Mixtures of block models for brain networks

Abstract

Block models are a popular method for simplifying a single graph into a set of blocks and interactions between those blocks. A recent innovation is to extend block modeling to a collection of graphs (e.g. RESCAL) to discover one common block structure amongst the graphs. However, these approaches are unsuitable in many domains where the collection can comprise items from significantly different groups. Consider the focus of this paper: fMRI analysis on scans of young healthy and Alzheimer's affected individuals. There are implicitly two underlying block structures (one for each group) and some individuals may exhibit the behavior of both. We propose a novel mixtures of block models (MBM) framework that explicitly models each single graph as a linear combination of a small number of block models. Experimental results on synthetic data show that our method is able to recover the ground-truth models. In real-world experiments with fMRI data we show that with proper factorization parameters, MBM (1) outperforms the single block structure models and (2) demonstrates significant structural patterns of brain networks at the cohort level.