Network Analysis of the Brain: from Generative Modeling to Multilayer Network Embedding of Functional Connectivity Data
Recent large-scale projects in neuroscience, such as the Human Connectome Project and the BRAIN initiative, emphasize the need of new statistical and computational techniques for analyzing functional connectivity within and across populations. Network-based models have greatly improved our understanding of brain structure and function, yet many important challenges remain. In this talk, I will consider two particularly important challenges: i) how does one characterize the generative mechanisms of functional connectivity, and ii) how does one identify discriminatory features among connectivity scans over disparate populations? To address the first challenge, I propose and describe a generative network model, called the correlation generalized exponential random graph model (cGERGM), that flexibly characterizes the joint network topology of correlation networks arising in functional connectivity. The model is the first of its kind to directly assess the network structure of a correlation network while simultaneously handling the mathematical constraints of a correlation matrix. I apply the cGERGM to resting state fMRI data from healthy individuals in the Human Connectome Project. The cGERGM reveals remarkably consistent organizational properties guiding subnetwork architecture, suggesting a fundamental organizational basis for subnetwork communication that differs from previous beliefs.
For the second challenge, I focus on learning interpretable features from complex multilayer networks arising in population studies of functional connectivity. I will introduce the multi-node2vec algorithm, an efficient and scalable feature engineering method that learns continuous node feature representations from multilayer networks. The multi-node2vec algorithm identifies maximum likelihood estimators of nodal features through the use of the Skip-gram neural network model. Asymptotic analysis of the algorithm reveals that it is a fast approximation to a multi-dimensional non-negative matrix factorization applied to a weighted average of the layers in the multilayer network. I apply multi-node2vec to a multilayer functional brain network from resting state fMRI scans over a population of 74 healthy individuals and 70 patients with varying degrees of schizophrenia. The identified functional embeddings closely associate with the functional organization of the brain and offer important insights into the differences between patient and healthy groups that is well-supported by theory.