To analyze data from multisubject experiments in neuroimaging studies, we develop a modeling framework for joint community detection in a group of related networks that can be considered as a sample from a population of networks. The proposed random effects stochastic block model facilitates the study of group differences and subject-specific variations in the community structure. The model proposes a putative mean community structure, which is representative of the group or the population under consideration but is not the community structure of any individual component network. Instead, the community memberships of nodes vary in each component network with a transition matrix, thus modeling the variation in community structure across a group of subjects. To estimate the quantities of interest, we propose two methods: a variational EM algorithm and a model-free “two-step” method called Co-OSNTF which is based on nonnegative matrix factorization. We also develop a resampling-based hypothesis test for differences between community structure in two populations both at the whole network level and node level. The methodology is applied to the COBRE dataset, a publicly available fMRI dataset from multisubject experiments involving schizophrenia patients. Our methods reveal an overall putative community structure representative of the group as well as subject-specific variations within each of the two groups, healthy controls and schizophrenia patients. The model has good predictive ability for predicting community structure in subjects from the same population but outside the training sample. Using our network level hypothesis tests, we are able to ascertain statistically significant difference in community structure between the two groups, while our node level tests help determine the nodes that are driving the difference.

中文翻译：

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用于多个网络中的联合社区检测的随机效应随机块模型及其在神经影像学中的应用

为了分析神经影像研究中多学科实验的数据，我们开发了一个模型框架，用于在一组相关网络中进行联合社区检测，这些相关网络可视为网络人口的样本。提出的随机效应随机区组模型有助于研究群体差异和社区结构中特定对象的差异。该模型提出了一个推定的平均社区结构，该结构代表了所考虑的群体或人口，而不是任何单个组成网络的社区结构。取而代之的是，节点的社区成员资格在每个组件网络中都具有一个过渡矩阵，从而可以跨一组主题对社区结构的变化建模。为了估算感兴趣的数量，我们提出了两种方法：一种基于非负矩阵分解的变分EM算法和一种称为Co-OSNTF的无模型“两步法”。我们还针对整个网络级别和节点级别的两个种群的社区结构之间的差异，开发了基于重采样的假设检验。该方法应用于COBRE数据集，COBRE数据集是来自精神分裂症患者多学科实验的可公开获得的fMRI数据集。我们的方法揭示了代表该组的总体推定的社区结构以及两组（健康对照组和精神分裂症患者）中每个受试者的特定变异。该模型具有很好的预测能力，可以预测来自相同人群但不在训练样本中的受试者的社区结构。使用我们的网络级假设检验，