Abstract:
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We consider the problem of aligning curves from exponential family distributions. The approach is based on the combination of alignment and functional principal components analysis, and is facilitated by recent extensions of FPCA to non-Gaussian settings. Our work is motivated by the study of physical activity using accelerometers, wearable devices that provide around-the-clock monitoring of activity and produce non-Gaussian measurements. We apply the proposed methods to activity counts using a Poisson distribution, and to a binary "active" vs "inactive" indicator using a binomial distribution. After alignment, the trajectories show clear peaks of activity in the morning and afternoon with a dip in the middle of the day.
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