A Geometric Approach to Visualization of Variability in Functional Data

Abstract

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.

Journal of the American Statistical Association, 2016

References in corpus (5)

• Generative Models for Functional Data using Phase and Amplitude Separation
• Functional Data Analysis of Amplitude and Phase Variation
• Registration of Functional Data Using Fisher-Rao Metric
• Precise Matching of PL Curves in $R^N$ in the Square Root Velocity Framework
• Concerns with functional depth

Cited by in corpus (8)

• Elastic depths for detecting shape anomalies in functional data
• Functional Outlier Detection and Taxonomy by Sequential Transformations
• Multimodal Bayesian Registration of Noisy Functions using Hamiltonian Monte Carlo
• A Geometric Approach for Computing Tolerance Bounds for Elastic Functional Data
• Functional outlier detection for density-valued data with application to robustify distribution to distribution regression
• Shape-Preserving Prediction for Stationary Functional Time Series
• Trajectory Functional Boxplots
• Functional Boxplots for Outlier Detection in Additive Manufacturing