Network representation learning (NRL) aims to learn low-dimensional vectors for vertices in a network. Most existing NRL methods focus on learning representations from local context of vertices (such as their neighbors). Nevertheless, vertices in many complex networks also exhibit significant global patterns widely known as communities. It's intuitive that vertices in the same community tend to connect densely and share common attributes. These patterns are expected to improve NRL and benefit relevant evaluation tasks, such as link prediction and vertex classification. Inspired by the analogy between network representation learning and text modeling, we propose a unified NRL framework by introducing community information of vertices, named as Community-enhanced Network Representation Learning (CNRL). CNRL simultaneously detects community distribution of each vertex and learns embeddings of both vertices and communities. Moreover, the proposed community enhancement mechanism can be applied to various existing NRL models. In experiments, we evaluate our model on vertex classification, link prediction, and community detection using several real-world datasets. The results demonstrate that CNRL significantly and consistently outperforms other state-of-the-art methods while verifying our assumptions on the correlations between vertices and communities.
Detecting communities from networks is a critical research filed in social science. In terms of community detection, traditional methods focus on partitioning the vertices into different groups, i.e., detecting non-overlapping communities. Existing non-overlapping community detection works mainly include clustering-based methods @cite_37 , modularity based methods @cite_1 @cite_29 @cite_56 , spectral algorithms @cite_15 , stochastic block models @cite_52 @cite_32 and so on. The major drawback of these traditional methods is that they cannot detect overlapping communities, which may not accord with real-world scenarios. To address this problem, CPM @cite_30 is proposed to generate overlapping communities by merging overlapping @math -cliques. Ahn @cite_31 proposes link clustering for overlapping community detection by employing non-overlapping community detection methods to partition the links instead of vertices and then assigning a single vertex to corresponding groups of its links.
@cite_30 @cite_37 @cite_31 @cite_29 @cite_1 @cite_52 @cite_32 @cite_56 @cite_15
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Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection for a family of probabilistic network models with overlapping communities, termed as the mixed membership Dirichlet model, first introduced by (2008). This model allows for nodes to have fractional memberships in multiple communities and assumes that the community memberships are drawn from a Dirichlet distribution. Moreover, it contains the stochastic block model as a special case. We propose a unified approach to learning these models via a tensor spectral decomposition method. Our estimator is based on low-order moment tensor of the observed network, consisting of 3-star counts. Our learning method is fast and is based on simple linear algebraic operations, e.g., singular value decomposition and tensor power iterations. We provide guaranteed recovery of community memberships and model parameters and present a careful finite sample analysis of our learning method. As an important special case, our results match the best known scaling requirements for the (homogeneous) stochastic block model. Community detection is an important technique to understand structures and patterns in complex networks. Recently, overlapping community detection becomes a trend due to the ubiquity of overlapping and nested communities in real world. However, existing approaches have ignored the use of implicit link preference information, i.e., links can reflect a node's preference on the targets of connections it wants to build. This information has strong impact on community detection since a node prefers to build links with nodes inside its community than those outside its community. In this paper, we propose a preference-based nonnegative matrix factorization (PNMF) model to incorporate implicit link preference information. Unlike conventional matrix factorization approaches, which simply approximate the original adjacency matrix in value, our model maximizes the likelihood of the preference order for each node by following the intuition that a node prefers its neighbors than other nodes. Our model overcomes the indiscriminate penalty problem in which non-linked pairs inside one community are equally penalized in objective functions as those across two communities. We propose a learning algorithm which can learn a node-community membership matrix via stochastic gradient descent with bootstrap sampling. We evaluate our PNMF model on several real-world networks. Experimental results show that our model outperforms state-of-the-art approaches and can be applied to large datasets. Detecting hidden communities from observed interactions is a classical problem. Theoretical analysis of community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we provide guaranteed community detection for a family of probabilistic network models with overlapping communities, termed as the mixed membership Dirichlet model, first introduced in (2008). This model allows for nodes to have fractional memberships in multiple communities and assumes that the community memberships are drawn from a Dirichlet distribution. Moreover, it contains the stochastic block model as a special case. We propose a unified approach to learning communities in these models via a tensor spectral decomposition approach. Our estimator uses low-order moment tensor of the observed network, consisting of 3-star counts. Our learning method is based on simple linear algebraic operations such as singular value decomposition and tensor power iterations. We provide guaranteed recovery of community memberships and model parameters, and present a careful finite sample analysis of our learning method. Additionally, our results match the best known scaling requirements for the special case of the (homogeneous) stochastic block model. Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals with the overlaps by employing the K-medians algorithm rather than the usual K-means for clustering in the spectral domain. We show that the algorithm is asymptotically consistent when networks are not too sparse and the overlaps between communities not too large. Numerical experiments on both simulated networks and many real social networks demonstrate that our method performs very well compared to a number of benchmark methods for overlapping community detection.