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Abstract:
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Accounting for phase variability is a critical challenge in functional data analysis. To separate it from amplitude variation, functional data are registered, i.e., their observed domains are deformed elastically to align the functions with template functions. Most available registration approaches are limited to complete, densely measured curves with Gaussian noise. However, many real-world functional data are not Gaussian and contain incomplete curves whose underlying processes are not recorded over their entire domain. We develop a method for joint likelihood-based registration and latent Gaussian process-based generalized functional principal component analysis that can handle such incomplete curves, and provide sophisticated open-source software for diverse non-Gaussian data settings. We register data from a seismological application comprising spatially indexed, incomplete ground velocity time series with a highly volatile Gamma structure. We describe, implement and evaluate the approach for such incomplete non-Gaussian functional data and compare it to existing routines.
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