Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold.

摘要: Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., structure connection similarities differences across set networks. We propose statistical these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed weighted sum patterns with rank one. pattern described random perturbation dictionary element. As hierarchical model, it enables heterogeneous populations matrices using mixtures. Our can also be used infer weight missing edges. estimate parameters an Expectation-Maximization-based algorithm. Experimenting synthetic data, show that algorithm able accurately in both low high dimensions. apply our large data functional connectivity from UK Biobank. results suggest proposed describes small number degrees freedom.