Abstract

Elastic Hyper-alignment of Functional Data -- Shapes and Signals

Shantanu Joshi
University of California, Los Angeles (UCLA)

This talk consists of several parts. In the first part, we present a framework for linear and quadratic discriminant classification on the tangent plane of the shape space of curves represented by square root velocities. The shape observations from the population are approximated by coefficients of a Fourier basis of the tangent space. The algorithms for linear and quadratic discriminant analysis are then defined on the tangent space represented by the truncated Fourier basis. We show classification results on synthetic data and shapes derived from brain imaging data. The second part of this talk presents approaches for spatio-temporal matching of shapes. The last part of this talk presents some new applications for functional magnetic resonance imaging (fMRI) time course and spectral alignment. We show elastic alignment of both amplitude and phase of the fMRI time courses as well as their power spectral densities. Experimental results show significant increases in pairwise node to node correlations and coherences following alignment.