# Adaptive Clustering Algorithm of Complex Network Based on Fuzzy Neural Networks

Authors: Zhixun Zhang; Juan Wang; Yanqiang Xu; Wei Han
Journal: Mobile Information Systems
 (2022)

---

## Abstract

Clustering analysis, as one of the important methods in data mining technology, merely provides a method for the research and analysis of large amounts of data. Starting with the most important nodes, this paper divides clustering based on data field characteristics. The sensitivity pruning algorithm is then used to further adjust and optimize the structure of the fuzzy neural network, allowing the network to automatically learn the structure and parameters of the system in different environments and obtain the optimal control rules. Finally, the clustering function brings the algorithm’s output result to a close. The experimental results show that the adaptive clustering algorithm of complex networks presented in this paper can effectively improve network cluster division, reduce algorithm time complexity, and avoid the problem of providing the number of cluster structures in advance. This method’s cluster structure efficiency can reach 97.6 percent, and its highest clustering accuracy can reach 96.8 percent. The adaptive clustering algorithm proposed in this paper not only overcomes the traditional algorithm’s flaws, such as the need to predetermine the number of clusters and the clustering result being dependent on the initial clustering center selection, but also has ideal clustering accuracy. This study introduces a novel and more effective method for addressing the difficult problems of practical complex control systems.


---

## Body

## 1. Introduction

Everything in the real world has both macro-abstraction and micro-concreteness, and the latter is referred to as complexity. Because of the rapid advancement of information network technology, the network is always present in our lives, work, study, and communication [1]. This leads to increasingly complex interpersonal relationships, indicating that people’s lives have progressed into the era of complex networks. With the advancement of computer technology, it has been demonstrated that the node degree distribution in complex networks follows the power law distribution, and a scale-free network model has been established on this basis [2]. A complex network is a unified whole with a large number of nodes and complex interactions and dependencies between them. The system elements are regarded as network nodes, and the correlation between elements is regarded as the basis for node connection, thus abstracting the complex system into a complex network. A large number of complex networks have community structure characteristics, and the purpose of the network’s community structure discovery algorithm is to find the communities that exist in the network based on the network’s topology. Researchers have discovered in recent years, through statistical analysis of a large number of actual networks in various fields, that completely regular or completely random networks do not exist or are few, and that the majority of them are complex networks with statistical characteristics that fall somewhere between regular and random. Complex networks have primarily evolved through three stages, beginning with completely regular networks and progressing to completely random networks, then to incomplete random networks with scale-free or small-world properties. The complex networks that have been built are more suitable for the real world and have attracted more people to this field. Community structure is also known as clustering in complex networks in the field of complex networks. People have been studying community structure for a long time, and algorithms for discovering community structure, such as the greedy algorithm, are becoming more mature.Although neural networks are capable of approximating real continuous functions on compact sets with arbitrary accuracy, as well as parallel computing, distributed storage, strong fault tolerance, and self-learning, they lack the ability to express human language, such as expert knowledge and experience. However, while a fuzzy system can express fuzzy or qualitative knowledge, it lacks the ability to self-learn and self-adapt. A fuzzy neural network is a hybrid of an artificial neural network [3–5] and a fuzzy logic system. On the one hand, it compensates for the shortcomings of pure fuzzy logic in learning, while on the other, it renders the “black box” problem of neural networks transparent. The application of cluster analysis in data mining can effectively speed up the positioning of information under the background of information technology with database as the core, and with the development of neural network, the application range of cluster analysis is wider. The fundamental premise of the complex network clustering algorithm [6–8] is to mine the real family structure using network topology, and the goal is to find the cluster structure. Because this type of algorithm can detect cluster structure in a network, it has significant theoretical and application value. Cluster analysis, as one of the important methods in data mining [9, 10] technology, has become a research hotspot in analyzing the growing large-scale data. Currently, as different types and large-scale data sets proliferate, the demand for clustering analysis methods is increasing. Long-term research has revealed that the community structure characteristics of complex networks, as well as the corresponding community structure algorithm, have laid the groundwork for the complex network clustering analysis proposal. Based on this, this paper proposes a fuzzy neural network-based adaptive clustering algorithm for complex networks. The following are its innovations:(1)
In this paper, the concept of data field in physics is introduced, and the central node is mined by putting forward the importance factor of the node. The influence range of the central node on the surrounding blessings is bound to be larger, so it constitutes a cluster in a complex network. The clustering algorithm which combines the community division technology of complex network with similarity measure solves the problem of determining the number of clusters in advance.(2)
In the learning process of fuzzy neural network, the error back propagation learning algorithm is used to modify the parameters, and the sensitivity pruning algorithm is used to further optimize the network structure, so as to achieve the purpose of self-adaptive adjustment of the network structure and parameters, thus obtaining the optimal fuzzy control rule base. Moreover, the adaptive neural fuzzy network is used to adjust the front and back parameters of the model, thus improving the convergence speed and modeling accuracy of the system.This paper focuses on the adaptive clustering algorithm of a complex network based on a fuzzy neural network. Its chapters are organized as follows: The first chapter is an introduction. This section provides the specific research content, research background, and research significance. It also introduces the research innovation and chapter structure of this paper. The second chapter is about related work. This chapter discusses the research status of the research topics in this paper at home and abroad, conducts a thorough examination of these documents, and presents the research work and methods of this paper. In chapter 3, the related theoretical foundation is introduced, and an adaptive clustering algorithm of complex networks based on fuzzy neural networks is designed and proposed. In chapter four, a large number of experiments are carried out to investigate the feasibility of the proposed method. The fifth chapter is a summary and prospect. This chapter summarizes the paper’s research findings. Finally, the shortcomings of this paper are discussed, as well as future research directions.


