Supplementary methods and results.

Mean and standard deviations (SD) of the symptom severity and intelligence scale in NYU dataset and PU dataset (Table A). Number of subjects in each group (TDC and ADHD) for each bin of the output graph of Mapper for NYU dataset (Table B). The effects of the phenotypic information to the magnitude of the disease component (Table C). The summary of receiver operating characteristic (ROC) analysis using the value of the filter function (Table D). The decomposition of the original functional connectivity vector T_i into the Normal component, which is the linear models fit onto the Healthy State Model, and the disease component vector of residuals. For example, decompositions of T_i with (A) small and (B) large disease component were visualized (Fig A). The areas under the receiver operating characteristics (ROC) curves for the value of the filter function were illustrated for (A) the NYU and (B) PU dataset, respectively (Fig B). Schematic diagram of topological data analysis using Mapper. (A) The data is sampled from a noisy Y-shape point cloud in the two-dimensional space, and the filter function is f(x,y) = y. We divided the range of the filter into 5 intervals and a 50% overlap. (B) For each interval, we compute the clustering of the points lying within the domain of the filter restricted to the interval. Distributions of the distances from single linkage dendrogram in each filter bin. For example, distance distributions for 1^st and 9^th filter bin were presented. The summation of frequencies appeared after zero bins is the number of clusters, (C) Finally, we have the simplicial complex by connecting the clusters whenever they have non-empty intersection. The color of vertices represents the average filter value (Fig C). Sample application of Mapper to the Y-shape noisy point cloud. In this example illustration, 5 intervals with 20–80% overlaps and 10 intervals with 80% overlap are the appropriate choose of the input parameters of Mapper (Fig D). Sample application of Mapper to O-shape noisy point cloud data. In this example illustration, 5 intervals with 50–80% overlaps, 10 intervals with 50–80% overlaps, and 15 intervals with 80% overlap are the appropriate choose of the input parameters of Mapper (Fig E). Visualization of the clinical phenotype data as a function of the node index in the PU data: (A) The average symptom severity in each bin of graph; (B) The average intelligence scores in each bin of graph (Fig F).

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