On the definition of phase and amplitude variability in functional data analysis
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Simone Vantini [1]
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[1] Polytechnic University of Milan
Polytechnic University of Milan
Milán, Italia
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 21, Nº. 4, 2012, págs. 676-696
- Idioma: inglés
- DOI: 10.1007/s11749-011-0268-9
- Texto completo no disponible (Saber más ...)
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Resumen
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.
