On the Definition of Phase and Amplitude Variability in Functional Data Analysis

Code:
33/2009
Title:
On the Definition of Phase and Amplitude Variability in Functional Data Analysis
Date:
Wednesday 11th November 2009
Author(s):
Vantini, Simone
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Abstract:
We introduce a mathematical framework in which a functional data registration problem can be soundly and coherently set. In detail, we show that the introduction of a metric/semi-metric and of a group of warping function respect to which the metric/semi-metric is invariant is the key to a clear and not ambiguous de nition of phase and amplitude variability. Moreover, an amplitude-to-total variability index is proposed. This index turns to be useful in practical situations to measure to what extent amplitude variability a ects the data and to compare the e ectiveness of diff erent registration methods.