Node Features Adjusted Stochastic Block Model

Stochastic block model (SBM) and its variants are popular models used in community detection for network data. In this paper, we propose a feature adjusted stochastic block model (FASBM) to capture the impact of node features on the network links as well as to detect the residual community structure beyond that explained by the node features. The proposed model can accommodate multiple node features and estimate the form of feature impacts from the data. Moreover, unlike many existing algorithms that are limited to binary-valued interactions, the proposed FASBM model and inference approaches are easily applied to relational data that generates from any exponential family distribution. We illustrate the methods on simulated networks and on two real world networks: a brain network and an US air-transportation network.