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Principal symmetric space analysis (1908.04553v1)
Published 13 Aug 2019 in math.ST, math.DG, and stat.TH
Abstract: We develop a novel analogue of Euclidean PCA (principal component analysis) for data taking values on a Riemannian symmetric space, using totally geodesic submanifolds as approximating lower dimnsional submanifolds. We illustrate the technique on n-spheres, Grassmannians, n-tori and polyspheres.