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RETRACTED ARTICLE: Investigation of the evaluation system of SMEs’ industrial cluster management performance based on wireless network development

This article was retracted on 18 January 2023

This article has been updated


Today, with the rapid development of mobile Internet technology, the operation of enterprises is basically based on the mobile network platform. Therefore, the study of the evaluation system of SMEs’ industrial cluster management performance based on wireless network development is proposed. After briefly describing the relevant research of industrial cluster performance evaluation, the knowledge innovation of wireless network era is the core of SME industrial cluster management, and a set of industrial cluster management performance evaluation index system has been constructed. Based on this, a comprehensive evaluation method based on neural network algorithm is designed. In a subsequent experiment, it is demonstrated that this method can evaluate the level of cluster management performance.

1 Introduction

With the continuous development of industrialization, industries will inevitably form an agglomeration effect after reaching a certain level or stage [1]. When the industrial agglomeration effect appears, the development of the industry will be stimulated and further optimization and upgrading is conducted, thereby attracting the relevant industry chain of the chain to achieve the scale and efficiency of the industry, and finally the phenomenon of industrial clusters will be achieved [2]. The advantages of industrial clusters relative to industrial competition lie in the benefits of industrial economies in clusters, and it has a good influence on the economic development of clusters and surrounding areas. Therefore, all countries in the world are very concerned about the development and research of industrial clusters [3].

The influence of informatization technology on various fields of social production is the main phenomenon of current social development [4]. Its application in communications, management, and production has further increased production efficiency and has formed a more positive impact on the emergence of industrial clusters. In addition, related industries developed on the basis of informatization technology have also experienced industrial agglomeration under the dual stimulation of the development level of information technology and huge social demand. Such industrial agglomeration mainly focuses on small-scale SMEs [5]. With more and more types of industrial agglomeration, research on this area has begun to gradually develop. Therefore, the study of the evaluation system of SME industrial cluster management performance based on wireless network development is proposed, hoping to provide some reference opinions for the industrial cluster management of Chinese enterprises.

2 State of the art

Industrial agglomeration is a phenomenon in which industrialized production develops to a certain degree and level. Therefore, the related research of industrial clusters also started earlier [6]. At the end of the nineteenth century, Marshall, an overseas scholar, began to pay attention to industrial agglomeration effects and proposed that small-scale enterprises with similar production characteristics would increase production efficiency by optimizing the division of labor in certain regions [7]. After more than a century of development, relevant research on foreign industrial clusters has yielded considerable results, and it has begun to move forward in a deeper direction. Judging from the current research, the spatial economy, innovation, and knowledge spillover of industrial clusters have become the main directions of foreign industrial cluster research [8]. The research on the performance evaluation system and evaluation methods of industrial clusters has become increasingly mature.

Compared with foreign research results in industrial clusters, domestic related research has been delayed by economic development [9]. Related content mainly focuses on the performance formation mechanism and performance measurement and evaluation [10]. After entering the twenty-first century, the rapid development of China’s economy has produced a large number of industrial clusters, which has prompted domestic related research to begin to develop in the direction of industrial clusters’ competitive advantages and cluster performance formation mechanisms, and has achieved certain results. As a whole, China still has a long way to go in its research on industrial clusters.

3 Methodology

3.1 The construction of industry cluster management performance evaluation index based on wireless network development

With the rapid development of information technology, the current social communication has undergone a revolutionary change. In the current society, people’s communication methods have evolved from traditional wired network communications to wireless network technologies. Although the wired network communication method still occupies a large proportion, wireless network technology has become an integral part of the current social production and life. In particular, the emergence of mobile Internet technology has caused fundamental changes in the Internet communication. In the era of wireless networks dominated by mobile Internet, virtual and the real world are blended with each other, and the distance between people, people, society, people, and groups has become zero. Based on this zero-distance basis, commerce has achieved a true sense of democracy. Correspondingly, the economy has become an era of knowledge economy. The use of knowledge innovation has become a necessary path for the development of individuals, groups, and organizations. In addition, the emergence of wireless network technology makes the performance management of groups, enterprises, or organizations show an era of net value, and the people in this network structure are the main factors that create value. Then, in the management performance of SME industrial clusters based on wireless networks, knowledge innovation, talent management, and business benefits of industrial clusters have become the main targets of cluster management. Based on the above analysis, the assessment system for the management performance of SME industrial clusters based on the development of wireless networks is shown in Table 1. The entire evaluation system is divided into five main components. The first is the scale of cluster management, including the three major contents of the number of companies, the number of corporate personnel, and corporate assets. The second is revenue based on business generated by wireless network business, including taxes on total revenue, profits, and profits. The third major content is technology innovation management. This content is the core content of the development of SME industry clusters based on wireless networks. The economy of the wireless network era is the era of knowledge economy and the era of knowledge innovation. Therefore, knowledge innovation is the main driving force for cluster development, including the number of companies involved in knowledge innovation, the number of employees involved, the number of innovative projects, and the funds invested in innovation. In addition, there are technological improvements and the number of patents and economic benefits resulting from innovation. There are seven indicators for the entire cluster’s knowledge innovation capability.

