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Matrix distributions and statistical shape analysis

Speaker: Alfred KUME (Kent)

Abstract

Shape is the geometrical information left after the information about location, scale and rotation is filtered out. In practise, the shape data are generated as coordinate locations of some k points in some R^d space. Arranging these coordinates as a matrix of dimension kxd, it is natural to construct the shape spaces as quotient spaces of matrices via the shape equivalence of rigid body transformations and/or scaling. In the talk we will give a quick introduction to the geometrical models for shape spaces which result in Riemannian manifolds of both non-negative and non-positive curvature.  We will then focus on the inferential issues related to shape data. In particular, we will focus on some models which are constructed by assuming that the shape-data generating process is induced by multivariate normal matrices. The relevant distribution theory and computational challenges will be discussed. The results will be illustrated with some examples