Multi-scale graph principal component analysis for connectomics

In brain connectomics, it is common to divide the cortical surface into discrete regions of interest (ROIs), and then to use these regions to induce a graph. Nodes correspond to regions of interest and edges encode summaries of the strength of connections between pairs of regions. These spatial weighted graphs are often reduced to adjacency matrices, which are then used as inputs to downstream statistical analysis. The structure of these adjacency matrices depends critically on the chosen parcellation, with finer resolutions producing unique spare patterns. Consequently, both the available methods of analysis and the conclusions from analysis depend heavily on the chosen parcellation. To solve this problem we develop a multi-scale graph factorization model, which links together scale-specific factorizations through a common set of individual-specific latent factors. These scores combine information across from different parcellations to produce a single interpretable summary of an individuals brain structure. We develop a simple, efficient algorithm, and illustrate substantial advantages over comparable single-scale methods in both simulations and analyses of the Human Connectome Project dataset.