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.
In recent years, community affiliation based algorithms show their effectiveness on overlapping community detection @cite_25 @cite_33 @cite_39 @cite_38 . Community affiliation based algorithms predefine the number of communities and learn a vertex-community strength vector for each vertex and assign communities to vertices according to the vector. For example, Yang @cite_38 proposes Non-negative Matrix Factorization (NMF) method, which approximates adjacency matrix @math by @math where matrix @math is vertex-community affinity matrix. Then the algorithm learns non-negative vertex embeddings and converts each dimension of the embeddings into a community. These community affiliation based algorithms try to approximate the adjacency matrix in value and design different objective functions for it. Our model follows the idea to represent the community relationship with a non-negative vector, but we don't explicitly set hard community membership for the vertices.
@cite_38 @cite_25 @cite_33 @cite_39
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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. One of the main organizing principles in real-world networks is that of network communities, where sets of nodes organize into densely linked clusters. Communities in networks often overlap as nodes can belong to multiple communities at once. Identifying such overlapping communities is crucial for the understanding the structure as well as the function of real-world networks. Even though community structure in networks has been widely studied in the past, practically all research makes an implicit assumption that overlaps between communities are less densely connected than the non-overlapping parts themselves. Here we validate this assumption on 6 large scale social, collaboration and information networks where nodes explicitly state their community memberships. By examining such ground-truth communities we find that the community overlaps are more densely connected than the non-overlapping parts, which is in sharp contrast to the conventional wisdom that community overlaps are more sparsely connected than the communities themselves. Practically all existing community detection methods fail to detect communities with dense overlaps. We propose Community-Affiliation Graph Model, a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully captures overlapping, non-overlapping as well as hierarchically nested communities, and identifies relevant communities more accurately than the state-of-the-art methods in networks ranging from biological to social and information networks. 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. We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that have significant membership in more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the data set analyzed. The number of communities can be given in advance, or determined by the algorithm itself, using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to, social networks, scientific collaboration networks, and cortical networks, with high confidence.