Bias-Adjusted Spectral Clustering in Multi-Layer Stochastic Block Models
研究了多层随机块模型中共同社区结构的估计问题，提出一种通过偏差去除步骤聚合各层信号的谱聚类方法，适用于单层信号稀疏的场景，并在基因共表达网络数据中验证了有效性。
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.