A geometric approach to visualization of variability in functional data

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

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: https://nottingham-repository.worktribe.com/output/833175
• Publisher URL: http://dx.doi.org/10.1080/01621459.2016.1256813
• 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