All Times ET
Keywords: Time-varying networks, Gene co-expression networks, Node clustering
We consider the problem of estimating node-wise community structures in multi-layer stochastic block-model networks, where multiple networks on a common set of nodes are observed but no single network has sufficient signal strength to recover the community structure. Other theoretical work studying this setting typically focus on homophilic networks, but we develop an estimator that can handle heterophilic networks. Specifically, we first consider the setting where the node communities are fixed (but unknown) across all layers, and the estimator applies spectral clustering to the sum of squared adjacency matrices after de-biasing the diagonal entries. Second, we consider the setting where the nodes' communities are unknown and slowly change over layers. We adapt our estimator by kernel-averaging across different networks to accommodate this setting. In both settings, we prove the statistical rates for our method that demonstrate the impact of aggregating information across layers as well as the network density requirements to achieve consistent estimation of the communities. We apply our methods to study gene coordination in gene co-expression networks.