature extraction accuracy of regional economic data and the development prediction reliability, a model for feature extraction and development prediction of regional economic data is constructed by integrating an improved grey wolf optimization algorithm, a support vector machine, and a generative adversarial network. On the F1 unimodal function and F2 multi-modal function tests, the convergence speed was significantly better than that of the wind-driven optimization and sine cosine algorithm, demonstrating stronger adaptability in complex optimization problems. The comparative experiment on the steel wire rope dataset showed that the algorithm improved the recognition rate by 1.25% compared to the ‌Principal Component Analysis-Grey Wolf Optimizer-Support Vector Machine, reaching 98.75%, and had higher efficiency in high-dimensional feature processing, verifying its superiority in feature extraction and classification recognition. The model was applied to the economic data in Anhui Province, selecting 8 core indicators such as the GDP of the primary industry and the income of urban and rural residents from 2011 to 2022. In 2011, when the true value was 16,311, the predicted value of the research model was 16,200. In 2015, when the true value was 23,808, the model predicted a value of 23,600. The minimum absolute error from 2011 to 2020 was only 103, and the error rate was as low as 0.005, demonstrating outstanding stability in medium and long-term forecasting. The proposed model can effectively capture the characteristics of regional economic data, improve prediction accuracy, and provide a scientific basis for regional economic development decisions.

Introduction

As the Chinese economy enters a stage of high-quality development, the complexity and multi-dimensionality of regional economic data are becoming increasingly prominent. Accurately extracting economic data features and scientifically predicting development trends have become important prerequisites for formulating regional economic policies and optimizing resource allocation^1,2. The regional economic system involves multidimensional indicators such as industrial structure, resident income, fiscal revenue and expenditure, and energy consumption. There are nonlinear correlations and dynamic coupling relationships between various indicators. Traditional statistical analysis methods and single machine learning models often face problems like insufficient feature extraction and limited prediction accuracy when processing High-Dimensional and non-stationary economic data^3,4.

Grey Wolf Optimization (GWO) is an intelligent optimization strategy that simulates the hunting behavior of grey wolves. Due to its simple structure and stable convergence performance, GWO has been widely used in function optimization, parameter optimization, feature selection, and other fields⁵. For example, Toktas et al.⁶ used the GWO algorithm to achieve efficient parameter optimization when designing multi-objective hyper chaotic systems, verifying the potential of the optimized GWO algorithm in complex multi-objective optimization scenarios. Liu et al.⁷ applied the GWO algorithm to multi-objective optimal power flow calculation in distribution networks. The adaptability of the algorithm to complex engineering problems was improved through a hybrid strategy. However, the standard GWO has a slow convergence speed and local optimal solutions when addressing complex optimization problems, which limits its application effectiveness in high-dimensional economic data processing⁸. Therefore, the academic community has conducted extensive research on the GWO algorithm by introducing adaptive weights, chaotic perturbations, or hybrid optimization strategies to enhance the global search capability and convergence accuracy. However, the adaptability of existing improved algorithms on data types such as economic data with strong noise and multi-scale features still needs further verification⁹.

Support Vector Machine (SVM) and Generative Adversarial Network (GAN) have obvious advantages in data feature learning and predictive modeling¹⁰. SVM maps linearly inseparable data in low-dimensional space to high-dimensional space through kernel functions, converting nonlinear problems into linearly separable problems. It can efficiently complete classification and regression tasks without explicitly calculating high-dimensional mapping. GAN relies on the adversarial training mechanism of generators and discriminators to deeply capture the potential distribution characteristics of data, thereby significantly enhancing the ability to fit complex patterns¹¹. Cao et al.¹² used SVM for fault diagnosis of railway switch equipment and verified the classification performance of SVM in small samples and nonlinear problems through multi-domain feature fusion and feature selection strategy. Liu et al.¹³ built a facial attribute manipulation model using GAN. The ability of GAN to mine potential distribution features of data was verified.

