Combination of links and node contents for community discovery using a graph regularization approach

Abstract

With the rapid growth of the networked data, the study of community detection is drawing increasing attention of researchers. A number of algorithms have been proposed and some of them have been well applied in many research fields, such as recommendation systems, information retrieval, etc. Traditionally, the community detection methods mainly use the knowledge of the topological structure which contains the most important clue for finding potential groups or communities. However, as we know, a wealth of content information exists on the nodes in real-world networks, and may help for community detection. Considering the above problem, we introduce a novel community detection method under the framework of nonnegative matrix factorization (NMF), and adopt the idea that two nodes with similar content will be most likely to belong to the same community to achieve the incorporation of links and node contents, i.e., we employ a graph regularization to penalize the dissimilarity of nodes denoted by community memberships. Besides, we introduce an intuitive manifold learning strategy to recover the intrinsic geometrical structure of the content information, i.e., K-near neighbor consistency. In addition, we found that, there are still drawbacks in this framework due to it does not consider the heterogeneous distribution of node degrees. This heterogeneous distribution can affect the function of graph regularization and isolates the original community memberships. We first proposed the node popularities satisfying the above interpretation and develop a new NMF-based model, named as Combination of Links and Node Contents for Community Discovery (CLNCCD). The experiments on both artificial and real-world networks compared with the state-of-the-art methods show that, the new model obtains significant improvement for community detection by incorporating node contents effectively.

Introduction

The development of social networking has led to yield variety of mass data, such as user relation networks, product reviews and online comments. For the analysis of the complex networked data, researchers try to access a first view on those data by finding the latent community structure. A community can be deemed as a group of nodes that are closely connected within a class and are sparsely connected between the different classes. Discovering communities consisting of “similar” users is very important, and it has been applied in many areas, e.g., sociology, biology and computer science. For instance, in biology, some different units, belonging to an organization, have related functions which are linked in special structure to draw the whole effect of the organization. The interaction among a set of proteins in a cell can form an RNA polymerase for transcription of genes [1]. As Sachan et al. [2] described, finding the salient communities from the organization of people can create a guidance which can be helpful for web marketing, behavior prediction of users belonging to a community and understanding the function of complex system.

The above data described is often treated as a graph in which nodes denote units or users in real-world networks. And the relations among units or users are represented by directed or undirected links which connect those nodes just described. In order to discovering communities in the graph, many earlier methods [3], [4], [5] considered the information of network topology alone. In addition to the linked graph, there also exist some datasets with content information alone, such as tweet, ImageNet. And some researchers presented many data clustering algorithms [6], [7], [8] for the analysis of these datasets, which usually make use of node contents to perform clustering. In fact, both the linkage and content information exist simultaneously in real-world networks. For example, in the social networks, the content information may be tweets, user profiles or the text on the web pages. In the citation networks, node content is regarded as the abstract of a paper or affiliation information of the authors. So it is realized that, using links or node contents alone, an algorithm is often limited to mine or explore the important information about the structure of communities from the attributed graph which consists of network topology and node contents. For example, the methods of clustering by using the node content information are difficult to process those data points without the content. If one considers the links between data points in addition to data point contents, the designed methods may be able to solve this difficulty. Conversely, node contents might give a guidance for discovering communities when there are a few links existed in the network.

Recently, several methods [2], [9], [10], [11], [12] based on combining topological and content information have been proposed. For example, Ruan et al. [12] believed that node contents can be regarded as another type of edges, thus constructed a new graph in which the edges consist of the original links and the links ‘simplified’ by node contents, and then partitioned the simplified graph into clusters. Approaches based on generative framework [9] statistically model network topology and node contents, respectively, with the main idea that these two kinds of information are ‘generated’ by communities. However, they still have some drawbacks. First, when considering the content information in networks, the similarity between node contents in these community detection methods is often based on Euclidean space. However, the structure of the space of the content information may be a manifold which is a geometrical space that locally resembles the Euclidean space near each point. In this scenario, it is not suitable that these methods measure the similarity just described based only on Euclidean space. Thus, these methods which did not consider the manifold structure of information of node contents often limits the applicability for community detection. Second, the current generative frameworks usually cannot model the unbalanced degree of nodes, and thus the community memberships themselves are insufficient to model the link–link patterns. In a word, these existing community detection methods mainly focus on the combination of network topology and node contents, while still have room for improvement in the performance because they often did not consider that the manifold structure intrinsically held in the space of content information, and also often ignored the impact of the heterogeneity of the degree of nodes in the network topology.

In this paper, we introduce and develop a nonnegative matrix factorization (NMF) method for community detection which models links with graph regularization to try to overcome the shortcomings of the existing approaches. The proposed model consists of two sub-models. In the first sub-model, its input is the adjacency matrix which describes the topological information, and the community memberships of nodes are obtained by factorizing this adjacency matrix. Next, it is intuitive that if two nodes are similar in terms of the content information, they will be most likely to belong to the same community, and thus we can make their community memberships similar; vice versa. We implement the above idea to construct the second sub-model by using the method of spectral clustering. By now, we can adopt a graph regularization term to add the second sub-model into the first sub-model, which achieves a combination of the linkage and node content information. By combining these two sub-models, the unified model not only combines node contents with network topology but also considers the manifold structure of the content information in the process of constructing the Laplacian matrix, so as to achieve an improvement for finding communities. Last but not least, in order to reduce the impact of the unbalance of the degree of nodes on graph regularization, we incorporate the node popularities into this unified model for enhancing the performance. Finally, our proposed method integrates topology and content of networks and is also a simple and unified method that considers the manifold structure of content information and the heterogeneity of the degree of nodes simultaneously. We name this method as Combination of Links and Node Contents for Community Discovery (CLNCCD). The processing of the proposed method, that is how to incorporate content information, is shown in Fig. 1.

The rest of our article is organized as follows. Section 2 briefly reviews the related work. In Section 3 we describe the proposed model and methods. In Section 4, we give the experimental evaluation, and discuss how to select the parameters. And finally, we discuss and draw some conclusions in Section 5.