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1403 Circle Drive, Knoxville, TN 37996

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Title: Topological Inference on Heat-diffusion Estimates of Persistence Diagrams

Speaker: Yuan Wang, Department of Epidemiology and Biostatistics, University of South Carolina

Abstract: Topological data analysis (TDA) has motivated the exploration of mesoscale features in brain signals and networks. Persistent homology is a key TDA algorithm for decoding and representing these features via persistence descriptors such as persistence diagram (PD), whose statistical significance is often revealed through permutation testing. But testing on PDs is challenging due to the heterogeneity of points in the diagrams that encode the birth and death times of features through a dynamic filtration of the subnetworks. This talk will showcase a transposition-based permutation testing framework based on heat-diffusion estimates of PDs to resolve computational bottlenecks associated with a large number of permutations required for convergence.

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