However, in many fields such as industrial fault prediction and environmental monitoring, optimization algorithms such as GWO and PSO are often combined with SVM, CNN, etc., to improve prediction accuracy.¹⁴ However, most fusion models have challenges such as insufficient parameter collaborative optimization and poor adaptability to complex time series data. Although there are many algorithm applications in the field of economic forecasting, most of them focus on the improvement of a single model, ignoring the high coupling and strong noise characteristics of economic data, and the lack of in-depth collaborative design of optimization algorithms and generative models. Therefore, the study improves the GWO algorithm. The Tent mapping initialization is used to enhance population traversability to adapt to sparse feature mining. Position update weights are reconstructed to improve high-quality solution tracking capabilities to adapt to nonlinear correlation capture. Nonlinear dynamic convergence factors are used to balance global exploration and local development to cope with time series changes. SVM classification advantages and GAN feature enhancement capabilities are integrated to build an Improved Gray Wolf Optimizer-Support Vector Machine-Generative Adversarial Network (IGWO-SVM-GAN), accurately solving regional economic data feature extraction and development prediction. The innovation lies in deeply integrating the IGWO algorithm with SVM and GAN, utilizing the powerful data generation and feature mapping capabilities of GAN to expand sample diversity, achieving precise feature screening with SVM's strong classification performance, and synergistically optimizing the key parameters of both through the IGWO algorithm. It breaks through the traditional model's dependence on linear relationship assumptions, significantly improving its adaptability to complex economic systems.

The overall goal of the research is to construct a regional economic data feature extraction and development prediction model based on IGWO-SVM-GAN, to solve the problems of inaccurate feature extraction, low prediction accuracy, and poor adaptability of traditional models, to achieve efficient mining of regional economic core features and reliable prediction of development trends, and to provide scientific support for regional economic decision-making. The study proposes the following hypotheses. Hypothesis 1: Compared with standard GWO and other comparative algorithms, the improved IGWO algorithm has faster convergence speed and higher optimization accuracy in high-dimensional economic data feature extraction; Hypothesis 2: The prediction performance of the IGWO-SVM-GAN fusion model is significantly better than that of a single model and other mainstream fusion models, and has higher stability and accuracy in medium and long-term economic forecasts; Hypothesis 3: The proposed model can effectively adapt to the high coupling and strong noise characteristics of regional economic data, and accurately capture the development patterns of core economic indicators.

Protocol

Improved GWO algorithm
In the field of feature extraction and development prediction of regional economic data, to effectively improve the extraction efficiency of key features in high-dimensional economic data, the WO algorithm is introduced for optimization. GWO simulates the hunting behavior of grey wolves. The core mechanism of the GWO algorithm lies in the bio-mimetic simulation of the social hierarchy structure and hunting strategy, which achieves optimization by simulating the hierarchical hierarchy of the first wolf a, second wolf b, and young wolf c, as well as hunting stages such as hunting, pursuit, and attack¹⁵. The specific process for updating the location of grey wolves is shown in Figure 1.

Figure 1: Flowchart of the grey wolf's position update. (A) Schematic diagram of the gray Wolf’s position update. (B) Flowchart of the GWO algorithm. Please click here to view a larger version of this figure.

Figure 1A shows the grey wolf position update. From Figure 1A, the updated grey wolf individual position is guided by the positions of the a, b, and c. Optimization is achieved by simulating the hunting behavior of the group, gradually approaching the optimal target¹⁶. The update process includes distance calculation and position adjustment. The coefficient vectors  and introduced during the position update process and dynamically changed through random values, achieving adaptive switching between exploration and development stages. Equation (1) displays the distance vector  between the grey wolf and its prey.

 (1)

In equation (1),  represents a random coefficient vector used to introduce randomness and balance exploration and development.  signifies the current Position Vector (PV) at time t.  represents the PV of the prey at time t. The grey wolf updates its position depending on the prey location and distance , and the position update is displayed in equation (2).

 (2)

In equation (2),  represents the coefficient vector that controls the direction of movement and step size. The distance vectors , , and  between the current grey wolf and the a, b, and c wolves are shown in equation (3).

 (3)

In equation (3), , , and respectively represent the PV of the three solutions with the best fitness in the current population (a, b, and c). Three candidate target positions are calculated according to the positions and distances of wolves a, b, and c, respectively, as displayed in equation (4).

(4)

In equation (4), , , and signify three candidate target positions calculated from the positions and distances of a, b, and c. , , and represent candidate positions calculated from the positions and distances of a, b, and c¹⁷. The PV of current grey wolves in the next generation (i.e., the updated position ) is displayed in equation (5).

