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Activity Number: 271
Type: Contributed
Date/Time: Tuesday, August 5, 2008 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301919
Title: Manifold Models for Functional Data
Author(s): Dong Chen*+ and Hans G. Müller
Companies: University of California, Davis and University of California, Davis
Address: Department of Statistics, 1 Shields Avenue, Davis, CA, 95616,
Keywords: functional manifold ; warping ; Isomap ; structural mean
Abstract:

In the situation where functional data scatter around a nonlinear manifold in function space, the usual sample mean and linear functional principal component representation are not effective. We demonstrate this for time-warped functional data, and develop a modified unwrapping method, based on a version of ISOMAP (Tenenbaum 2000). Our modification is geared towards the case of noisy data by changing the distance on which the core multidimensional scaling step is based. We demonstrate in simulations and applications that the nonlinear representations resulting from unwrapping functional data indeed are of interest.

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