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Title: Regression and alignment for functional data and network topology Authors:  Danni Tu - University of Pennsylvania (United States) [presenting]
Julia Wrobel - University of Colorado School of Public Health (United States)
Azeez Adebimpe - University of Pennsylvania (United States)
Theodore Satterthwaite - University of Pennsylvania (United States)
Jeff Goldsmith - Columbia University (United States)
Jan Gertheiss - Helmut Schmidt University (Germany)
Danielle Bassett - University of Pennsylvania (United States)
Russell Shinohara - University of Pennsylvania (United States)
Abstract: The human functional brain network dynamically reorganizes during adolescence. Changes in mesoscale topology can be assessed by modularity and participation coefficient, two diagnostics which capture the community structure of the brain network. By proportionally thresholding the network edges, we obtain a sequence of diagnostics for each threshold, resulting in diagnostic curves that describe network structure at multiple scales. Previous methods that evaluate network diagnostic curves have relied on permutation-based or pointwise comparisons, which are less powerful and less informative than comparisons of curves in their entirety. We propose a functional regression framework that addresses biases introduced by systematic differences in the distribution of edge strengths between networks, which we conceptualize as phase variation in diagnostic curves. Our novel method therefore simultaneously performs regression and curve alignment through an iterative, penalized estimation procedure. The illustrated procedure is widely applicable to domains of neuroscience where the goal is to study heterogeneity among a mixture of function- and scalar-valued measures.