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Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

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Document pages: 18 pages

Abstract: Functional magnetic resonance imaging (fMRI) is a crucial technology forgaining insights into cognitive processes in humans. Data amassed from fMRImeasurements result in volumetric data sets that vary over time. However,analysing such data presents a challenge due to the large degree of noise andperson-to-person variation in how information is represented in the brain. Toaddress this challenge, we present a novel topological approach that encodeseach time point in an fMRI data set as a persistence diagram of topologicalfeatures, i.e. high-dimensional voids present in the data. This representationnaturally does not rely on voxel-by-voxel correspondence and is robust tonoise. We show that these time-varying persistence diagrams can be clustered tofind meaningful groupings between participants, and that they are also usefulin studying within-subject brain state trajectories of subjects performing aparticular task. Here, we apply both clustering and trajectory analysistechniques to a group of participants watching the movie Partly Cloudy . Weobserve significant differences in both brain state trajectories and overalltopological activity between adults and children watching the same movie.

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