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Title: Multiple change point detection for manifold-valued data with applications to dynamic functional connectivity Authors:  Qiang Sun - University of Toronto (United States) [presenting]
Abstract: In neuroscience, functional connectivity describes the connectivity between brain regions that share functional properties. It is often characterized by a time series of covariance matrices between functional measurements of distributed neuron areas. An effective statistical model for functional connectivity and its changes over time is critical for better understanding neurological diseases. To this end, we propose a log-mean model with an additive heterogeneous noise for modeling random symmetric positive definite matrices that lie in a Riemannian manifold. The heterogeneity of error terms is introduced specifically to capture the curved nature of the manifold. A scan statistic is then developed for the purpose of multiple change point detection. Despite that the proposed model is linear and additive, it is able to account for the curved nature of the Riemannian manifold. Theoretically, we establish the sure coverage property. Simulation studies and an application to the Human Connectome Project lend further support to the proposed methodology.