Bias-Adjusted Spectral Clustering in Multi-Layer Stochastic Block Models
Bias-Adjusted Spectral Clustering in Multi-Layer Stochastic Block Models
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DOI：
10.1080/01621459.2022.2054817
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发表时间：
2020-03
影响因子：
3.7
通讯作者：
Jing Lei;K. Lin
中科院分区：
文献类型：
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作者：
Jing Lei;K. Lin
摘要我们考虑了多层随机区组模型中常见群落结构的估计问题，其中每一层可能没有足够的信号强度来恢复完整的群落结构。为了有效地聚合不同层上的信号，我们认为即使在各个层非常稀疏的情况下，平方和邻接矩阵也包含足够的信号。我们的方法使用了一个偏差消除步骤，当平方噪声矩阵可能在非常稀疏的区域中淹没信号时，该步骤是必要的。我们方法的分析依赖于几个新的尾概率界，这些尾概率界可能是独立感兴趣的具有矩阵值系数和矩阵值二次形式的矩阵线性组合的。我们的方法的性能和消除偏差的必要性在合成数据和关于基因共表达网络的微阵列分析中得到了证明。这篇文章的补充材料可以在网上找到。
Abstract We consider the problem of estimating common community structures in multi-layer stochastic block models, where each single layer may not have sufficient signal strength to recover the full community structure. In order to efficiently aggregate signal across different layers, we argue that the sum-of-squared adjacency matrices contain sufficient signal even when individual layers are very sparse. Our method uses a bias-removal step that is necessary when the squared noise matrices may overwhelm the signal in the very sparse regime. The analysis of our method relies on several novel tail probability bounds for matrix linear combinations with matrix-valued coefficients and matrix-valued quadratic forms, which may be of independent interest. The performance of our method and the necessity of bias removal is demonstrated in synthetic data and in microarray analysis about gene co-expression networks. Supplementary materials for this article are available online.