Fast embedding of multilayer networks: An algorithm and application to group fMRI

Learning interpretable features from complex multilayer networks is a challenging and important problem. The need for such representations is particularly evident in multilayer networks of the brain, where nodal characteristics may help model and differentiate regions of the brain according to individual, cognitive task, or disease. Motivated by this problem, we introduce the multi-node2vec algorithm, an efficient and scalable feature engineering method that automatically learns continuous node feature representations from multilayer networks. Multi-node2vec relies upon a second-order random walk sampling procedure that efficiently explores the inner- and intra- layer ties of the observed multilayer network is utilized to identify multilayer neighborhoods. Maximum likelihood estimators of the nodal features are identified through the use of the Skip-gram neural network model on the collection of sampled neighborhoods. We investigate the conditions under which multi-node2vec is an approximation of a closed-form matrix factorization problem. We demonstrate the efficacy of multi-node2vec on a multilayer functional brain network from resting state fMRI scans over a group of 74 healthy individuals. We find that multi-node2vec outperforms contemporary methods on complex networks, and that multi-node2vec identifies nodal characteristics that closely associate with the functional organization of the brain.