A random effects stochastic block model for joint community detection in multiple networks with applications to neuroimaging

Abstract

Motivated by multi-subject experiments in neuroimaging studies, we develop a modeling framework for joint community detection in a group of related networks, which can be considered as a sample from a population of networks. The proposed random effects stochastic block model facilitates the study of group differences and subject-specific variations in the community structure. The model proposes a putative mean community structure which is representative of the group or the population under consideration but is not the community structure of any individual component network. Instead, the community memberships of nodes vary in each component network with a transition matrix, thus modeling the variation in community structure across a group of subjects. To estimate the quantities of interest we propose two methods, a variational EM algorithm, and a model-free "two-step" method based on either spectral or non-negative matrix factorization (NMF). Our NMF based method Co-OSNTF is of independent interest and we study its convergence properties to a stationary point. We also develop a resampling-based hypothesis test for differences in community structure in two populations both at the whole network level and node level. The methodology is applied to a publicly available fMRI dataset from multi-subject experiments involving schizophrenia patients. Our methods reveal an overall putative community structure representative of the group as well as subject-specific variations within each group. Using our network level hypothesis tests we are able to ascertain statistically significant difference in community structure between the two groups, while our node level tests help determine the nodes that are driving the difference.

References in corpus (16)

• Fast unfolding of communities in large networks
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Statistical Mechanics of Community Detection
• Dynamic reconfiguration of human brain networks during learning
• Measuring and modelling correlations in multiplex networks
• Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels
• Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds
• Community detection, link prediction, and layer interdependence in multilayer networks
• Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel
• Inferring the mesoscale structure of layered, edge-valued and time-varying networks
• Consistent estimation of dynamic and multi-layer block models
• Assessing the consistency of community structure in complex networks
• Structural and Functional Discovery in Dynamic Networks with Non-negative Matrix Factorization
• Orthogonal symmetric non-negative matrix factorization under the stochastic block model
• Null Models and Community Detection in Multi-Layer Networks
• Stochastic blockmodels for exchangeable collections of networks

Cited by in corpus (4)

• Bias-Variance Tradeoffs in Joint Spectral Embeddings
• Community Detection in Weighted Multilayer Networks with Ambient Noise
• A Bayesian State-Space Approach to Mapping Directional Brain Networks
• Interpretable Network Representation Learning with Principal Component Analysis