Table 1 Performance evaluation index system of industrial cluster management based on wireless network development

In addition to the knowledge innovation capability, there is also a need for a physical mechanism that is equivalent to it. Therefore, in performance management, physical institutions involved in knowledge innovation are also very important influencing factors. Besides, the evaluation system includes four major indicators such as the number of companies that have R&D institutions, the number of R&D institutions, the number of R&D personnel, and the expenditure of R&D institutions. Cluster innovation capability and supporting physical institutions constitute the core of the entire cluster management performance evaluation, which is also the core competitiveness of enterprise development in the wireless network era. In addition, in the management of industrial clusters, the construction of cluster projects is also an important part of management. Therefore, it must be included in the evaluation system. This includes the number of projects under construction, new additions, and production, as well as five indicators such as investment rate and investment amount. Through the above five major criteria layers, a cluster management performance evaluation system is constructed with the core of knowledge innovation capability in the wireless network era, supporting personnel, institutions, and resources as inputs, plus the necessary organizational structure.

3.2 Comprehensive evaluation model of industrial cluster management performance based on neural network algorithm

After the construction of management performance evaluation system, what kind of evaluation method to be chosen is the most important part. There are many methods for evaluating industrial clusters that are currently known. However, the SME clusters based on the development of wireless networks are studied in this paper. In the era of wireless networks, the knowledge economy as the main business model will inevitably produce a large amount of data. Therefore, using the current big data algorithm is the best way to evaluate cluster management performance. In an industrial cluster, the elements that form a cluster are very complex, and individuals have the characteristics of network organization in the cluster. Therefore, the most mature neural network evaluation method in current cluster evaluation method is selected as the main method of management performance evaluation. Neural network algorithm is a kind of information processing method for simulating biological neural network, and it deals with problems through multiple nonlinear dynamic methods. The basic structure is shown in Fig. 1. The entire neural network includes the input layer, the output layer, and the hidden layer in the middle. The use of neural network algorithms to evaluate the performance of SME industrial cluster management can be accomplished in the following manner. Two kinds of different neural network algorithm evaluation methods are designed for the existence of cluster management performance evaluation samples, and a comprehensive evaluation of cluster management performance is conducted in two ways.

Fig. 1
figure 1

Basic structure of neural network model

The first is the evaluation that uses neural network algorithms to achieve the industrial cluster management without a sample. There are three main steps. First, an industrial cluster organization neural network is built. Function newff() is used to build the neural network function. The input elements are the neural network inter-layer transfer function, training function, the number of neurons, and the R × 2 matrix composed of the maximum value and the minimum value in the R-dimensional sample. The second step is to initialize the weights. The weight can be achieved by the newff() function. Reinitialization is achieved through init() function. The third step is cluster network simulation. Through the calculation of variable p, ()sim function, and network type, the output value α is obtained. However, the model implementation also needs to provide a target value reference for neural network algorithm training. This process needs to be achieved through principal component analysis. The specific approach is to use the method of dimension reduction to convert the variables of the evaluation index system into comprehensive factors. Then, the comprehensive factor is used to calculate the final score of the system evaluation and the weight value of the relevant indicator. It is assumed that the sample comes from n industrial clusters and all samples have p-specific indicators; then, the industry cluster management performance index matrix can be obtained. The formula is as follows:

$$ X=\left\{\begin{array}{llll}{x}_{11}& {x}_{12}& \cdots & {x}_{1p}\\ {}{x}_{21}& {x}_{22}& \cdots & {x}_{2p}\\ {}\cdots & \cdots & \cdots & \cdots \\ {}{x}_{n1}& {x}_{n2}& \cdots & {x}_{np}\end{array}\right. $$

First, the correlation coefficient matrix is calculated. The formula is as follows:

$$ R=\left\{\begin{array}{llll}{r}_{11}& {r}_{12}& \cdots & {r}_{1p}\\ {}{r}_{21}& {r}_{22}& \cdots & {r}_{2p}\\ {}\cdots & \cdots & \cdots & \cdots \\ {}{r}_{p1}& {r}_{p2}& \cdots & {r}_{pp}\end{array}\right. $$

rij in the formula represents the correlation coefficient between variables xi and xj, and i, j = 1, 2, 3, , p. The specific formula is

$$ {r}_{ij}=\frac{\sum \limits_{k=1}^n\left({x}_{ki}-{\overline{x}}_i\right)\left({x}_{kj}-{\overline{x}}_j\right)}{\sqrt{\sum \limits_{k=1}^n{\left({x}_{ki}-{\overline{x}}_i\right)}^2\sum \limits_{k=1}^n{\left({x}_{kj}-{\overline{x}}_j\right)}^2}} $$

