Data Science Day @ Columbia University

We propose a new nonparametric method, "Concurrence Topology (CT)", for describing dependence among dichotomous variables. CT starts by translating the data into a "filtration", i.e., a series of shapes. Holes in the filtration correspond to relatively weak or negative association among the variables. CT uses computational topology to describe the pattern of holes in the filtration. CT is able to describe high-order dependence while avoiding combinatorial explosion. We employed CT to investigate brain functional connectivity based on dichotomized functional MRI data. The data set includes subjects diagnosed with ADHD and healthy controls. In an exploratory analysis, working in both the time and Fourier domains, CT found a number of differences between ADHD subjects and controls in the topology of their filtrations. A paper based on this work has been published.