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.
Detection of overlapping communities. To cope with this contrast, a recently emerging topic covers the detection of overlapping communities by investigating the structural properties of such communities, especially in the case of social networks @cite_6 @cite_14 @cite_1 . As the computational complexity increases drastically for the recovery of overlapping communities instead of partitioned communities, the research has focused either on detecting communities based on local expansion @cite_24 @cite_27 or on employing scalable techniques such as NMF @cite_47 @cite_19 @cite_20 and label propagation @cite_9 .
@cite_14 @cite_9 @cite_1 @cite_6 @cite_24 @cite_19 @cite_27 @cite_47 @cite_20
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The proposed survey discusses the topic of community detection in the context of Social Media. Community detection constitutes a significant tool for the analysis of complex networks by enabling the study of mesoscopic structures that are often associated with organizational and functional characteristics of the underlying networks. Community detection has proven to be valuable in a series of domains, e.g. biology, social sciences, bibliometrics. However, despite the unprecedented scale, complexity and the dynamic nature of the networks derived from Social Media data, there has only been limited discussion of community detection in this context. More specifically, there is hardly any discussion on the performance characteristics of community detection methods as well as the exploitation of their results in the context of real-world web mining and information retrieval scenarios. To this end, this survey first frames the concept of community and the problem of community detection in the context of Social Media, and provides a compact classification of existing algorithms based on their methodological principles. The survey places special emphasis on the performance of existing methods in terms of computational complexity and memory requirements. It presents both a theoretical and an experimental comparative discussion of several popular methods. In addition, it discusses the possibility for incremental application of the methods and proposes five strategies for scaling community detection to real-world networks of huge scales. Finally, the survey deals with the interpretation and exploitation of community detection results in the context of intelligent web applications and services. We propose an algorithm for finding overlapping community structure in very large networks. The algorithm is based on the label propagation technique of Raghavan, Albert and Kumara, but is able to detect communities that overlap. Like the original algorithm, vertices have labels that propagate between neighbouring vertices so that members of a community reach a consensus on their community membership. Our main contribution is to extend the label and propagation step to include information about more than one community: each vertex can now belong to up to v communities, where v is the parameter of the algorithm. Our algorithm can also handle weighted and bipartite networks. Tests on an independently designed set of benchmarks, and on real networks, show the algorithm to be highly effective in recovering overlapping communities. It is also very fast and can process very large and dense networks in a short time. One of the main organizing principles in real-world social, information and technological networks is that of network communities, where sets of nodes organize into densely linked clusters. Even though detection of such communities is of great interest, understanding the structure communities in large networks remains relatively limited. Due to unavailability of labeled ground-truth data it is practically impossible to evaluate and compare different models and notions of communities on a large scale. In this paper we identify 6 large social, collaboration, and information networks where nodes explicitly state their community memberships. We define ground-truth communities by using these explicit memberships. We then empirically study how such groundtruth communities emerge in networks and how they overlap. We observe some surprising phenomena. First, ground-truth communities contain high-degree hub nodes that reside in community overlaps and link to most of the members of the community. Second, the overlaps of communities are more densely connected than the nonoverlapping parts of communities, in contrast to the conventional wisdom that community overlaps are more sparsely connected than the communities themselves. Existing models of network communities do not capture dense community overlaps. We present the Community-Affiliation Graph Model (AGM), a conceptual model of network community structure, which reliably captures the overall structure of networks as well as the overlapping nature of network communities. Overlap is one of the characteristics of social networks, in which a person may belong to more than one social group. For this reason, discovering overlapping structures is necessary for realistic social analysis. In this paper, we present a novel, general framework to detect and analyze both individual overlapping nodes and entire communities. In this framework, nodes exchange labels according to dynamic interaction rules. A specific implementation called Speaker-listener Label Propagation Algorithm (SLPA) demonstrates an excellent performance in identifying both overlapping nodes and overlapping communities with different degrees of diversity. Identifying overlapping communities in networks is a challenging task. In this work we present a probabilistic approach to community detection that utilizes a Bayesian non-negative matrix factorization model to extract overlapping modules from a network. The scheme has the advantage of soft-partitioning solutions, assignment of node participation scores to modules, and an intuitive foundation. We present the performance of the method against a variety of benchmark problems and compare and contrast it to several other algorithms for community detection. Community detection is an important task in network analysis. A community (also referred to as a cluster) is a set of cohesive vertices that have more connections inside the set than outside. In many social and information networks, these communities naturally overlap. For instance, in a social network, each vertex in a graph corresponds to an individual who usually participates in multiple communities. In this paper, we propose an efficient overlapping community detection algorithm using a seed expansion approach. The key idea of our algorithm is to find good seeds, and then greedily expand these seeds based on a community metric. Within this seed expansion method, we investigate the problem of how to determine good seed nodes in a graph. In particular, we develop new seeding strategies for a personalized PageRank clustering scheme that optimizes the conductance community score. An important step in our method is the neighborhood inflation step where seeds are modified to represent their entire vertex neighborhood. Experimental results show that our seed expansion algorithm outperforms other state-of-the-art overlapping community detection methods in terms of producing cohesive clusters and identifying ground-truth communities. We also show that our new seeding strategies are better than existing strategies, and are thus effective in finding good overlapping communities in real-world networks. Network communities represent basic structures for understanding the organization of real-world networks. A community (also referred to as a module or a cluster) is typically thought of as a group of nodes with more connections amongst its members than between its members and the remainder of the network. Communities in networks also overlap as nodes belong to multiple clusters at once. Due to the difficulties in evaluating the detected communities and the lack of scalable algorithms, the task of overlapping community detection in large networks largely remains an open problem. In this paper we present BIGCLAM (Cluster Affiliation Model for Big Networks), an overlapping community detection method that scales to large networks of millions of nodes and edges. We build on a novel observation that overlaps between communities are densely connected. This is in sharp contrast with present community detection methods which implicitly assume that overlaps between communities are sparsely connected and thus cannot properly extract overlapping communities in networks. In this paper, we develop a model-based community detection algorithm that can detect densely overlapping, hierarchically nested as well as non-overlapping communities in massive networks. We evaluate our algorithm on 6 large social, collaboration and information networks with ground-truth community information. Experiments show state of the art performance both in terms of the quality of detected communities as well as in speed and scalability of our algorithm. Complex networks are ubiquitous in our daily life, with the World Wide Web, social networks, and academic citation networks being some of the common examples. It is well understood that modeling and understanding the network structure is of crucial importance to revealing the network functions. One important problem, known as community detection, is to detect and extract the community structure of networks. More recently, the focus in this research topic has been switched to the detection of overlapping communities. In this paper, based on the matrix factorization approach, we propose a method called bounded nonnegative matrix tri-factorization (BNMTF). Using three factors in the factorization, we can explicitly model and learn the community membership of each node as well as the interaction among communities. Based on a unified formulation for both directed and undirected networks, the optimization problem underlying BNMTF can use either the squared loss or the generalized KL-divergence as its loss function. In addition, to address the sparsity problem as a result of missing edges, we also propose another setting in which the loss function is defined only on the observed edges. We report some experiments on real-world datasets to demonstrate the superiority of BNMTF over other related matrix factorization methods.