Multivariate Functional Data Visualization and Outlier Detection

Type
Article

Authors
Dai, Wenlin
Genton, Marc G.

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program

Preprint Posting Date
2017-03-19

Online Publication Date
2018-08-24

Print Publication Date
2018-10-02

Date
2018-08-24

Abstract
This article proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional outlyingness, which measures the centrality of functional data by simultaneously considering the level and the direction of their deviation from the central region. The MS-plot intuitively presents not only levels but also directions of magnitude outlyingness on the horizontal axis or plane, and demonstrates shape outlyingness on the vertical axis. A dividing curve or surface is provided to separate nonoutlying data from the outliers. Both the simulated data and the practical examples confirm that the MS-plot is superior to existing tools for visualizing centrality and detecting outliers for functional data. Supplementary material for this article is available online.

Citation
Dai W, Genton MG (2018) Multivariate Functional Data Visualization and Outlier Detection. Journal of Computational and Graphical Statistics: 1–12. Available: http://dx.doi.org/10.1080/10618600.2018.1473781.

Acknowledgements
This research was supported by the King Abdullah University of Science and Technology (KAUST).

Publisher
Informa UK Limited

Journal
Journal of Computational and Graphical Statistics

DOI
10.1080/10618600.2018.1473781

arXiv
1703.06419

Additional Links
https://www.tandfonline.com/doi/full/10.1080/10618600.2018.1473781

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