(5)

By solving the mean of three candidate positions, the population gradually approaches the optimal region guided by wolves a, b, and c. Figure 1B displays the workflow of the GWO. From Figure 1B, the execution steps of the GWO algorithm include initializing the grey wolf population. Then, the fitness value in the population is calculated. The current optimal solution and sub-optimal solution are determined by comparing individual fitness values. All fitness values are sorted, and the top three individuals are labeled as a, b, and c. The individual positions in the population are updated based on the location information of dominant individuals. Whether the preset termination conditions are met is determined. If they are met, the algorithm terminates. Otherwise, the fitness value of each gray wolf in the population is calculated.

To improve the optimization accuracy in data feature extraction, an improved GWO algorithm (IGWO) is proposed, which includes initializing the grey wolf population using tent mapping to enhance the diversity and traversal. The position update weight coefficients of grey wolf individuals are reconstructed to optimize the algorithm's ability to track high-quality solution areas. A nonlinear control mechanism is introduced to dynamically update the convergence factor q. The coefficient vector  and a random coefficient vector  used to control the direction of movement and step size are synchronously optimized to balance the global exploration and local development abilities¹⁸. Figure 2 presents the flowchart of IGWO.

Figure 2: Process of the IGWO. Please click here to view a larger version of this figure.

From Figure 2, the IGWO has formed a more targeted iterative process while retaining the core framework of the GWO. The initial population is generated through tent mapping to avoid the uneven population distribution that may arise from traditional random initialization, laying a solid foundation for subsequent optimization. In each iteration, the algorithm first calculates individual fitness values and selects a, b, and c wolves. Based on the improved position update weight equation, combined with nonlinear convergence factors and optimized coefficient vectors, the position update of grey wolf individuals is completed. Meanwhile, by dynamically adjusting the range of values of the random coefficient vector, the local search accuracy in the later stages of iteration is optimized, reducing the local optima. Finally, whether the maximum iteration has been reached is determined. If the maximum iteration has been reached, the optimal solution is provided as the output. Conversely, it returns to the fitness value calculation stage for the next iteration. To improve the convergence speed of the IGWO, a guidance mechanism is introduced, and its effectiveness is shown in Figure 3.

Figure 3: Schematic diagram of whether there is a guiding mechanism or not. (A) No guiding mechanism. (B) Guiding mechanism. Please click here to view a larger version of this figure.

As shown in Figure 3, the guidance mechanism assigns fixed weight allocation strategies to a, b, and c wolves during the position update stage. By significantly increasing the weight proportion of the a wolf and reducing the influence of b and c wolves, more individuals in the population are guided to update their positions along the search direction of the a wolf, so that their distribution focuses on the area in front of the a wolf, rather than the uniform distribution state around the a wolf in traditional GWO algorithms. This improvement can strengthen the guiding role of elite individuals in the optimization direction of the population, reduce ineffective search costs, and improve the convergence performance.

Improved GWO algorithm based on SVM and GAN
To optimize the classification performance and generalization ability of GWO after data feature extraction, the SVM algorithm is introduced for collaborative optimization. The schematic diagram of the optimal classification surface of linear and nonlinear SVM is shown in Figure 4.

Figure 4: Schematic diagrams of the optimal classification surfaces of linear and nonlinear support vector machines. (A) Optimal classification surface of support vector machine. (B) Optimal classification surface of nonlinear support vector machine. Please click here to view a larger version of this figure.

Figure 4A presents the optimal classification surface of a linear SVM. From Figure 4A, in a two-dimensional data space, the optimal classification surface g(x) of SVM can completely separate two types of samples¹⁹. The expression for a hyperplane g(x) is presented in equation (6).

 (6)

In equation (6), w signifies the normal vector of the hyperplane, which decides its direction. b signifies the intercept term, which decides the offset of the hyperplane. x signifies the feature vector of the input sample²⁰. SVM has linear separable SVM and nonlinear separable SVM. Assuming that the dataset of linear separable SVM is , its goal is to maximize the classification interval while achieving correct classification of all samples²¹. The constraint condition for this problem is shown in equation (7).

 (7)

In equation (7), y_i signifies the class label of the i-th sample, which is the benchmark identifier for the model to perform classification, feature matching, or constraint determination, and x_i represents its feature vector. The corresponding original optimization problem is shown in equation (8).