## 2. Related Work

In the real world, complex networks are becoming increasingly intertwined with people, and they are becoming increasingly inseparable from daily life. To make better use of these networks, we can study them using a variety of methods, the most efficient of which is to employ the concept of complex networks. Complex network clustering algorithms are important not only for solving graph segmentation in computer science, but also for discovering communities in sociology. Simultaneously, it is the primary method for biology and other disciplines to study their respective fields. There are numerous studies being conducted on fuzzy neural networks and complex network clustering algorithms at the moment.In order to reduce the computational cost of clustering without reducing the quality of the solution. Burlak and Medina-Ángel used ant colony optimization technology to find factions in the network and assign these factions as meta-nodes, and then used traditional algorithms to find community members [11]. Xu and Yan proposed a fitness model, which uses fitness to determine whether nodes are connected [12]. Peng and Chen used the fuzzy likelihood function to define the clustering criteria to cluster the sample data, so as to realize the identification of the fuzzy model. However, this method must pre-set the number of rules [13]. Chao and Yan used the quadratic optimization method to minimize the pre-specified cut function, and when the network was divided into a network with the smallest cut, it was considered to be the optimal network division. However, this method cannot ensure that the division result obtained by the idea of recursive bisection is in line with the actual multi-network cluster structure [14]. Xia et al. proposed an adaptive fuzzy identification method based on the BP algorithm, but there are still the shortcomings of the BP algorithm falling into local solutions and slow speed [15]. By analyzing the parameters, Dong et al. constructed a model to explain the phenomenon that the real network does not fully satisfy the power-law distribution [16]. F. Shanshan and R. Zhiqiang et al. proposed a fuzzy neural network identification method based on clustering, which identifies the structure and parameters of the antecedents through fuzzy clustering, and then uses linear fitting or gradient algorithm to obtain the parameters of the posteriors [17]. Tang pointed out that the core of fuzzy logic system is fuzzy rule base, and it takes a long time to build fuzzy rule base, especially for very complex systems, it is very difficult to establish correct fuzzy rules and membership functions [18]. Sathiamoorthy and Ramakrishnan proposed an algorithm to replace the edge betweenness of the algorithm with the connecting clustering coefficient. The idea is that the short-circuit path basically does not appear on the path between the connecting clusters, otherwise the edges between the connecting clusters will increase in multiples, resulting in an increase in the density of the edges between the clusters; therefore, the algorithm sets the connecting clustering coefficient within the connecting clusters. The heuristic rule [19] that connects the clustering coefficients of connections between clusters should be exceeded. Aiming at the problem that the scale-free network model only has point addition operations, Lotte et al. proposed an optimization model that incorporates the effects of edge addition and edge reconnection on the network into the scope of investigation [20].Because the traditional clustering method cannot actively discover the total number of family structures, it has defects in practical application. Based on the research of related literature, this paper proposes an adaptive clustering algorithm for complex networks based on fuzzy neural network by constructing a clustering evaluation function and actively finding the optimal number of clusters. In this paper, the fuzzy C-means clustering algorithm is used to determine the input space partition of the system according to the number of fuzzy rules. Then, the fuzzy space of the system is divided based on the fuzzy competitive learning algorithm, and the appropriate number of fuzzy rules and the applicability of each sample to each rule are obtained. In the learning process of the network, the error back propagation learning algorithm and sensitivity pruning method are used to optimize the parameters and structure of the network, so as to achieve the purpose of adaptively adjusting the weight parameters and structure.


