Title: Fast embedding of multilayer networks: An algorithm and application to group fMRI,
Abstract: 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.