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Activity Number: 329 - Novel Developments in Functional Data Analysis
Type: Topic Contributed
Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #328445 Presentation
Title: Registration for Exponential Functional Data
Author(s): Julia Wrobel* and Jeff Goldsmith
Companies: and Columbia University
Keywords: accelerometers; alignment; fpca; functional data; binary curves

We introduce a novel method for separating amplitude and phase variability in exponential family functional data. Our method alternates between two steps: the first uses generalized functional principal components analysis to calculate template functions, and the second estimates smooth warping functions that map observed curves to templates. Existing approaches to registration have primarily focused on continuous functional observations, and the few approaches for discrete functional data require a pre-smoothing step; these methods are frequently computationally intensive. In contrast, we focus on the likelihood of the observed data and avoid the need for preprocessing. Our motivation comes from the Baltimore Longitudinal Study on Aging, in which accelerometer data provides valuable insights into the timing of sedentary behavior. We analyze binary functional data with observations each minute over 24 hours for 592 subjects, where values represent activity and inactivity. Diurnal patterns of activity are obscured due to misalignment in the original data but are clear after curves are aligned. Simulations outperform competing approaches. Code is publicly available.

Authors who are presenting talks have a * after their name.

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