Abstract

We consider the problem of community detection in overlapping weighted networks, where nodes can belong to multiple communities and edge weights can be finite real numbers. To model such complex networks, we propose a general framework—the mixed membership distribution-free (MMDF) model. MMDF has no distribution constraints of edge weights and can be viewed as generalizations of some previous models, including the well-known mixed membership stochastic blockmodels. Especially, overlapping signed networks with latent community structures can also be generated from our model. We use an efficient spectral algorithm with a theoretical guarantee of convergence rate to estimate community memberships under the model. We also propose the fuzzy weighted modularity to evaluate the quality of community detection for overlapping weighted networks with positive and negative edge weights. We then provide a method to determine the number of communities for weighted networks by taking advantage of our fuzzy weighted modularity. Numerical simulations and real data applications are carried out to demonstrate the usefulness of our mixed membership distribution-free model and our fuzzy weighted modularity.

中文翻译：

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混合会员免分配模式

摘要

我们考虑重叠加权网络中的社区检测问题，其中节点可以属于多个社区，边权重可以是有限实数。为了对此类复杂网络进行建模，我们提出了一个通用框架——混合成员资格无分布（MMDF）模型。MMDF 没有边权重的分布约束，可以看作是一些先前模型的推广，包括众所周知的混合隶属随机块模型。特别是，具有潜在社区结构的重叠签名网络也可以从我们的模型中生成。我们使用具有收敛速度理论保证的高效谱算法来估计模型下的社区成员资格。我们还提出了模糊加权模块化来评估具有正边缘权重和负边缘权重的重叠加权网络的社区检测质量。然后，我们提供了一种方法，利用我们的模糊加权模块化来确定加权网络的社区数量。进行数值模拟和实际数据应用来证明我们的混合隶属度无分布模型和模糊加权模块化的有用性。