论文标题
多层随机块模型中的偏置调整光谱聚类
Bias-adjusted spectral clustering in multi-layer stochastic block models
论文作者
论文摘要
我们考虑了在多层随机块模型中估算共同社区结构的问题，其中每个单层可能没有足够的信号强度来恢复完整的社区结构。为了有效地跨不同层聚集信号，我们认为即使单个层非常稀疏，相位的邻接矩阵也包含足够的信号。我们的方法使用一个偏置驱动步骤，当平方噪声矩阵可能淹没信号非常稀疏时，这是必要的。我们方法的分析依赖于几种新型的尾巴概率边界，用于矩阵线性组合具有基质值系数和基质值二次形式，这可能具有独立的关注。我们的方法的性能和偏差消除的必要性在合成数据和有关基因共表达网络的微阵列分析中得到了证明。
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.
