Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify the community from a few exemplary seed members. In this paper, we propose a novel approach for finding overlapping communities called LEMON (Local Expansion via Minimum One Norm). Different from PageRank-like diffusion methods, LEMON finds the community by seeking a sparse vector in the span of the local spectra such that the seeds are in its support. We show that LEMON can achieve the highest detection accuracy among state-of-the-art proposals. The running time depends on the size of the community rather than that of the entire graph. The algorithm is easy to implement, and is highly parallelizable. Moreover, given that networks are not all similar in nature, a comprehensive analysis on how the local expansion approach is suited for uncovering communities in different networks is still lacking. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the quality and quantity of the seed set would affect the performance are provided.
Various community detection algorithms have been developed in the past decade. And most of the algorithms fall into the category of global approach. One stream of global algorithms attempt to find communities by optimizing an objective function. For example, OSLOM @cite_3 is based on the optimization of a fitness function, which expresses the statistical significance of clusters with respect to random fluctuations (i.e., the random graph generated by the configuration model @cite_25 during community expansion). However, the communities identified by mathematical construction may structurally diverge from real communities as pointed out in @cite_4 . Another main stream of research adopts the label propagation approach @cite_24 , which defines rules that simulate the spread of labels of vertices in the network. The DEMON algorithm @cite_0 , for example, democratically lets each vertex vote for the communities it sees surrounding it in its limited view of the global system using a label propagation algorithm, and then merges the local communities into a global collection. Other approaches such as Link Community (LC) @cite_7 partitions the graph by first building a hierarchical link dendrogram according to the link similarity and then cutting the dendrogram at some threshold to yield link communities.
@cite_4 @cite_7 @cite_3 @cite_24 @cite_0 @cite_25
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Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (http: www.oslom.org), and we believe it will be a valuable tool in the analysis of networks. Link prediction is a challenging task due to the inherent skew ness of network data. Typical link prediction methods can be categorized as either local or global. Local methods consider the link structure in the immediate neighborhood of a node pair to determine the presence or absence of a link, whereas global methods utilize information from the whole network. This paper presents a community (cluster) level link prediction method without the need to explicitly identify the communities in a network. Specifically, a variable-cost loss function is defined to address the data skew ness problem. We provide theoretical proof that shows the equivalence between maximizing the well-known modularity measure used in community detection and minimizing a special case of the proposed loss function. As a result, any link prediction method designed to optimize the loss function would result in more links being predicted within a community than between communities. We design a boosting algorithm to minimize the loss function and present an approach to scale-up the algorithm by decomposing the network into smaller partitions and aggregating the weak learners constructed from each partition. Experimental results show that our proposed Link Boost algorithm consistently performs as good as or better than many existing methods when evaluated on 4 real-world network datasets. We develop an information-theoretic view of the stochastic block model, a popular statistical model for the large-scale structure of complex networks. A graph G from such a model is generated by first assigning vertex labels at random from a finite alphabet, and then connecting vertices with edge probabilities depending on the labels of the endpoints. In the case of the symmetric two-group model, we establish an explicit single-letter characterization of the per-vertex mutual information between the vertex labels and the graph, when the graph average degree diverges. The explicit expression of the mutual information is intimately related to estimation-theoretic quantities, and -in particular- reveals a phase transition at the critical point for community detection. Below the critical point the per-vertex mutual information is asymptotically the same as if edges were independent of the vertex labels. Correspondingly, no algorithm can estimate the partition better than random guessing. Conversely, above the threshold, the per-vertex mutual information is strictly smaller than the independent-edges upper bound. In this regime there exists a procedure that estimates the vertex labels better than random guessing. We propose a community structure-based approach that does not require community labels of nodes, for network immunization. Social networks have been widely used as daily communication infrastructures these days. However, fast spreading of information over networks may have downsides such as computer viruses or epidemics of diseases. Because contamination is propagated among subgraphs communities along links in a network, use of community structure of the network would be effective for network immunization. However, despite various research efforts, it is still difficult to identify ground-truth community labels of nodes in a network. Because communities are often interwoven through intermediate nodes, we propose to identify such nodes based on the community structure of a network without requiring community labels. By regarding the community structure in terms of nodes, we construct a vector representation of nodes based on a quality measure of communities. The distribution of the constructed vectors is used for immunizing intermediate nodes among communities, through the hybrid use of the norm and the relation in the vector representation. Experiments are conducted over both synthetic and real-world networks, and our approach is compared with other network centrality-based approaches. The results are encouraging and indicate that it is worth pursuing this path. In many applications we have a social network of people and would like to identify the members of an interesting but unlabeled group or community. We start with a small number of exemplar group members -- they may be followers of a political ideology or fans of a music genre -- and need to use those examples to discover the additional members. This problem gives rise to the seed expansion problem in community detection: given example community members, how can the social graph be used to predict the identities of remaining, hidden community members? In contrast with global community detection (graph partitioning or covering), seed expansion is best suited for identifying communities locally concentrated around nodes of interest. A growing body of work has used seed expansion as a scalable means of detecting overlapping communities. Yet despite growing interest in seed expansion, there are divergent approaches in the literature and there still isn't a systematic understanding of which approaches work best in different domains. Here we evaluate several variants and uncover subtle trade-offs between different approaches. We explore which properties of the seed set can improve performance, focusing on heuristics that one can control in practice. As a consequence of this systematic understanding we have found several opportunities for performance gains. We also consider an adaptive version in which requests are made for additional membership labels of particular nodes, such as one finds in field studies of social communities. This leads to interesting connections and contrasts with active learning and the trade-offs of exploration and exploitation. Finally, we explore topological properties A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results.