1.

INTRODUCTION

Complex networks are often used to describe real systems in various domains, such as social systems, biological systems, and technological systems. These systems always demonstrate a community (modular) structure from the perspective of the complex network¹. Research on community detection in networks can be divided into two phases.

The first stage of the work is the traditional community discovery algorithm, mainly through the traditional statistical inference and machine learning methods. For example, the community detection algorithm based on modularity optimization widely used today (such as the GN algorithm², FN algorithm³, Louvain algorithm⁴, etc.) mainly adopts the idea of hierarchical clustering which repeatedly adjusts the community according to the number of connections, so as to achieve the optimal modularity and realize the community division of the network. However, with the deeper research on community detection, traditional community detection algorithms are difficult to face complex system scenarios, especially due to the fact that algorithms are highly dependent on data characteristics⁵.

With the generation and propulsion of deep learning research, the research work of community detection in the network has entered the second stage. Not only can the deep learning model learn the representation of network data at multiple levels of abstraction, but also it has a strong learning ability of nonlinear characteristics⁶. What’s more, the deep neural network model can greatly enrich the community exploration tasks in the network. Currently, community discovery methods in the field of deep learning mainly use deep neural networks, deep graph embedding, and graph neural network models.

The first model can better capture and model complex relationships, including convolutional neural networks (CNN, convolutional neural networks), autoencoders (AE, auto-encoders), and generative adversarial networks (GAN, generative adversarial networks). For example, Xin et al. proposed a new CNN model to detect communities in networks with missing part of edge information⁷. Jang proposed a convolutional variational autoencoder (CVAE)⁸. In order to make use of the attribute characteristics of nodes, Cao et al. proposed a cascading autoencoder that integrates network structure and node attributes to achieve community division⁹. The community discovery method based on the depth map embedding model is to map node information to lower-dimensional vector space while preserving structural information as much as possible and then implement community division by machine learning method. For example, Xie et al. proposed a network representation method based on deep sparse filtering¹⁰, which is an unsupervised network feature extraction method, especially suitable for community discovery of large-scale networks. The community discovery method based on a graph neural network is essentially the fusion of graph mining technology and deep learning, the core of which is to form aggregate features of node structure information through deep learning technology and then realize the community division of the network. For example, Chen et al. defined the adjacency matrix by using a nonbacktracking operator, and on this basis of which, it completed the community division task through supervised learning¹¹.

Based on the brief review of relevant work above, it is not difficult to learn that the deep learning model has further promoted the development of community detection research on complex networks, but the work in this area is still in the exploratory stage which deserves further development. On the one hand, the core idea of community division in complex networks stems from the theory of “homogeneity attracts” in sociology, and the connection between nodes is regarded as a reflection of the interaction between individuals with similar attributes in the system¹². However, under the theory of “difference preference” in sociology, individuals with different attributes in the system can also establish connections. Therefore, it is inevitable to deviate from the core idea of “homogeneity attracts” to divide communities by reflecting the attributes and characteristics of individuals who establish links and exploring network communities by only using linking relations. On the other hand, the existing network community detection methods using a deep learning model often adopt supervised or semi-supervised learning, besides, the number of communities needs to be specified in advance, hence it is difficult to apply to the situation where the number of communities is unknown. Therefore, the unsupervised deep learning method that integrates the edge information and attribute information of nodes can not only better reflect the core idea of community division that “homogeneity attracts”, but also apply more effectively the community division method to realistic scenes such as system recommendation¹³ and social opinion mining¹⁴. At the same time, some studies have found that excessive reliance on the structural information of nodes in recommendation tends to make the development of network structure appear to be differentiated, and the addition of node attributes can effectively alleviate the differentiation of the network¹⁵. This means that community division only based on network structure information may hurt the integrity and stability of the subsequent development of the network when community structure is used for system recommendation. Therefore, it is necessary to take the attribute information of nodes into consideration in community detection.

In this regard, this paper proposes a deep learning model that integrates network structure and node attributes. The model extracts the attributes of network nodes, and by adding convolutional neural networks and community division indicators, it can achieve effective convergence between similarity nodes, better reflect the idea of “homogeneity attracts” in community division, and also provide new ideas for real community division tasks such as community opinion mining.

2.

VNSA MODEL

According to the research work of Kipf and Welling¹⁶, VGAE is to encode the known graph to learn the distribution of its node vector representation, then sample the node vector representation from the distribution, and finally decode to reconstruct the graph structure. Hence, the VNSA model proposed in this paper draws on the encoding process of the VGAE, integrates node attributes, and introduces the community division index. The framework of the model mainly includes three steps, as shown in Figure 1.

Figure 1.

Framework of VNSA model.

(2)

Community division

Community division mainly draws on the part of VGAE coding which adopts the multi-layer convolutional neural network to achieve the embedding of the network. Meanwhile, some studies have shown that when the number of convolutional layers exceeds two, the learning effect is not significantly improved. Therefore, on the basis of (1), a two-layer convolutional network is selected to achieve network embedding, as shown in equations (1) and (2) respectively. In the equation (1), represents the node characteristic matrix obtained after the first convolution layer operation, Wis the hyperparameter matrix of m × p(ą < p < m), where the parameter q is the given number of divided communities. In equation (2), is the sign matrix of nodes obtained through the second convolution layer.

According to the network embedding result , this paper uses the argmax activation function to determine the most likely community to which the node belongs, and then obtain the community division result.

(3)

The results of evaluation

According to the goal of community division, the results of community division are evaluated from two aspects: modularity (Q) and average similarity degree of node attributes within the community (S), and the result score E is recorded as shown in equation (3). Q value adopts the traditional module-degree calculation method, S value is the Euclidean distance after the normalization of node attribute vector, and w is the community division target weight, of which the value ranges from 0 to 1. Then, within a given range, adjust the value of parameter q, repeat steps (2), and finally select the community division result with the maximum value of E. According to Equation (3), when the value of w is small, if E wants to reach the maximum value, the value of S learned by the model can only be increased, thereby indirectly learning the mechanism of heterogeneity. Instead, the model can learn the mechanism of homogeneity.

3.

EMPIRICAL ANALYSIS

This section takes two knowledge collaboration networks in two different fields as examples, one in the field of technology research, and another in the field of open-source software development. Then, this section uses the proposed model to divide them into communities to test the effectiveness of the model.

4.

CONCLUSION

In this paper, a community discovery model (VNSA) for complex networks is proposed, which takes both node structure and attribute information into account. Compared with some traditional methods (Louvain and Spectral Clustering) and deep learning methods (Node2vec and Deepwalk), the proposed model is validated. In terms of node similarity comparison, the model can better reflect the core idea of “homogeneity attracts”, and provide some exploration for network community exploration tasks (e.g., e-commerce recommendation) that need to be considered more node attribute information. In the following work, the author intends to further test the effectiveness of the proposed method through larger-scale network data, study the optimization of the fusion model of node connection information and attribute information in the method, so as to apply it to more complex network community detection scenarios (such as community detection of heterogeneous networks).