## 3. Methodology

### 3.1. Fuzzy Neural Networks and Complex Networks

With the continuous penetration of Internet technology in biotechnology, artificial intelligence and other fields [21], the research on artificial neural network has gradually surfaced. The development of artificial network has experienced a road consisting of three stages: rise, depression and prosperity. A large number of neurons with the same form are connected together to form a neural network, which is a highly nonlinear dynamic system. Although the structure and function of each neuron are not complicated, the dynamic behavior of neural network is very complicated. Nowadays, after decades of research by many scholars, the neural network is becoming more and more mature, and the research trend is crossing with other disciplines and merging with other new technologies, and it has achieved fruitful results. The application of fuzzy neural network has developed rapidly in recent years. Fuzzy neural network combines the low-level learning and computing ability of neural network with the high-level human-like thinking and reasoning ability of fuzzy logic system, and realizes the complementary advantages of both. The fuzzy neural network formed by the organic combination of fuzzy system and neural network combines the advantages of both. It can not only express approximate and qualitative knowledge like fuzzy system, but also has strong learning and nonlinear expression ability of neural network. Moreover, the physical meaning of parameters of fuzzy neural network is very clear. But in the process of development, there is always a difficult problem. It is the problem of structural identification, that is, how to divide the input and output space properly and how to extract a simplified fuzzy rule base from the observed data.The fuzzy system modeling process in the design process of a fuzzy neural network consists primarily of two parts: structure identification and parameter estimation. The partition and fuzzy rules of the input space are determined by structure identification. The membership function corresponding to the input variables divides the input space, so determining the shape, number, and fuzzy rules of the membership function is the task to be completed for structure identification [22]. Because effective input space partitioning can effectively reduce the number of fuzzy rules, input space partitioning is also very important. As a result, determining the number of membership functions and their parameters is critical. Many academics are interested in clustering. There have been a large number of classical algorithms developed thus far. At the moment, clustering algorithm research is primarily divided into two schools, namely the classical clustering algorithm and the fuzzy clustering algorithm. Clustering algorithm, as an unsupervised classification method, can distinguish and classify things based on certain requirements and rules. Because the fuzzy clustering algorithm divides the input space directly, it employs multidimensional membership functions. As a result, the number of fuzzy rules in the fuzzy system is greatly reduced. As a result, the “dimension disaster” of the traditional method of dividing the input dimension is avoided. The complex network clustering analysis methods used in the process of realizing neural network technology primarily include the K-Lin algorithm, traditional spectrum bisection method, and splitting algorithm. Figure 1 shows the composition of fuzzy control system and classification of clustering algorithm.Figure 1
Composition of fuzzy control system and classification of clustering algorithm.Complexity is developed along with the cross research of many disciplines at present, and it originated from graph theory in mathematics. It is used to study rule networks. Because the number of nodes in a network is small and the connection rules of edges are not complicated, a regular network cannot be called a complex network in a strict sense. Complex network is a network with certain organization, attractor, small world, scale-free, some or all properties, and has high self-similarity in structure and form. The discovery of complex network cluster structure is of great reference value for intuitive understanding of network functions, in-depth analysis of network topology, effective discovery of hidden characteristics and rules in the network, and prediction of network behavior. The research of family structure is widely used in the fields of community detection in sociology, understanding of metabolic function in biology, and distinguishing the major functions of the Internet. In the actual network, many network nodes with the same nature are closely connected and gathered into a community, but there is no dense connection between network nodes with different properties, which is the community structure. Community can contain modules, classes, groups, groups and other meanings. Finding the community structure in the network is of great significance for analyzing the basic characteristics and common characteristics of the community structure in the network. In a complex network, degree is used to describe the characteristics of the network. That is, the number of lines connecting a node with other nodes. The more lines, the greater the degree of the node, and the greater the influence of the node on the network. Mining the important nodes according to the network topology is the goal of network centralization research, and the difference of the importance of nodes is determined by the heterogeneous topology of complex networks. Radial basis function network is a single hidden layer feedforward neural network with good performance. It can determine the corresponding network topology structure according to different problems, and has the advantages of better approximation ability, smaller network training scale, faster learning speed and no local minimum problem.


