Functional Data Visualization

Abstract

This article reviews tools to visualize functional data, that is, curves, surfaces/images, and trajectories. These tools are based on ranking functional data by means of notions of depth/outlyingness and make use of methods for functional outlier detections. For univariate functional data, the functional boxplot and surface boxplot are emphasized. For multivariate functional data, the magnitude–shape plot, the two-stage functional boxplot, and the trajectory functional boxplot are described. A bivariate functional dataset of the angles formed by the hip and knee of 39 children over their gait cycles is used throughout for illustration of the various visualization tools.