A Geometric Approach to Visualization of Variability in Functional Data

Handle URI:
http://hdl.handle.net/10754/622993
Title:
A Geometric Approach to Visualization of Variability in Functional Data
Authors:
Xie, Weiyi; Kurtek, Sebastian; Bharath, Karthik; Sun, Ying ( 0000-0001-6703-4270 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Xie W, Kurtek S, Bharath K, Sun Y (2016) A Geometric Approach to Visualization of Variability in Functional Data. Journal of the American Statistical Association: 0–0. Available: http://dx.doi.org/10.1080/01621459.2016.1256813.
Publisher:
Informa UK Limited
Journal:
Journal of the American Statistical Association
KAUST Grant Number:
OSR-2015-CRG4-2582
Issue Date:
19-Dec-2016
DOI:
10.1080/01621459.2016.1256813
Type:
Article
ISSN:
0162-1459; 1537-274X
Sponsors:
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).
Is Supplemented By:
Weiyi Xie, Kurtek, S., Bharath, K., & Sun, Y. (2016). A Geometric Approach to Visualization of Variability in Functional Data. Figshare. https://doi.org/10.6084/m9.figshare.4478426; DOI:10.6084/m9.figshare.4478426; HANDLE:http://hdl.handle.net/10754/624779
Additional Links:
http://www.tandfonline.com/doi/full/10.1080/01621459.2016.1256813
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorXie, Weiyien
dc.contributor.authorKurtek, Sebastianen
dc.contributor.authorBharath, Karthiken
dc.contributor.authorSun, Yingen
dc.date.accessioned2017-03-15T07:15:25Z-
dc.date.available2017-03-15T07:15:25Z-
dc.date.issued2016-12-19en
dc.identifier.citationXie W, Kurtek S, Bharath K, Sun Y (2016) A Geometric Approach to Visualization of Variability in Functional Data. Journal of the American Statistical Association: 0–0. Available: http://dx.doi.org/10.1080/01621459.2016.1256813.en
dc.identifier.issn0162-1459en
dc.identifier.issn1537-274Xen
dc.identifier.doi10.1080/01621459.2016.1256813en
dc.identifier.urihttp://hdl.handle.net/10754/622993-
dc.description.abstractWe 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.en
dc.description.sponsorshipWe 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).en
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://www.tandfonline.com/doi/full/10.1080/01621459.2016.1256813en
dc.rightsArchived with thanks to Journal of the American Statistical Association This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 16 Dec 2016, available online: http://wwww.tandfonline.com/10.1080/01621459.2016.1256813.en
dc.subjectamplitude and phase variabilitiesen
dc.subjectFisher–Rao metricen
dc.subjectfunctional outlier detectionen
dc.subjectsquare-root slope functionen
dc.titleA Geometric Approach to Visualization of Variability in Functional Dataen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of the American Statistical Associationen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Statistics, The Ohio State Universityen
dc.contributor.institutionSchool of Mathematical Sciences, University of Nottinghamen
kaust.authorSun, Yingen
kaust.grant.numberOSR-2015-CRG4-2582en
dc.relation.isSupplementedByWeiyi Xie, Kurtek, S., Bharath, K., & Sun, Y. (2016). A Geometric Approach to Visualization of Variability in Functional Data. Figshare. https://doi.org/10.6084/m9.figshare.4478426en
dc.relation.isSupplementedByDOI:10.6084/m9.figshare.4478426en
dc.relation.isSupplementedByHANDLE:http://hdl.handle.net/10754/624779en
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