### 3.2. Complex Network Adaptive Clustering Algorithm

There are many similarities between neural network and fuzzy reasoning technology in terms of information processing and control, and their complementary nature can penetrate and promote the formation of new processing structures and algorithms via neural network and fuzzy reasoning technology. Clustering is a data structure exploration tool, and its core is clustering. Clustering is the process of dividing a data set into multiple classes based on a predefined standard. The similarity between data objects within the same class is high, but the similarity between data objects within different classes is low. There are two basic methods for analyzing fuzzy clusters: systematic clustering and stepwise clustering. The fuzzy equivalence relation underpins the system clustering method. The fuzzy division underpins the step-by-step clustering method. The system clustering method can only obtain the final clustering result once and has a high distinguishing ability. The number of clusters must be determined in advance using the step-by-step clustering method. If the number of clusters is insufficient, the clustering operation will be repeated. The fuzzy system modeling process in the design process of a fuzzy neural network consists primarily of two parts: structure identification and parameter estimation. Because effective input space partitioning can effectively reduce the number of fuzzy rules, input space partitioning is critical. After determining the structure, parameter estimation is used to determine all of the parameters in the system.The key to designing fuzzy systems is to acquire fuzzy knowledge. The traditional method is to acquire some fuzzy rules through experience. The disadvantages of this method are strong subjective assumption, poor adaptability, long design cycle and no self-learning and adaptive ability. Using the self-learning ability of neural network to extract fuzzy rules or parameters of fuzzy rules, and applying the learning ability of neural network to expand the knowledge base in real time can solve this problem to a great extent. In fuzzy clustering, similarity coefficient and distance coefficient are usually selected as similarity coefficients. Distance coefficient is a mathematical quantity, which refers to the similarity of values between data. Similarity coefficient describes the shape similarity between data. When the similarity coefficient value is equal to 0, it means that they are completely different from each other, while when the value is equal to 1, it means that they are completely the same. The adaptive clustering algorithm for complex networks proposed in this paper is characterized by the fact that it can automatically merge and divide clusters without any prior knowledge of data sets. The clustering analysis experiment shows that the algorithm is effective and feasible, and it can complete the clustering analysis of data without any prior knowledge. The flow chart of adaptive clustering algorithm of complex network based on fuzzy neural network is shown in Figure2.Figure 2
Flow chart of complex network adaptive clustering algorithm based on fuzzy neural network.This paper consists of two parts: the antecedent network and the consequent network. The antecedent network is used to match the antecedent of fuzzy rules, and the consequent network is used to generate the consequent of fuzzy rules. The basic idea of the adaptive clustering algorithm in this paper is to start from the central node of a cluster, and use the influence of potential function to divide other nodes into clusters which are greatly influenced by the central node. The discovery of cluster center nodes is based on the node importance factor proposed by the advantages and disadvantages of each node centrality. The improved adaptive clustering algorithm includes not only the similarity of values between data, but also the shape similarity between data. In this way, not only the flexibility of clustering is improved, but also the final clustering result is more reliable. GN (Girvan Newman) algorithm is a community discovery algorithm based on edge betweenness, and it is also a typical splitting method [23]. Although GN algorithm is better than other original algorithms in analyzing community structure, and its accuracy is higher, it is no longer suitable for analyzing large-scale complex networks because of its high time complexity. In order to analyze and deal with large-scale complex networks, algorithms with less time complexity are needed. This paper introduces Newman fast algorithm. In this paper, in Newman’s fast algorithm, the accuracy of the algorithm is not measured by modularity. Instead, modularity is used as an optimization value, and nodes are merged by connecting edges that increase modularity, so as to form a community. Each node and all parameters in fuzzy neural network have obvious physical significance, which is the advantage of fuzzy neural network over pure neural network. The initial values of these parameters can be determined according to the fuzzy qualitative or qualitative knowledge of the system, and then the learning algorithm can quickly converge to the required input-output relationship.The datasetXx1,x2,x3,…,xn⊂RP is divided into c groups to minimize the weighted sum of squared distances from the samples in each category to the cluster centers. In fuzzy clustering, the objective function often takes the following form:(1)JmU,v=∑k=1n∑i=1cμikmdik2,1≤m<∞.Its constraints are:(2)∑i=1cμikm=1,1≤k≤n,(3)μik≥0,1≤i≤c,1≤k≤n.Among them,n is the total number of sample data points; c is the number of cluster centers; U is the membership function matrix; μik is the element in row i and column k of matrix U. The necessary conditions for the objective function Jm to reach the minimum value are:(4)vi=∑k=1nμikmχk∑k=1nμikm,(5)μik=∑j=1cdikdjk2/m−1−1.After obtaining the cluster centers and membership functions, use the following formula to calculate the fuzzy covariance matrix:(6)Fi=∑j=1nμijmxj−vixj−viT∑j=1nμijm,1≤i≤c.Newman’s degree correlation coefficient is calculated as:(7)r=M−1∑ijiki−M−1∑i0.5∗ji+ki2M−1∑i0.5∗ji2+ki2−M−1∑i0.5∗ji+ki2.Among them,ji and ki represent the degrees of two nodes on the i th edge, and M is the total number of edges in the network. The strength of node i is shown below.(8)Si=∑j∈Niwij.Among them,Ni represents the set of node i neighbors.Characteristics of “class” in clustering analysis: the class mentioned in clustering is not given in advance, but divided according to the similarity and distance of data. The measurement method of similarity between data greatly affects the clustering effect, which can be said to be the core of clustering algorithm. The initial clustering center of the adaptive clustering algorithm in this paper is not chosen at random, but is divided from the approximate cluster structure’s center node. Instead of providing a fixed number of clusters, the number of clusters is determined adaptively based on the cluster evaluation function. It is unaffected by boundary nodes, but divides the potential superposition of undivided nodes based on the family’s divided nodes. The main disadvantage of partition coefficient is that it does not have a direct relationship with the geometric structure of the data set and can only reflect the average degree of separation of samples between data clusters. The proposed validity function incorporates into the partition coefficient geometric structure information reflecting the compactness of samples in the data clustering class. Because training samples will inevitably contain errors, if the network structure is redundant, these errors will affect the training convergence direction of the entire fuzzy neural network in the later stage of network training, causing deviation of the global optimal point and reducing generalization ability. This is referred to as over-training or over-fitting. Because each node in the network can connect to any other node, many complex networks will form. However, in reality, only one network is required, necessitating the evolution of various complex networks that have been constructed. Nodes in a complex network do not exist independently. They are interconnected and influence each other, and the influence range of important nodes is broad, whereas that of other nodes is narrow. When a network has modularity and clustering, the mutual influence between nodes has local characteristics, and as network distance increases, the influence of each node rapidly declines. The fuzzy system produces the following results:(9)Y=∑i=1cβiyi=∑i=1cβiz^Tθi.Define the total error function as:(10)E=1N−1∑k=1Nyk−y∗k2.Among them,yk is the output of the fuzzy system, and y∗k is the expected value. In this paper, three indicators, accuracy rate, recall rate and F1 value are selected to evaluate the clustering results. It is calculated as follows:(11)Correct rate=nrnt,where nr is the number of correctly classified data in the cluster, and nt is the number of theoretical data in the cluster.(12)Recall=nrna.Among them,na is the number of data actually allocated in the cluster.(13)F1Score=2×Correct rate×RecallCorrect rate+Recall.Since theF1 value can reflect the correct rate and recall rate in a balanced way, when the F1 value of a classification is higher, it indicates that the classification accuracy of the class is better.In this paper, it is considered that when there is no other empirical knowledge, the simplest network that can match the given sample is the best choice, which is equivalent to making the deviation of the sample point approach the unknown nonlinear mapping with the smoothest function within the allowable range. The learning algorithm of fuzzy classifier divides the training samples into a corresponding class through competitive learning, and then obtains the membership degree of the sample belonging to a certain class through fuzzy membership function, that is, the compliance degree of the sample belonging to each rule. Complex network clustering methods have certain defects, either the calculation accuracy can not meet the requirements, or the time complexity is too high, or a specific parameter value needs to be given in advance, such as the number of clusters. The observed values in the data set are taken as the matrix of the original object, and all the original data are converted into data in the interval [0, 1], and then the range normalization calculation is carried out, that is, all the data are located in the interval [0, 1]. When genetic algorithm is used to optimize the network structure, each network individual in the neural network population is a possible potential solution to the optimization classification problem, and all of them have to be trained. Firstly, the variables representing the network structure are expressed as gene codes. Then, a series of genetic operations simulating biological evolution-selection and regeneration based on fitness, crossover and mutation are carried out on the population. So as to produce a better new generation. In this paper, the idea of structural adaptation is introduced, and a new fuzzy rule is established by adding a new clustering center and radius for the samples not included in the existing fuzzy hyperellipsoid space. Then, based on the result of this fuzzy classifier, a fuzzy neural network is constructed, and the parameters of the latter network are optimized, so that the identified model has higher accuracy and fully reflects the characteristics of the system. Because the short-range field plays an important role in revealing the cluster structure in the network, the mutual influence between nodes is generally measured by Gaussian function with short-range field, which is continuous, smooth, limited, isotropic and monotonically decreasing.


