Multiscale graph principal component analysis for connectomics
Abstract
In brain connectomics, the cortical surface is parcellated into different regions of interest (ROIs) prior to statistical analysis. The brain connectome for each individual can then be represented as a graph, with the nodes corresponding to ROIs and edges to connections between ROIs. Such a graph can be summarized as an adjacency matrix, with each cell containing the strength of connection between a pair of ROIs. These matrices are symmetric with the diagonal elements corresponding to selfconnections typically excluded. A major disadvantage of such representations of the connectome is their sensitivity to the chosen ROIs, including critically the number of ROIs and hence the scale of the graph. As the scale becomes finer and more ROIs are used, graphs become increasingly sparse. Clearly, the results of downstream statistical analyses can be highly dependent on the chosen parcellation. To solve this problem, we propose a multiscale graph factorization, which links together scalespecific factorizations through a common set of individualspecific scores. These scores summarize an individual's brain structure combining information across measurement scales. We obtain a simple and efficient algorithm for implementation, and illustrate substantial advantages over single scale approaches in simulations and analyses of the Human Connectome Project dataset.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.02332
 Bibcode:
 2020arXiv201002332W
 Keywords:

 Statistics  Methodology;
 Statistics  Applications