 (8)

In equation (8),  signifies the mathematical equivalent of maximizing the interval. To solve this constrained optimization problem, the Lagrange multiplier is introduced to transform it into an unconstrained form²². The Lagrange function is shown in equation (9).

 (9)

In equation (9), α_i represents the Lagrange multiplier, which is a dual variable introduced to transform the original constraints of SVM into an unconstrained optimization problem. Its value directly reflects the contribution of the i-th sample to the determination of the classification hyperplane. According to the Monte-Carlo-Kuhn-Tucker condition, the complementary relaxation condition for the optimal solution is shown in equation (10).

 (10)

The expression of w is taken into the Lagrange function to obtain the dual problem, as shown in equation (11).

 (11)

In equation (11), j is the sample in the dataset. For nonlinear separable data, kernel techniques transform linearly inseparable data in the original space into linearly separable problems in high-dimensional space through implicit nonlinear mapping. The inner product x_i·y_i in the dual problem is replaced with a kernel function K(x_i·y_i), thereby avoiding the complexity of directly calculating the inner product in high-dimensional space. Figure 4B is a schematic diagram of the optimal classification surface of a nonlinear SVM. From Figure 4B, in the original two-dimensional input space, the two types of samples exhibit a nonlinear distribution and cannot be effectively separated by a straight line. At this time, the distribution pattern of data points may exhibit complex patterns such as interleaving and circling²³. Through the mapping effect of kernel functions, these data points in two-dimensional space are transformed into higher-dimensional feature spaces, and the originally entangled sample points exhibit obvious separability. In high-dimensional space, nonlinear SVMs can construct an optimal hyperplane to precisely partition two types of samples. The final classification decision function f(x) is presented in equation (12).

 (12)

In equation (12), K(x_i, x) signifies the kernel function. The kernel functions enable SVM to flexibly handle nonlinear problems, significantly expanding its applicability. The flowchart of the IGWS-SVM data feature recognition model is shown in Figure 5.

Figure 5: Flowchart of the IGWO-SVM data feature recognition model. Please click here to view a larger version of this figure.

In Figure 5, the preprocessed feature data were input into the IGWO algorithm, and its iterative optimization mechanism adaptively optimized the core parameters of SVM. The algorithm dynamically adjusted the population search strategy to efficiently locate the optimal parameter combination in the parameter space that maximized SVM classification accuracy, addressing the low efficiency and susceptibility to local optima inherent in traditional grid search or random search methods. The parameters optimized by IGWO were subsequently input into the SVM model, and the optimized classifier was employed to learn from and predict the feature data. For linearly separable data, the model achieved direct partitioning by constructing the optimal hyperplane. Nonlinear data were mapped into high-dimensional space through kernel functions to complete classification, and the final category labels were output. To further enhance the fitting capability to complex data distributions and the authenticity of feature generation, the GAN was incorporated. Figure 6 displays the GAN.

Figure 6: GAN structure. Please click here to view a larger version of this figure.

In Figure 6, the GAN has a generative model and a discriminator model, which achieve collaborative optimization through adversarial learning mechanisms²⁴. This generative model utilizes random noise as input and generates fake samples that are similar to the distribution of real data through a nonlinear transformation. The discriminator model obtains real and generated samples as inputs, and its core task is to distinguish the authenticity of the input data and output the probability that the samples come from the real dataset²⁵. The original optimization objective of GAN is presented in equation (13).

(13)

In equation (13), V(D, G) is the value function, which measures the performance of the discriminator given generator G and discriminator D. D(x) represents the discriminative probability on the real sample x. D(z) represents the generator mapping the noise z into generated samples. pdata(x) signifies the probability distribution of real data. pz(z) signifies the prior distribution of z. E refers to the expected value, representing the mean of all samples in the distribution^26,27. The optimization objective of the discriminator is shown in equation (14).

(14)

The optimized generator is shown in equation (15).

(15)

In summary, the study proposes a collaborative optimization algorithm based on IGWO-SVM-GAN to achieve efficient feature extraction and accurate classification in complex data scenarios.

