A Geometric Approach to Visualization of Variability in Functional Data

Weiyi Xie, Sebastian Kurtek, Karthik Bharath, Ying Sun

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We propose a new method for the construction and visualization of boxplot-type displays for functional data. We use a recent functional data analysis framework, based on a representation of functions called square-root slope functions, to decompose observed variation in functional data into three main components: amplitude, phase, and vertical translation. We then construct separate displays for each component, using the geometry and metric of each representation space, based on a novel definition of the median, the two quartiles, and extreme observations. The outlyingness of functional data is a very complex concept. Thus, we propose to identify outliers based on any of the three main components after decomposition. We provide a variety of visualization tools for the proposed boxplot-type displays including surface plots. We evaluate the proposed method using extensive simulations and then focus our attention on three real data applications including exploratory data analysis of sea surface temperature functions, electrocardiogram functions and growth curves.
Original languageEnglish (US)
Pages (from-to)979-993
Number of pages15
JournalJournal of the American Statistical Association
Issue number519
StatePublished - Dec 16 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-2015-CRG4-2582
Acknowledgements: We would like to thank the reviewers for their valuable comments, which greatly improved the quality of this manuscript. This research was partially supported by NSF DMS 1613054 (to Sebastian Kurtek and Karthik Bharath), and the KAUST Office of Sponsored Research under award OSR-2015-CRG4-2582 (to Ying Sun).


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