LAUSR

The study of functional networks of the human brain has been of significant interest in cognitive neuroscience for over two decades, albeit they are typically extracted at a single scale using various methods, including decompositions like ICA. However, since numerous studies have suggested that the functional organization of the brain is hierarchical, analogous decompositions might better capture functional connectivity patterns. Moreover, hierarchical decompositions can efficiently reduce the very high dimensionality of functional connectivity data. This paper provides a novel method for the extraction of hierarchical connectivity components in the human brain using resting-state fMRI. The method builds upon prior work of Sparse Connectivity Patterns (SCPs) by introducing a hierarchy of sparse, potentially overlapping patterns. The components are estimated by cascaded factorization of correlation matrices generated from fMRI. The goal of the paper is to extract sparse interpretable hierarchically-organized patterns using correlation matrices where a low rank decomposition is formed by a linear combination of a higher rank decomposition. We formulate the decomposition as a non-convex optimization problem and solve it using gradient descent algorithms with adaptive step size. Along with the hierarchy, our method aims to capture the heterogeneity of the set of common patterns across individuals. We first validate our model through simulated experiments. We then demonstrate the effectiveness of the developed method on two different real-world datasets by showing that multi-scale hierarchical SCPs are reproducible between sub-samples and are more reproducible as compared to single scale patterns. We also compare our method with an existing hierarchical community detection approach.