Multivariate Functional Data Visualization and Outlier Detection
提出一种新的图形工具——幅度-形状图，用于同时可视化多元函数型数据的幅度和形状异常程度，帮助识别异常值。
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.