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Title: Elastic linear regression for curves in $R^d$ Authors:  Sonja Greven - Humboldt University of Berlin (Germany) [presenting]
Lisa Steyer - Humboldt University of Berlin (Germany)
Almond Stoecker - Humboldt University of Berlin (Germany)
Abstract: Regression models are proposed for curve-valued responses in two or more dimensions, where only the image but not the parametrisation of the curves is of interest. Examples of such data are handwritten letters, movement paths or outlines of objects. In the square-root-velocity framework, a parametrisation invariant distance for curves is obtained as the quotient space metric with respect to the action of re-parametrisation, which is by isometries. With this special case in mind, we discuss the generalisation of 'linear' regression to quotient spaces more generally, before illustrating the usefulness of our approach for curves modulo re-parametrisation. We test this model in simulations and apply it to human hippocampi data, obtained from MRI scans. Here we model how the shape of the hippocampus is related to age and Alzheimer's disease. We address the issue of irregularly sampled curves by using splines for modelling smooth predicted curves.