On the definition of phase and amplitude variability in functional data analysis

Simone Vantini ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2012, vol. 21, issue 4, 676-696

Abstract: We introduce a modeling and mathematical framework in which the problem of registering a functional data set can be consistently set. In detail, we show that the introduction, in a functional data analysis, of a metric/semi-metric and of a group of warping functions, with respect to which the metric/semi-metric is invariant, enables a sound and not ambiguous definition of phase and amplitude variability. Indeed, in this framework, we prove that the analysis of a registered functional data set can be re-interpreted as the analysis of a set of suitable equivalence classes associated to original functions and induced by the group of the warping functions. Moreover, an amplitude-to-total variability index is proposed. This index turns out to be useful in practical situations for measuring to what extent phase variability affects the data and for comparing the effectiveness of different registration methods. Copyright Sociedad de Estadística e Investigación Operativa 2012

Keywords: Functional data analysis; Phase variability; Amplitude variability; Registration; Alignment; Synchronization; Warping; 62H05; 62H35; 62H99; 62A01 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s11749-011-0268-9

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