The second is the calculation of eigenvalues and eigenvectors. λi(i = 1, 2, , p) can be obtained through |λI − R| = 0. After being arranged in the order of size, the corresponding feature vector ei(i = 1, 2, , p) is found using the feature value. The third step is to calculate the principal component contribution rate and cumulative contribution rate. It is assumed that the principal component contribution rate is zi, and then, the calculation formula is

$$ {z}_i={\gamma}_i/\sum \limits_{k=1}^p{\gamma}_k $$

Therefore, the calculation formula of the cumulative contribution rate is

$$ \sum \limits_{i=1}^m{z}_i=\sum \limits_{k=1}^m{\gamma}_k/\sum \limits_{k=1}^p{\gamma}_k $$

In an actual case, the feature value λ1, λ2, , λm having a cumulative contribution rate of 85% or more corresponds to the first, second,... vth principal component.

Finally, the load of the main component is calculated. The formula is as follows:

$$ P\left({z}_k,{x}_i\right)=\sqrt{\gamma_k{e}_{ki}} $$

The results of the principal component analysis of the cluster management performance can be finally obtained. The formula is as follows:

$$ R=\left\{\begin{array}{llll}{z}_{11}& {z}_{12}& \cdots & {z}_{1m}\\ {}{z}_{21}& {z}_{22}& \cdots & {z}_{2m}\\ {}\cdots & \cdots & \cdots & \cdots \\ {}{z}_{n1}& {z}_{n2}& \cdots & {z}_{nm}\end{array}\right. $$

The above steps can realize the evaluation of the management performance of the sample-free industrial cluster. Then, for the existing industrial clusters, the self-organizing neural network algorithm can be used to classify the performance level. The specific steps are to perform network initialization first, that is, to set the initial weight value between the neural network mapping layer and the input layer in a random manner.

The second step is to input vector x = (x1, x2, , xn)T into the input layer.

The third step is to calculate the distance between the input vector and the mapping layer over weight vector, and the calculation formula is

$$ {d}_j=\sqrt{\sum \limits_{i=1}^n{\left({x}_i-{w}_{ij}\right)}^2} $$

wij in the formula is the weight between the input layer neuron i and the mapping layer neuron j.

In the fourth step, neurons are selected. This step is done by the nearest distance to the weight. It is assumed that dj is the neuron with the closest distance to the weight, and the neuron is considered to win the competition and is denoted as j. Then, the set of neighboring neurons can be gotten.

The fifth step, weight learning, that is, the weights between the competing winning neurons and neighboring neurons are updated according to the following formula:

$$ \varDelta {w}_{ij}=\eta exp\left[-\frac{{\left|j-j\ast \right|}^2}{\sigma^2}\right]\left({x}_i-{w}_{ij}\right) $$

η in the formula is a constant and satisfies 0 < η < 1. σ2 is the variance.

The sixth step is whether it meets the preset requirements. If yes, then the algorithm ends; otherwise, it returns to the second step.

After determining two evaluation methods, the comprehensive evaluation method of industrial cluster management performance based on neural network algorithm is shown in Fig. 2. The first is to obtain the data of the original index of the industrial cluster, and then to process the raw data by means of de-calcification. According to the condition of the sample, the neural network algorithm is selected for learning. For the sample data, the management performance level is classified after competition learning through the self-organizing neural network algorithm. Otherwise, the target value is obtained by means of principal component analysis, and the index data obtained after processing is used as the output value for BP neural network training. Finally, the evaluation of the cluster performance level can be gotten. The two algorithms cooperate with each other to finally complete the comprehensive evaluation of industrial cluster management performance.

Fig. 2
figure 2

Construction of performance evaluation model for industrial cluster management of small- and medium-sized enterprises based on BP neural network algorithm

4 Result analysis and discussion

In order to verify the feasibility of the comprehensive evaluation model of industrial cluster management performance based on the neural network algorithm designed in this paper, the J region industrial cluster is chosen as the experimental object to carry out experiments. Because the evaluation of industrial cluster management performance is a nonlinear mapping between each index and the final evaluation, the number of BP neural networks is set to three levels. The three-level algorithm can satisfy any precision approximation mapping. First, the model is trained. The training is performed by using a gradient function traingd, and the accuracy is set to 1e−5. The learning rate is set to 0.05. Figure 3 shows the BP neural network training results. As can be seen from the figure, the initial accuracy of the BP neural network algorithm is 10e−2. After 10,559 trainings, the accuracy reaches the preset 1e−5. The training results show that the BP neural network can be used to evaluate the management performance of industrial clusters.

