A geometric approach to visualization of variability in functional data
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 ma...
| Main Authors: | , , , |
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| Format: | Article |
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Taylor & Francis
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40806/ |
| _version_ | 1848796137967845376 |
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| author | Xie, Weiyi Kurtek, Sebastian Bharath, Karthik Sun, Ying |
| author_facet | Xie, Weiyi Kurtek, Sebastian Bharath, Karthik Sun, Ying |
| author_sort | Xie, Weiyi |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:12Z |
| format | Article |
| id | nottingham-40806 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:12Z |
| publishDate | 2016 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-408062020-05-04T18:25:34Z https://eprints.nottingham.ac.uk/40806/ A geometric approach to visualization of variability in functional data Xie, Weiyi Kurtek, Sebastian Bharath, Karthik Sun, Ying 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. Taylor & Francis 2016-12-16 Article PeerReviewed Xie, Weiyi, Kurtek, Sebastian, Bharath, Karthik and Sun, Ying (2016) A geometric approach to visualization of variability in functional data. Journal of the American Statistical Association, 112 (519). pp. 979-993. ISSN 1537-274X Amplitude and phase variabilities Fisher–Rao metric Functional outlier detection Square-root slope function http://dx.doi.org/10.1080/01621459.2016.1256813 doi:10.1080/01621459.2016.1256813 doi:10.1080/01621459.2016.1256813 |
| spellingShingle | Amplitude and phase variabilities Fisher–Rao metric Functional outlier detection Square-root slope function Xie, Weiyi Kurtek, Sebastian Bharath, Karthik Sun, Ying A geometric approach to visualization of variability in functional data |
| title | A geometric approach to visualization of variability in functional data |
| title_full | A geometric approach to visualization of variability in functional data |
| title_fullStr | A geometric approach to visualization of variability in functional data |
| title_full_unstemmed | A geometric approach to visualization of variability in functional data |
| title_short | A geometric approach to visualization of variability in functional data |
| title_sort | geometric approach to visualization of variability in functional data |
| topic | Amplitude and phase variabilities Fisher–Rao metric Functional outlier detection Square-root slope function |
| url | https://eprints.nottingham.ac.uk/40806/ https://eprints.nottingham.ac.uk/40806/ https://eprints.nottingham.ac.uk/40806/ |