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A geometric approach to visualization of variability in functional data

Xie, Weiyi; Kurtek, Sebastian; Bharath, Karthik; Sun, Ying

Authors

Weiyi Xie

Sebastian Kurtek

Ying Sun



Abstract

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.

Citation

Xie, W., Kurtek, S., Bharath, K., & Sun, Y. (in press). A geometric approach to visualization of variability in functional data. Journal of the American Statistical Association, 112(519), https://doi.org/10.1080/01621459.2016.1256813

Journal Article Type Article
Acceptance Date Oct 24, 2016
Online Publication Date Dec 16, 2016
Deposit Date Feb 23, 2017
Publicly Available Date Feb 23, 2017
Journal Journal of the American Statistical Association
Print ISSN 0162-1459
Electronic ISSN 1537-274X
Publisher Taylor & Francis Open
Peer Reviewed Peer Reviewed
Volume 112
Issue 519
DOI https://doi.org/10.1080/01621459.2016.1256813
Keywords Amplitude and phase variabilities, Fisher–Rao metric, Functional outlier detection, Square-root slope function
Public URL http://eprints.nottingham.ac.uk/id/eprint/40806
Publisher URL http://dx.doi.org/10.1080/01621459.2016.1256813
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information The Version of Record of this manuscript has been published and is available in Journal of the American Statistical Association 16 Dec 2016 http://www.tandfonline.com/doi/full/10.1080/01621459.2016.1256813

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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