The discovery of community structures in social networks has gained significant attention since it is a fundamental problem in understanding the networks’ topology and functions. However, most social network data are collected from partially observable networks with both missing nodes and edges . In this article, we address a new problem of detecting overlapping community structures in the context of such an incomplete network, where communities in the network are allowed to overlap since nodes belong to multiple communities at once. To solve this problem, we introduce KroMFac , a new framework that conducts community detection via regularized nonnegative matrix factorization (NMF) based on the Kronecker graph model. Specifically, from an inferred Kronecker generative parameter matrix, we first estimate the missing part of the network. As our major contribution to the proposed framework, to improve community detection accuracy, we then characterize and select influential nodes (which tend to have high degrees) by ranking, and add them to the existing graph. Finally, we uncover the community structures by solving the regularized NMF-aided optimization problem in terms of maximizing the likelihood of the underlying graph. Furthermore, adopting normalized mutual information (NMI), we empirically show superiority of our KroMFac approach over two baseline schemes by using both synthetic and real-world networks.

中文翻译：

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部分可观察社交网络中的社区检测

社交网络中社区结构的发现受到了广泛关注，因为它是理解网络拓扑和功能的一个基本问题。然而，大多数社交网络数据都是从部分可观察的网络中收集的缺少节点和边. 在本文中，我们解决了一个新的检测问题重叠在这样的背景下的社区结构不完整网络，其中网络中的社区允许重叠，因为节点同时属于多个社区。为了解决这个问题，我们引入KroMFac，一个通过正则化进行社区检测的新框架非负矩阵分解 (NMF)基于克罗内克图模型。具体来说，根据推断的 Kronecker 生成参数矩阵，我们首先估计网络的缺失部分。作为我们对提出的框架的主要贡献，为了提高社区检测的准确性，我们然后表征和选择有影响节点（往往具有较高的度数）通过排名，并将它们添加到现有图表。最后，我们通过解决正则化 NMF 辅助优化问题来揭示社区结构，以最大化底层图的可能性。此外，采用归一化互信息（NMI），我们凭经验证明了我们的优势KroMFac通过使用合成网络和真实网络来处理两个基线方案。