Fig. 3
figure 3

BP neural network training process

After the BP neural network algorithm has reached the requirement of accuracy after training, the three large industrial clusters of BJ (Bei Jing) City, TJ (Tian Jing) City, and HB Province in the J region are used to perform the verification. The verification process is shown in Fig. 4. The figure shows the evaluation results of the principal component analysis results and the BP neural network algorithm. It can be seen from the figure that the main component analysis results of the industrial clusters in the three regions are significantly different from the BP neural network algorithm evaluation results. The main component analysis result of BJ City is − 0.6588, and the difference between − 0.7528 and BP neural network evaluation result is the largest, and the difference is 0.094. The principal component analysis result of TJ City is − 0.7844, and the difference value of − 0.8398 from the evaluation result of BP neural network algorithm is 0.0554. The result of principal component analysis in the province of HB is − 0.8626, which is a difference of − 0.02846 from the evaluation result of the BP neural network algorithm − 0.8846. It can be seen that the difference of BJ City is the largest and the difference of HB Province is the smallest. The overall average variance error for the three regions is calculated to be 0.0041. From the overall error results, the method designed in this paper has strong feasibility.

Fig. 4
figure 4

Comparison between network output value and target value

The performance evaluation of SME industrial cluster management based on the wireless network development in J area proves that the method designed in this paper has strong feasibility. Therefore, a comprehensive evaluation of SMEs’ industrial cluster management performance based on wireless network development in seven provinces and cities, including GD, JS, SC, HeN, HuN, AH, and GZ, is conducted. The results of the evaluation are divided into performance scores and performance levels. According to the order of GD, JS, SC, HeN, HuN, AH, and GZ, their performance scores are 1, 0.759, − 0.6756, − 0.7102, − 0.7654, − 0.7704, and − 0.9635, respectively. Their corresponding performance levels are 3, 3, 5, 1, 2, 2, and 4 respectively. By comparing with the performance score, it can be known that when the performance level is 3, the performance score is positive, indicating that the industrial cluster management performance of GD and JS provinces is very high. The corresponding SC Province has a performance level of 5 and a performance score of − 0.6756, which is worse than the previous two. By analogy, it can be known that HN provincial management performance is moderate. The degree of performance management in HN Province and AH Province is in the middle and lower level. The management performance of GZ is at a low level. This evaluation result is basically consistent with the economic development level of these provinces, indicating that the method designed has high practicality (Fig. 5).

Fig. 5
figure 5

Comprehensive analysis of performance of industrial cluster management in small- and medium-sized enterprises

5 Conclusion

The rapid development of information technology has led to the emergence of industrial agglomeration for SMEs that are based on the development of wireless networks. The agglomeration of regional industries has a very important impact on the development of the regional economy. Therefore, the research on the management performance of SME industrial clusters has become very important. The study of the evaluation system of SMEs’ industrial cluster management performance based on wireless network development is proposed in this paper. Based on the core of the development of industrial clusters in the wireless network era, a set of management performance evaluation system is constructed, and a comprehensive rating model is designed based on the selection of neural network algorithm. In subsequent experiments, the method is verified by using the three largest industrial clusters in the J region as an example. The verification results show that this method has strong feasibility. Then, this method is used to evaluate the management performance of SME industrial clusters in different provinces. The final results of the evaluation show that the level of management performance is consistent with the level of economic development in the region, indicating that the methodology of this paper is practical.

Change history



An Hui


Bei Jing


Guang Dong


Gui Zhou


He Nan


Hu Nan


Jiang Dong


Si Chuan


Tian Jing


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JL has made many contributions to the collection of wireless network and finally made a great contribution to the summary of the whole article. WC has done a lot of research on the small business industry and provided a lot of data; ZW made a lot of records on the management of small enterprises and observed the management performance of small enterprises for a long time. All authors read and approved the final manuscript.

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Correspondence to Jiang Lan.

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Jiang Lan; associate professor; PhD candidate in the school of management, Xi’an University of Architecture and Technology; main research fields: engineering economics and management.

Wang Chengjun; professor; doctoral supervisor; dean in the school of management, Xi’an University of Architecture and Technology; main research fields: complex system analysis.

Zhang Wei; lecturer; teacher in the Teaching & Research Section of Ideological and Political Theory Apartment, Shaanxi Railway Institute; main research fields: technological and social progress.

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Lan, J., Chengjun, W. & Wei, Z. RETRACTED ARTICLE: Investigation of the evaluation system of SMEs’ industrial cluster management performance based on wireless network development. J Wireless Com Network 2019, 1 (2019).

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