## 3.1. Fuzzy Neural Networks and Complex Networks

With the continuous penetration of Internet technology in biotechnology, artificial intelligence and other fields [21], the research on artificial neural network has gradually surfaced. The development of artificial network has experienced a road consisting of three stages: rise, depression and prosperity. A large number of neurons with the same form are connected together to form a neural network, which is a highly nonlinear dynamic system. Although the structure and function of each neuron are not complicated, the dynamic behavior of neural network is very complicated. Nowadays, after decades of research by many scholars, the neural network is becoming more and more mature, and the research trend is crossing with other disciplines and merging with other new technologies, and it has achieved fruitful results. The application of fuzzy neural network has developed rapidly in recent years. Fuzzy neural network combines the low-level learning and computing ability of neural network with the high-level human-like thinking and reasoning ability of fuzzy logic system, and realizes the complementary advantages of both. The fuzzy neural network formed by the organic combination of fuzzy system and neural network combines the advantages of both. It can not only express approximate and qualitative knowledge like fuzzy system, but also has strong learning and nonlinear expression ability of neural network. Moreover, the physical meaning of parameters of fuzzy neural network is very clear. But in the process of development, there is always a difficult problem. It is the problem of structural identification, that is, how to divide the input and output space properly and how to extract a simplified fuzzy rule base from the observed data.The fuzzy system modeling process in the design process of a fuzzy neural network consists primarily of two parts: structure identification and parameter estimation. The partition and fuzzy rules of the input space are determined by structure identification. The membership function corresponding to the input variables divides the input space, so determining the shape, number, and fuzzy rules of the membership function is the task to be completed for structure identification [22]. Because effective input space partitioning can effectively reduce the number of fuzzy rules, input space partitioning is also very important. As a result, determining the number of membership functions and their parameters is critical. Many academics are interested in clustering. There have been a large number of classical algorithms developed thus far. At the moment, clustering algorithm research is primarily divided into two schools, namely the classical clustering algorithm and the fuzzy clustering algorithm. Clustering algorithm, as an unsupervised classification method, can distinguish and classify things based on certain requirements and rules. Because the fuzzy clustering algorithm divides the input space directly, it employs multidimensional membership functions. As a result, the number of fuzzy rules in the fuzzy system is greatly reduced. As a result, the “dimension disaster” of the traditional method of dividing the input dimension is avoided. The complex network clustering analysis methods used in the process of realizing neural network technology primarily include the K-Lin algorithm, traditional spectrum bisection method, and splitting algorithm. Figure 1 shows the composition of fuzzy control system and classification of clustering algorithm.Figure 1
Composition of fuzzy control system and classification of clustering algorithm.Complexity is developed along with the cross research of many disciplines at present, and it originated from graph theory in mathematics. It is used to study rule networks. Because the number of nodes in a network is small and the connection rules of edges are not complicated, a regular network cannot be called a complex network in a strict sense. Complex network is a network with certain organization, attractor, small world, scale-free, some or all properties, and has high self-similarity in structure and form. The discovery of complex network cluster structure is of great reference value for intuitive understanding of network functions, in-depth analysis of network topology, effective discovery of hidden characteristics and rules in the network, and prediction of network behavior. The research of family structure is widely used in the fields of community detection in sociology, understanding of metabolic function in biology, and distinguishing the major functions of the Internet. In the actual network, many network nodes with the same nature are closely connected and gathered into a community, but there is no dense connection between network nodes with different properties, which is the community structure. Community can contain modules, classes, groups, groups and other meanings. Finding the community structure in the network is of great significance for analyzing the basic characteristics and common characteristics of the community structure in the network. In a complex network, degree is used to describe the characteristics of the network. That is, the number of lines connecting a node with other nodes. The more lines, the greater the degree of the node, and the greater the influence of the node on the network. Mining the important nodes according to the network topology is the goal of network centralization research, and the difference of the importance of nodes is determined by the heterogeneous topology of complex networks. Radial basis function network is a single hidden layer feedforward neural network with good performance. It can determine the corresponding network topology structure according to different problems, and has the advantages of better approximation ability, smaller network training scale, faster learning speed and no local minimum problem.


