Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition
Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition
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DOI：
10.1214/21-aos2079
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发表时间：
2020-02
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通讯作者：
Bing-Yi Jing;Ting Li;Zhongyuan Lyu;Dong Xia
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作者：
Bing-Yi Jing;Ting Li;Zhongyuan Lyu;Dong Xia
我们研究多层网络中的社区检测问题，其中节点对可以以多种方式相关。我们介绍了一个通用框架，即混合多层随机块模型（MMSBM），其中包括许多早期模型作为特例。我们提出了一种基于张量的算法（TWIST）来揭示节点的全局/局部成员资格以及层的成员资格。我们表明，随着节点数量和/或层数的增加，TWIST 过程可以准确地检测误分类误差较小的社区。数值研究证实了我们的理论发现。据我们所知，这是首次使用张量分解对混合多层网络进行系统研究。该方法应用于两个真实数据集：全球贸易网络和疟疾寄生虫基因网络，产生了新的有趣的发现。
We study the problem of community detection in multi-layer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, i.e., mixture multi-layer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or the number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multi-layer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.