Multivariate Functional Data Visualization and Outlier Detection

Wenlin Dai, Marc G. Genton

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)923-934
Number of pages12
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - Aug 24 2018


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