A general framework for multivariate functional principal component analysis of amplitude and phase variation

Clara Happ, Fabian Scheipl, Alice Agnes Gabriel, Sonja Greven

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Functional data typically contain 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 compare their strengths and limitations. In the context of PCA, our results offer arguments in favour of the centred log-ratio transformation. We further embed two existing approaches from the literature for joint PCA of amplitude and phase variation into the framework of multivariate functional PCA, where we study the properties of the estimators based on an appropriate metric. The approach is illustrated through an application from seismology.
Original languageEnglish (US)
Issue number1
StatePublished - Feb 26 2019
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-10
Acknowledged KAUST grant number(s): ORS-2016-CRG5-3027, ORS-2017-CRG6 3389.02
Acknowledgements: We would like to thank Almond Stöcker for drawing our attention to the theory of Bayes spaces for probability densities and David Rügamer for his valuable comments on the text. Regarding the seismological application, we are grateful to Helmut Küchenhoff and Alexander Bauer for their collaboration. Fabian Scheipl's work has been supported by the German Federal Ministry of Education and Research (BMBF) under Grant No. 01IS18036A. Alice-Agnes Gabriel's work was supported by the German Research Foundation (DFG) (projects no. KA 2281/4-1, GA 2465/2-1, GA 2465/3-1), by BaCaTec (project no. A4), by KONWIHR - the Bavarian Competence Network for Technical and Scientific High Performance Computing (project NewWave), by the Volkswagen Foundation (ASCETE, grant no. 88479), by KAUST-CRG (GAST, grant no. ORS-2016-CRG5-3027 and FRAGEN, grant no. ORS-2017-CRG6 3389.02), by the European Union's Horizon 2020 research and innovation program (ExaHyPE, grant no. 671698 and ChEESE, grant no. 823844). Computing resources were provided by the Institute of Geophysics of LMU Munich (Oeser et al., 2006), the Leibniz Supercomputing Centre (LRZ, projects no. h019z, pr63qo, and pr45fi on SuperMUC).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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