The discovery of community structures in social networks has gained significant attention since it is a fundamental problem in understanding the networks' topology and functions. However, most social network data are collected from partially observable networks with both missing nodes and edges. In this paper, we address a new problem of detecting overlapping community structures in the context of such an incomplete network, where communities in the network are allowed to overlap since nodes belong to multiple communities at once. To solve this problem, we introduce KroMFac, a new framework that conducts community detection via regularized nonnegative matrix factorization (NMF) based on the Kronecker graph model. Specifically, from a generative parameter matrix acquired by the expectation-maximization (EM) algorithm, we first estimate the missing part of the network. As our major contribution to the proposed framework, to improve community detection accuracy, we then characterize and select influential nodes (which tend to have high degrees) by ranking, and add them to the existing graph. Finally, we uncover the community structures by solving the regularized NMF-aided optimization problem in terms of maximizing the likelihood of the underlying graph. Furthermore, adopting normalized mutual information (NMI), we empirically show superiority of our KroMFac approach over two baseline schemes.
Community detection in incomplete networks. Recently, research on community detection in incomplete networks with missing edges has attracted wide attention due to a lack of information caused by users' privacy settings and limited resources. Most of these studies predict the missing links between nodes based on the incorporated additional information @cite_41 or the similarity of topological structures @cite_3 @cite_35 , and then discover communities in the underlying recovered networks. @cite_29 , a hierarchical gamma process infinite edge partition model was presented to detect communities and recover missing edges in parallel. In contrast to edge recovery, approaches for node recovery are largely still missing.
@cite_41 @cite_35 @cite_29 @cite_3
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Community detection algorithms are fundamental tools that allow us to uncover organizational principles in networks. When detecting communities, there are two possible sources of information one can use: the network structure, and the features and attributes of nodes. Even though communities form around nodes that have common edges and common attributes, typically, algorithms have only focused on one of these two data modalities: community detection algorithms traditionally focus only on the network structure, while clustering algorithms mostly consider only node attributes. In this paper, we develop Communities from Edge Structure and Node Attributes (CESNA), an accurate and scalable algorithm for detecting overlapping communities in networks with node attributes. CESNA statistically models the interaction between the network structure and the node attributes, which leads to more accurate community detection as well as improved robustness in the presence of noise in the network structure. CESNA has a linear runtime in the network size and is able to process networks an order of magnitude larger than comparable approaches. Last, CESNA also helps with the interpretation of detected communities by finding relevant node attributes for each community. Community detection and edge prediction are both forms of link mining: they are concerned with discovering the relations between vertices in networks. Some of the vertex similarity measures used in edge prediction are closely related to the concept of community structure. We use this insight to propose a novel method for improving existing community detection algorithms by using a simple vertex similarity measure. We show that this new strategy can be more effective in detecting communities than the basic community detection algorithms. A hierarchical gamma process innite edge partition model is proposed to factorize the binary adjacency matrix of an unweighted undirected relational network under a Bernoulli-Poisson link. The model describes both homophily and stochastic equivalence, and is scalable to big sparse networks by focusing its computation on pairs of linked nodes. It can not only discover overlapping communities and inter-community interactions, but also predict missing edges. A simplied version omitting inter-community interactions is also provided and we reveal its interesting connections to existing models. The number of communities is automatically inferred in a nonparametric Bayesian manner, and ecient inference via Gibbs sampling is derived using novel data augmentation techniques. Experimental results on four real networks demonstrate the models’ scalability and state-of-the-art performance. Many algorithms have been proposed for predicting missing edges in networks, but they do not usually take account of which edges are missing. We focus on networks which have missing edges of the form that is likely to occur in real networks, and compare algorithms that find these missing edges. We also investigate the effect of this kind of missing data on community detection algorithms.