Most of the existing graph embedding methods focus on nodes, which aim to output a vector representation for each node in the graph such that two nodes being "close" on the graph are close too in the low-dimensional space. Despite the success of embedding individual nodes for graph analytics, we notice that an important concept of embedding communities (i.e., groups of nodes) is missing. Embedding communities is useful, not only for supporting various community-level applications, but also to help preserve community structure in graph embedding. In fact, we see community embedding as providing a higher-order proximity to define the node closeness, whereas most of the popular graph embedding methods focus on first-order and or second-order proximities. To learn the community embedding, we hinge upon the insight that community embedding and node embedding reinforce with each other. As a result, we propose ComEmbed, the first community embedding method, which jointly optimizes the community embedding and node embedding together. We evaluate ComEmbed on real-world data sets. We show it outperforms the state-of-the-art baselines in both tasks of node classification and community prediction.
In terms of interaction between node and community, there are a few graph embedding models that use node embedding to assist community detection @cite_5 @cite_10 , but they do not have the notion of community in their node embedding. There is little work that allows community feedback to guide the node embedding @cite_11 , but it lacks the concept of community embedding and its community feedback requires extra supervision on must-links. In contrast, we optimize node embedding, community embedding and community detection in a closed loop, and let them reinforce each other.
@cite_5 @cite_10 @cite_11
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In this paper, we study an important yet largely under-explored setting of graph embedding, i.e., embedding communities instead of each individual nodes. We find that community embedding is not only useful for community-level applications such as graph visualization, but also beneficial to both community detection and node classification. To learn such embedding, our insight hinges upon a closed loop among community embedding, community detection and node embedding. On the one hand, node embedding can help improve community detection, which outputs good communities for fitting better community embedding. On the other hand, community embedding can be used to optimize the node embedding by introducing a community-aware high-order proximity. Guided by this insight, we propose a novel community embedding framework that jointly solves the three tasks together. We evaluate such a framework on multiple real-world datasets, and show that it improves graph visualization and outperforms state-of-the-art baselines in various application tasks, e.g., community detection and node classification. Across many scientific domains, there is a common need to automatically extract a simplified view or coarse-graining of how a complex system’s components interact. This general task is called community detection in networks and is analogous to searching for clusters in independent vector data. It is common to evaluate the performance of community detection algorithms by their ability to find so-called ground truth communities. This works well in synthetic networks with planted communities because these networks’ links are formed explicitly based on those known communities. However, there are no planted communities in real-world networks. Instead, it is standard practice to treat some observed discrete-valued node attributes, or metadata, as ground truth. We show that metadata are not the same as ground truth and that treating them as such induces severe theoretical and practical problems. We prove that no algorithm can uniquely solve community detection, and we prove a general No Free Lunch theorem for community detection, which implies that there can be no algorithm that is optimal for all possible community detection tasks. However, community detection remains a powerful tool and node metadata still have value, so a careful exploration of their relationship with network structure can yield insights of genuine worth. We illustrate this point by introducing two statistical techniques that can quantify the relationship between metadata and community structure for a broad class of models. We demonstrate these techniques using both synthetic and real-world networks, and for multiple types of metadata and community structures. Identification of module or community structures is important for characterizing and understanding complex systems. While designed with different objectives, i.e., stochastic models for regeneration and modularity maximization models for discrimination, both these two types of model look for low-rank embedding to best represent and reconstruct network topology. However, the mapping through such embedding is linear, whereas real networks have various nonlinear features, making these models less effective in practice. Inspired by the strong representation power of deep neural networks, we propose a novel nonlinear reconstruction method by adopting deep neural networks for representation. We then extend the method to a semi-supervised community detection algorithm by incorporating pairwise constraints among graph nodes. Extensive experimental results on synthetic and real networks show that the new methods are effective, outperforming most state-of-the-art methods for community detection. Recently community detection has attracted much interest in social media to understand the collective behaviours of users and allow individuals to be modeled in the context of the group. Most existing approaches for community detection exploit either users' social links or their published content, aiming at discovering groups of densely connected or highly similar users. They often fail to find effective communities due to excessive noise in content, sparsity in links, and heterogenous behaviours of users in social media. Further, they are unable to provide insights and rationales behind the formation of the group and the collective behaviours of the users. To tackle these challenges, we propose to discover communities in a low- dimensional latent space in which we simultaneously learn the representation of users and communities. In particular, we integrated different social views of the network into a low-dimensional latent space in which we sought dense clusters of users as communities. By imposing a Laplacian regularizer into affiliation matrix, we further incorporated prior knowledge into the community discovery process. Finally community profiles were computed by a linear operator integrating the profiles of members. Taking the wellness domain as an example, we conducted experiments on a large scale real world dataset of users tweeting about diabetes and its related concepts, which demonstrate the effectiveness of our approach in discovering and profiling user communities.