## 3.2. Complex Network Adaptive Clustering Algorithm

There are many similarities between neural network and fuzzy reasoning technology in terms of information processing and control, and their complementary nature can penetrate and promote the formation of new processing structures and algorithms via neural network and fuzzy reasoning technology. Clustering is a data structure exploration tool, and its core is clustering. Clustering is the process of dividing a data set into multiple classes based on a predefined standard. The similarity between data objects within the same class is high, but the similarity between data objects within different classes is low. There are two basic methods for analyzing fuzzy clusters: systematic clustering and stepwise clustering. The fuzzy equivalence relation underpins the system clustering method. The fuzzy division underpins the step-by-step clustering method. The system clustering method can only obtain the final clustering result once and has a high distinguishing ability. The number of clusters must be determined in advance using the step-by-step clustering method. If the number of clusters is insufficient, the clustering operation will be repeated. The fuzzy system modeling process in the design process of a fuzzy neural network consists primarily of two parts: structure identification and parameter estimation. Because effective input space partitioning can effectively reduce the number of fuzzy rules, input space partitioning is critical. After determining the structure, parameter estimation is used to determine all of the parameters in the system.The key to designing fuzzy systems is to acquire fuzzy knowledge. The traditional method is to acquire some fuzzy rules through experience. The disadvantages of this method are strong subjective assumption, poor adaptability, long design cycle and no self-learning and adaptive ability. Using the self-learning ability of neural network to extract fuzzy rules or parameters of fuzzy rules, and applying the learning ability of neural network to expand the knowledge base in real time can solve this problem to a great extent. In fuzzy clustering, similarity coefficient and distance coefficient are usually selected as similarity coefficients. Distance coefficient is a mathematical quantity, which refers to the similarity of values between data. Similarity coefficient describes the shape similarity between data. When the similarity coefficient value is equal to 0, it means that they are completely different from each other, while when the value is equal to 1, it means that they are completely the same. The adaptive clustering algorithm for complex networks proposed in this paper is characterized by the fact that it can automatically merge and divide clusters without any prior knowledge of data sets. The clustering analysis experiment shows that the algorithm is effective and feasible, and it can complete the clustering analysis of data without any prior knowledge. The flow chart of adaptive clustering algorithm of complex network based on fuzzy neural network is shown in Figure2.Figure 2
Flow chart of complex network adaptive clustering algorithm based on fuzzy neural network.This paper consists of two parts: the antecedent network and the consequent network. The antecedent network is used to match the antecedent of fuzzy rules, and the consequent network is used to generate the consequent of fuzzy rules. The basic idea of the adaptive clustering algorithm in this paper is to start from the central node of a cluster, and use the influence of potential function to divide other nodes into clusters which are greatly influenced by the central node. The discovery of cluster center nodes is based on the node importance factor proposed by the advantages and disadvantages of each node centrality. The improved adaptive clustering algorithm includes not only the similarity of values between data, but also the shape similarity between data. In this way, not only the flexibility of clustering is improved, but also the final clustering result is more reliable. GN (Girvan Newman) algorithm is a community discovery algorithm based on edge betweenness, and it is also a typical splitting method [23]. Although GN algorithm is better than other original algorithms in analyzing community structure, and its accuracy is higher, it is no longer suitable for analyzing large-scale complex networks because of its high time complexity. In order to analyze and deal with large-scale complex networks, algorithms with less time complexity are needed. This paper introduces Newman fast algorithm. In this paper, in Newman’s fast algorithm, the accuracy of the algorithm is not measured by modularity. Instead, modularity is used as an optimization value, and nodes are merged by connecting edges that increase modularity, so as to form a community. Each node and all parameters in fuzzy neural network have obvious physical significance, which is the advantage of fuzzy neural network over pure neural network. The initial values of these parameters can be determined according to the fuzzy qualitative or qualitative knowledge of the system, and then the learning algorithm can quickly converge to the required input-output relationship.The datasetXx1,x2,x3,…,xn⊂RP is divided into c groups to minimize the weighted sum of squared distances from the samples in each category to the cluster centers. In fuzzy clustering, the objective function often takes the following form:(1)JmU,v=∑k=1n∑i=1cμikmdik2,1≤m<∞.Its constraints are:(2)∑i=1cμikm=1,1≤k≤n,(3)μik≥0,1≤i≤c,1≤k≤n.Among them,n is the total number of sample data points; c is the number of cluster centers; U is the membership function matrix; μik is the element in row i and column k of matrix U. The necessary conditions for the objective function Jm to reach the minimum value are:(4)vi=∑k=1nμikmχk∑k=1nμikm,(5)μik=∑j=1cdikdjk2/m−1−1.After obtaining the cluster centers and membership functions, use the following formula to calculate the fuzzy covariance matrix:(6)Fi=∑j=1nμijmxj−vixj−viT∑j=1nμijm,1≤i≤c.Newman’s degree correlation coefficient is calculated as:(7)r=M−1∑ijiki−M−1∑i0.5∗ji+ki2M−1∑i0.5∗ji2+ki2−M−1∑i0.5∗ji+ki2.Among them,ji and ki represent the degrees of two nodes on the i th edge, and M is the total number of edges in the network. The strength of node i is shown below.