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We introduce a novel framework for the classification of functional data supported on nonlinear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer’s disease from their cortical surface geometry and associated cortical thickness map. The proposed model is based upon a reformulation of the classification problem as a regularized multivariate functional linear regression model. This allows us to adopt a direct approach to the estimation of the most discriminant direction while controlling for its complexity with appropriate differential regularization. Our approach does not require prior estimation of the covariance structure of the functional predictors, which is computationally prohibitive in our application setting. We provide a theoretical analysis of the out-of-sample prediction error of the proposed model and explore the finite sample performance in a simulation setting. We apply the proposed method to a pooled dataset from the Alzheimer’s Disease Neuroimaging Initiative and the Parkinson’s Progression Markers Initiative. Through this application, we identify discriminant directions that capture both cortical geometric and thickness predictive features of Alzheimer’s disease that are consistent with the existing neuroscience literature. 

The Human Connectome Project (HCP) has become a keystone dataset in human neuroscience, with a plethora of important applications in advancing brain imaging methods and an understanding of the human brain. We focused on tractometry of HCP diffusion-weighted MRI (dMRI) data. We used an open-source software library (pyAFQ;https://yeatmanlab.github.io/pyAFQ) to perform probabilistic tractography and delineate the major white matter pathways in the HCP subjects that have a complete dMRI acquisition (n = 1,041). We used diffusion kurtosis imaging (DKI) to model white matter microstructure in each voxel of the white matter, and extracted tract profiles of DKI-derived tissue properties along the length of the tracts. We explored the empirical properties of the data: first, we assessed the heritability of DKI tissue properties using the known genetic linkage of the large number of twin pairs sampled in HCP. Second, we tested the ability of tractometry to serve as the basis for predictive models of individual characteristics (e.g., age, crystallized/fluid intelligence, reading ability, etc.), compared to local connectome features. To facilitate the exploration of the dataset we created a new web-based visualization tool and use this tool to visualize the data in the HCP tractometry dataset. Finally, we used the HCP dataset as a test-bed for a new technological innovation: the TRX file-format for representation of dMRI-based streamlines. We released the processing outputs and tract profiles as a publicly available data resource through the AWS Open Data program's Open Neurodata repository. We found heritability as high as 0.9 for DKI-based metrics in some brain pathways. We also found that tractometry extracts as much useful information about individual differences as the local connectome method. We released a new web-based visualization tool for tractometry --- “Tractoscope” (https://nrdg.github.io/tractoscope). We found that the TRX files require considerably less disk space - a crucial attribute for large datasets like HCP. In addition, TRX incorporates a specification for grouping streamlines, further simplifying tractometry analysis.