The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Matrix Factorization Techniques for Recommender Systems

2005년 대한 생화학·분자생물학회 하계학술대회를 다녀와서

A modularity-specialized label propagation algorithm (LPAm) for detecting network communities was recently proposed. This promising algorithm offers some desirable qualities. However, LPAm favors community divisions where all communities are similar in total degree and thus it is prone to get stuck in poor local maxima in the modularity space. To escape local maxima, we employ a multistep greedy agglomerative algorithm (MSG) that can merge multiple pairs of communities at a time. Combining LPAm and MSG, we propose an advanced modularity-specialized label propagation algorithm (LPAm+). Experiments show that LPAm+ successfully detects communities with higher modularity values than ever reported in two commonly used real-world networks. Moreover, LPAm+ offers a fair compromise between accuracy and speed.

Advanced modularity-specialized label propagation algorithm for detecting communities in networks

Community detection in networks receives much attention recently. Most of the previous works are for unipartite networks composed of only one type of nodes. In real world situations, however, there are many bipartite networks composed of two types of nodes. In this paper, we propose a fast algorithm called LP&BRIM for community detection in large-scale bipartite networks. It is based on a joint strategy of two developed algorithms -- label propagation (LP), a very fast community detection algorithm, and BRIM, an algorithm for generating better community structure by recursively inducing divisions between the two types of nodes in bipartite networks. Through experiments, we demonstrate that this new algorithm successfully finds meaningful community structures in large-scale bipartite networks in reasonable time limit.

Community Detection in Large-Scale Bipartite Networks

The study of networked systems has experienced a particular surge of interest in the last decade. One issue that has received a considerable amount of attention is the detection and characterization of community structure in networks, meaning the appearance of densely connected groups of vertices, with only sparser connections between groups. In this paper, we present an approach for the problem of community detection using genetic algorithm (GA) in conjunction with the method of clustering. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes daunting complex real-world systems of scale-free network structure.

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Effective Algorithm for Detecting Community Structure in Complex Networks Based on GA and Clustering

We propose a general view that demonstrates the relationship between network embedding approaches and matrix factorization. Unlike previous works that present the equivalence for the approaches from a skip-gram model perspective, we provide a more fundamental connection from an optimization (objective function) perspective. We demonstrate that matrix factorization is equivalent to optimizing two objectives: one is for bringing together the embeddings of similar nodes; the other is for separating the embeddings of distant nodes. The matrix to be factorized has a general form: S-β. The elements of $\mathbfS $ indicate pairwise node similarities. They can be based on any user-defined similarity/distance measure or learned from random walks on networks. The shift number β is related to a parameter that balances the two objectives. More importantly, the resulting embeddings are sensitive to β and we can improve the embeddings by tuning β. Experiments show that matrix factorization based on a new proposed similarity measure and β-tuning strategy significantly outperforms existing matrix factorization approaches on a range of benchmark networks.

Xin Liu

Papers

Advanced modularity-specialized label propagation algorithm for detecting communities in networks

Community Detection in Large-Scale Bipartite Networks

Effective Algorithm for Detecting Community Structure in Complex Networks Based on GA and Clustering

A General View for Network Embedding as Matrix Factorization

An unsupervised learning method with convolutional auto-encoder for vessel trajectory similarity computation