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Activity Number: 64
Type: Topic Contributed
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: International Indian Statistical Association
Abstract - #305578
Title: Registration of Functional Data Using Fisher-Rao Metric
Author(s): Wei Wu*+
Companies:
Address: 7959 Preservation Rd, Tallahassee, FL, 32312, United States
Keywords: Function Registration ; Fisher-Rao Metric ; Proper Distance ; Time Warping ; Karcher Mean ; L2 Metric
Abstract:

We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a proper distance on the quotient space of functions modulo the time-warping group. A convenient square-root velocity function (SRVF) representation transforms the Fisher-Rao metric into the standard L2 metric, simplifying the computations. This distance is then used to define a Karcher mean template and warp the individual functions to align them with the Karcher mean template. The strength of this framework is demonstrated by deriving a consistent estimator of a signal observed under random warping, scaling, and vertical translation. These ideas are demonstrated using both simulated and real data from different application domains: the Berkeley growth study, handwritten signature curves, neuroscience spike trains, and gene expression signals. The proposed method is empirically shown to be be superior in performance to several recently published methods for functional alignment.


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