(8)Si=∑j∈Niwij.Among them,Ni represents the set of node i neighbors.Characteristics of “class” in clustering analysis: the class mentioned in clustering is not given in advance, but divided according to the similarity and distance of data. The measurement method of similarity between data greatly affects the clustering effect, which can be said to be the core of clustering algorithm. The initial clustering center of the adaptive clustering algorithm in this paper is not chosen at random, but is divided from the approximate cluster structure’s center node. Instead of providing a fixed number of clusters, the number of clusters is determined adaptively based on the cluster evaluation function. It is unaffected by boundary nodes, but divides the potential superposition of undivided nodes based on the family’s divided nodes. The main disadvantage of partition coefficient is that it does not have a direct relationship with the geometric structure of the data set and can only reflect the average degree of separation of samples between data clusters. The proposed validity function incorporates into the partition coefficient geometric structure information reflecting the compactness of samples in the data clustering class. Because training samples will inevitably contain errors, if the network structure is redundant, these errors will affect the training convergence direction of the entire fuzzy neural network in the later stage of network training, causing deviation of the global optimal point and reducing generalization ability. This is referred to as over-training or over-fitting. Because each node in the network can connect to any other node, many complex networks will form. However, in reality, only one network is required, necessitating the evolution of various complex networks that have been constructed. Nodes in a complex network do not exist independently. They are interconnected and influence each other, and the influence range of important nodes is broad, whereas that of other nodes is narrow. When a network has modularity and clustering, the mutual influence between nodes has local characteristics, and as network distance increases, the influence of each node rapidly declines. The fuzzy system produces the following results:(9)Y=∑i=1cβiyi=∑i=1cβiz^Tθi.Define the total error function as:(10)E=1N−1∑k=1Nyk−y∗k2.Among them,yk is the output of the fuzzy system, and y∗k is the expected value. In this paper, three indicators, accuracy rate, recall rate and F1 value are selected to evaluate the clustering results. It is calculated as follows:(11)Correct rate=nrnt,where nr is the number of correctly classified data in the cluster, and nt is the number of theoretical data in the cluster.(12)Recall=nrna.Among them,na is the number of data actually allocated in the cluster.(13)F1Score=2×Correct rate×RecallCorrect rate+Recall.Since theF1 value can reflect the correct rate and recall rate in a balanced way, when the F1 value of a classification is higher, it indicates that the classification accuracy of the class is better.In this paper, it is considered that when there is no other empirical knowledge, the simplest network that can match the given sample is the best choice, which is equivalent to making the deviation of the sample point approach the unknown nonlinear mapping with the smoothest function within the allowable range. The learning algorithm of fuzzy classifier divides the training samples into a corresponding class through competitive learning, and then obtains the membership degree of the sample belonging to a certain class through fuzzy membership function, that is, the compliance degree of the sample belonging to each rule. Complex network clustering methods have certain defects, either the calculation accuracy can not meet the requirements, or the time complexity is too high, or a specific parameter value needs to be given in advance, such as the number of clusters. The observed values in the data set are taken as the matrix of the original object, and all the original data are converted into data in the interval [0, 1], and then the range normalization calculation is carried out, that is, all the data are located in the interval [0, 1]. When genetic algorithm is used to optimize the network structure, each network individual in the neural network population is a possible potential solution to the optimization classification problem, and all of them have to be trained. Firstly, the variables representing the network structure are expressed as gene codes. Then, a series of genetic operations simulating biological evolution-selection and regeneration based on fitness, crossover and mutation are carried out on the population. So as to produce a better new generation. In this paper, the idea of structural adaptation is introduced, and a new fuzzy rule is established by adding a new clustering center and radius for the samples not included in the existing fuzzy hyperellipsoid space. Then, based on the result of this fuzzy classifier, a fuzzy neural network is constructed, and the parameters of the latter network are optimized, so that the identified model has higher accuracy and fully reflects the characteristics of the system. Because the short-range field plays an important role in revealing the cluster structure in the network, the mutual influence between nodes is generally measured by Gaussian function with short-range field, which is continuous, smooth, limited, isotropic and monotonically decreasing.


