A General Framework for Multivariate Functional Principal Component Analysis of Amplitude and Phase Variation

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we focus on joint principal component analysis (PCA) of amplitude and phase variation. As the space of warping functions has a complex geometric structure, one key element of the analysis is transforming the warping functions to L2(T ). We present different transformation approaches and show how they fit into a general class of transformations. This allows us to com- pare their strengths and limitations. In the context of PCA, our results offer arguments in favour of the centered log-ratio transformation. We further embed existing approaches from Hadjipantelis, Aston, Müller, and Evans (2015) and Lee and Jung (2016) for joint PCA of amplitude and phase variation into the framework of multi- variate functional PCA, where we study the properties of the estimators based on an appropriate metric. The approach is illustrated through an application from seismology.

@article{id2413,
  author = {Happ, Clara and Scheipl, Fabian and Gabriel, Alice-Agnes and Greven, Sonja},
  doi = {10.1002/sta4.220},
  journal = {Stat},
  language = {en},
  number = {1},
  pages = {e220},
  title = {A General Framework for Multivariate Functional Principal Component Analysis of Amplitude and Phase Variation},
  url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sta4.220},
  volume = {8},
  year = {2019},
}

%O Journal Article
%A Happ, Clara
%A Scheipl, Fabian
%A Gabriel, Alice-Agnes
%A Greven, Sonja
%R 10.1002/sta4.220
%J Stat
%G en
%N 1
%P e220
%T A General Framework for Multivariate Functional Principal Component Analysis of Amplitude and Phase Variation
%U https://onlinelibrary.wiley.com/doi/abs/10.1002/sta4.220
%V 8
%D 2019