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• W2512102792 abstract "The problems of analysis and modeling of spherical trajectories, that is, continuous longitudinal data on S2, are important in several disciplines. These problems are challenging for two reasons: (1) nonlinear geometry of S2 and (2) the presence of phase variability in given data. This article develops a geometric framework for separating phase variability from given trajectories, leaving only the shape or the amplitude variability. The key idea is to represent each trajectory with a pair of variables, a starting point, and a transported square-root velocity curve (TSRVC), a curve in the tangent (vector) space at the starting point. The space of all such curves forms a vector bundle and the L2 norm, along with the standard Riemannian metric on S2, provides a natural, warping-invariant metric on this vector bundle. This leads to an efficient algorithm for registration of trajectories, that is, phase-amplitude separation, and computational tools, such as clustering, sample means, and principal component analysis (PCA) of the two components separately. It also helps derive simple statistical models of phase-amplitude components of spherical trajectories. This comprehensive framework is demonstrated using two datasets: a set of bird-migration trajectories and a set of hurricane paths in the Atlantic ocean. Supplementary material for this article is available online." @default.
• W2512102792 created "2016-09-16" @default.
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• W2512102792 date "2018-01-02" @default.
• W2512102792 modified "2023-09-26" @default.
• W2512102792 title "Phase-Amplitude Separation and Modeling of Spherical Trajectories" @default.
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• W2512102792 doi "https://doi.org/10.1080/10618600.2017.1340892" @default.
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