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Activity Number: 225 - The Interface of Functional Data Analysis and Biomedical Applications
Type: Topic Contributed
Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract #327241
Title: Multiple Change Point Detection for Symmetric Positive Definite Matrices
Author(s): Dehan Kong* and Zhenhua Lin and Qiang Sun
Companies: University of Toronto and University of Toronto and University of Toronto
Keywords: Change point; functional connectivity; Riemannian manifold; sure coverage property; symmetric positive definite matrix

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-linear mean model with a heterogeneous noise for modeling random symmetric positive definite matrices that lie in a Riemannian manifold. A screening procedure 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 symmetric positive definite matrix 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.

Authors who are presenting talks have a * after their name.

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