Phase Angle Spatial Embedding Research Articles

Resting-state functional magnetic resonance imaging (rs-fMRI) is widely used in connectomics for studying the functional relationships between regions of the human brain. rs-fMRI connectomics, however, has inherent analytical challenges, such as how to properly model negative correlations between BOLD time series. In addition, functional relationships between brain regions do not necessarily correspond to their anatomical distance, making the functional topology of the brain less well understood. Recent machine learning techniques, such as word2vec, have used embedding methods to map high-dimensional data into vector spaces, where words with more similar meanings are mapped closer to one another. Inspired by this approach, we have developed the graph embedding pipeline rest2vec for studying the vector space of functional connectomes. We demonstrate how rest2vec uses the phase angle spatial embedding (PhASE) method with dimensionality reduction to embed the connectome into lower dimensions, where the functional definition of a brain region is represented continuously in an intrinsic “functional space.” Furthermore, we show how the “functional distance” between brain regions in this space can be applied to discover biologically-relevant connectivity gradients. Interestingly, rest2vec can be conceptualized in the context of the recently proposed maximum mean discrepancy (MMD) metric, followed by a double-centering approach seen in kernel PCA. In sum, rest2vec creates a low-dimensional representation of the rs-fMRI connectome where brain regions are mapped according to their functional relationships, giving a more informed understanding of the functional organization of the brain.