Regional economic data extraction and development prediction based on the IGWO-SVM-GAN algorithm
As an important component of the national economic system, precisely analyzing regional economic development and scientifically predicting future trends has important theoretical and practical value for formulating regional development strategies, optimizing resource allocation, and avoiding economic risks. However, regional economic data often present complex features such as high dimensionality, non-linearity, and dynamism, and are influenced by multiple factors such as policies, industrial structure, and external environment. Traditional feature extraction methods and prediction models are hard to capture the deep correlations behind the data, resulting in limited accuracy. The IGWO-SVM-GAN is applied to the field of regional economic analysis. By integrating the advantages of the algorithm in feature extraction, classification learning, and data generation, an analysis model suitable for regional economic data is constructed. The flowchart of the regional economic data feature extraction and development prediction model based on IGWO-SVM-GAN is presented in Figure 7.

Figure 7: Process of regional economic data feature extraction and development prediction model based on IGWO-SVM-GAN algorithm. Please click here to view a larger version of this figure.

According to Figure 7, high-dimensional indicators of regional economy are collected, including GDP, industrial output value, fiscal revenue and expenditure, employment rate, etc. The raw data is cleaned and standardized, including filling in missing values and correcting outliers. The feature filtering is performed on preprocessed data through IGWO, redundant information is removed, and a subset of core features is output. The generator of GAN generates synthetic economic data with high consistency with real data based on the distribution pattern of core feature subsets to alleviate sample sparsity or uneven distribution. The core feature subset is fused with synthetic economic data and input into an SVM model. The non-linear relationship between features is processed through a kernel function to construct an economic development prediction model. The model outputs quantitative predictions of regional economic development, including future economic growth rates, changes in the proportion of industrial structure, etc. The model effectively addresses the high-dimensional, nonlinear, and sparse nature of regional economic data by leveraging IGWO's feature purification, GAN's data augmentation, and SVM's nonlinear modeling, thereby enhancing robustness and accuracy.

To prove the effectiveness of the regional economic data feature extraction and development prediction model constructed based on the IGWO-SVM-GAN algorithm, Anhui Province is selected as a case study. The research data are all sourced from authoritative statistical materials, including the Anhui Statistical Yearbook from 2005 to 2022 and the Anhui National Economic and Social Development Statistical Bulletin from 2005 to 2023, to ensure the data objectivity and reliability. The core economic indicators selected for performance analysis are as follows: Gross Domestic Product (GDP) of the primary industry (X1), GDP of the secondary industry (X2), GDP of the tertiary industry (X3), per capita disposable income of rural residents (X4), per capita disposable income of urban residents (X5), total fiscal expenditure (X6), total energy consumption (X7), and education investment expenditure (X8). The study used the Z-score standardization method to normalize the 8 indicator data to eliminate the interference of dimensional differences on model training. By consulting supplementary statistical data for the corresponding years and using linear interpolation of adjacent year data to complete a small amount of missing data, the final data set had no missing values. The 3σ criterion was used to identify abnormal data, and the two detected outliers were Winsorized to avoid abnormal data from affecting the model training effect. The time series cross-validation method was used, using the 2011-2017 data as the training set (7 samples), the 2018-2019 data as the validation set (2 samples), and the 2020 data as the test set (1 sample), to simulate real economic forecasting scenarios, avoid data leakage issues, and improve the reliability of model generalization ability evaluation. The materials required for the method are shown in Table of Materials.

Results

Performance testing of the IGWO-SVM-GAN algorithm
To systematically verify the optimization performance, feature extraction effectiveness, and prediction quality improvement mechanism of the IGWO-SVM-GAN algorithm, the research was conducted in three phases: The first phase employed the benchmark test function to verify the algorithm optimization capabilities. The second phase used the wire rope data set to verify the feature extraction and classification performance. The third phase was to clarify t...

Discussion

The study applies the IGWO-SVM-GAN algorithm to feature extraction and development prediction of regional economic data and verifies its feasibility and effectiveness with Anhui Province as an example. Based on the fast convergence and high recognition accuracy demonstrated by the algorithm in function testing and steel wire rope dataset testing, it is believed that it can adapt to the high-dimensional and strong dynamic characteristics of regional economic data, providing a new tool for economic analysis.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Intel Core i5-9300HF processor	Intel Corporation	CL8068404069607 (OEM/Ray version)
MATLAB 2020b Programming Platform	MathWorks	R2020b (version number)
Windows 10 64 bit operating system	Microsoft Corporation	FQC-09131 (Windows 10 Pro Retail SKU)