## 4. Result Analysis and Discussion

The data used in this paper are selected from the IRIS data set in the UCI database, which is used to test the clustering algorithm internationally, and are actually tested, to demonstrate the effectiveness of the adaptive clustering algorithm of complex networks based on fuzzy neural network proposed in this paper. The IRIS data set is a sample set of three different types of flowers. Each flower has 50 data sets, for a total of 150 data sets. Each data set contains four flower attributes: sepal length, sepal width, petal length, and petal width, making it a four-dimensional data set. The first species is entirely distinct from the other two, and the second species intersects with the third. The data set contains 150 data objects, which are divided into three categories, each with 50 data objects. The value table of IRIS data set classification validity function is shown in Table1.Table 1
IRIS data set classification validity function value table.
Class numberCorresponding value21.23631.17841.11650.98560.95471.00380.74590.689100.612It can be seen from Table1 that the maximum value of the validity function of IRIS data is obtained when the number of classes is 3, and the second maximum value is obtained when the number of classes is 2, which is completely consistent with the actual distribution of IRIS data. Evolve the complex network, connect each complex network with the adjacent complex network to form a small group, and take node 8 as an example to form a small group. We carry out the recall experiment and get the recall results of different algorithms, as shown in Figure 3.Figure 3
Comparison result of recall rate.A computer-generated network data set is commonly used to assess the accuracy of cluster structure division. This information is a network diagram of a collection of known topological structures generated at random by a computer. Each network has 128 nodes and four distinct cluster structures, each with 32 nodes. Multiple rules are frequently activated at the same time in fuzzy systems, and the output is the result of the interaction of multiple rules, so that deviation from one rule has little influence on the result. The contribution of each neuron and connection to the overall function of a neural network is so small that the failure of a few neurons and connections has little impact on network function. The execution of programs is the final step in the evolution of small groups of complex networks. The evolution of small groups represents the evolution of each complex network in small groups, and its operations include crossover and mutation. Figure4 depicts the clustering errors of the K-means, Kernighan-Lin, and this algorithms based on experiments.Figure 4
Error comparison of the three algorithms.In this paper, each clustering result is regarded as a node of a complex network, and the data in each node are messy and need to be processed. For the processing of nodes in each complex network, the key is to find the two individuals who are closest to each other and then use the algorithm to find the shortest distance between the two individuals. The network that is often used to verify the validity of cluster structure discovered by clustering algorithm in complex networks is Zachary Karate Club Network, which is a typical small social network. In order to get the accuracy of the results, this paper uses Zachary network and computer-generated network for simulation analysis. The precision results shown in Table2 are obtained.Table 2
Clustering accuracy results of different algorithms on different networks.
AlgorithmPrecisionZachary karate club networkComputer-generated networkKerni ghan-lin algorithm0.7420.856K-means algorithm0.6830.841K2 means algorithm0.7090.896CNM clustering algorithm0.8950.914Adaptive clustering algorithm in this paper0.9560.968In order to reflect the experimental results more intuitively, this paper plots the efficiency of different algorithms on different networks as a line graph. The cluster structure efficiency obtained by different algorithms on the Zachary network is shown in Figure5. The cluster structure efficiency obtained by different algorithms on the computer-generated network is shown in Figure 6.Figure 5
The cluster structure efficiency obtained by different algorithms on the zachary network.Figure 6
The cluster structure efficiency obtained by different algorithms on the computer-generated network.From the comparison between Figures5 and 6, it can be concluded that the cluster structure obtained by the complex network adaptive clustering algorithm in this paper has higher efficiency. This algorithm can accurately divide the number of actual cluster structures in different networks, and the accuracy rate is high. The efficiency of cluster structure obtained on Zachary network can reach about 96.8%, and the efficiency of cluster structure obtained on computer generated network can reach about 97.6%. In practical engineering applications, the order of the model is usually unknown, so it is necessary not only to determine the scale of the hidden layer and nodes of the neural network but also to select the appropriate model input. Sensitivity pruning algorithm can accomplish this work effectively. Parameter identification takes into account that there are both linear and nonlinear parts in the calculation of network output. For the linear part, the least square method can be used; for the nonlinear part, the gradient descent algorithm can be used to train the weights, that is, the mixed algorithm of the least square method and the gradient descent algorithm can be used together. Comparison of F1 values of different algorithms is shown in Figure 7.Figure 7
F1 value of different algorithms.According to the data in Figure7, the F1 value of this algorithm is the highest, reaching 95%. K-means algorithm is the second, and Kerni ghan-Lin algorithm is the lowest. This result further demonstrates the effectiveness of the proposed algorithm. The adaptive clustering algorithm of complex network based on fuzzy neural network proposed in this paper does not need to determine the number of clusters in advance, but only needs to select the appropriate similarity measure and transform it into the matrix required by the adaptive clustering algorithm, and then get the clustering results with the help of the adaptive clustering algorithm. Simulation experiments in this chapter show that the cluster structure efficiency of this method can reach 97.6%, and the highest clustering accuracy can reach 96.8%. The adaptive clustering algorithm proposed in this paper not only overcomes the defects of the traditional algorithm that the number of clusters needs to be determined in advance, and the clustering result depends on the selection of the initial clustering center, but also has ideal clustering accuracy.


## 5. Conclusions

Everything in the real world has both macro-abstraction and micro-concreteness, and the latter is referred to as complexity. Because of the rapid advancement of information network technology, the network is always present in our lives, work, study, and communication. The application scope of big data technology is constantly expanding today, thanks to the rapid development of computer network information technology. To realize effective data management and use, a scientific complex network clustering analysis method must be used to optimize the network and make it more widely used in practice. The traditional clustering algorithm is improved in this paper to address the issues of determining the number of categories and initializing the clustering center. The supervised error back propagation learning algorithm is used in this paper to adjust the network parameters, which improves the system’s accuracy. The number of rules and initial parameters are generated based on the improved algorithm’s clustering results, and the input variable space is divided to generate the initial fuzzy rule base. As a result, the network’s learning amount is reduced, and the fuzzy neural network has a fast convergence speed and high modeling accuracy. Simultaneously, the sensitivity pruning algorithm is used to further adjust and optimize the structure of the fuzzy neural network, so that the network can automatically learn the structure and parameters of the system in different environments and obtain the optimal control rules, giving it some adaptive ability. According to simulation results, the cluster structure efficiency of this method can reach 97.6 percent, with the highest clustering accuracy reaching 96.8 percent. In the results of this paper, the classification accuracy and convergence speed of the complex network adaptive clustering algorithm are validated. This study has both theoretical and practical implications. Despite the accomplishments of this paper, there are still many problems to be solved due to the diversity of complex network structures and clustering algorithms, as well as a lack of further research on the subject. Further research on how to consider the attributes of nodes in high dimensions, how to avoid the explosion of fuzzy rule combinations, and how to establish the corresponding fuzzy neural network model suitable for fuzzy clustering is required in this paper.



---

*Source: 9220581-2022-06-24.xml*