Metric-Based Boxplots for Functional Data in the Presence of Time-Warping Variability

• Activity Number: 418
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Scientific and Public Affairs Advisory Committee
• Author(s): Weiyi Xie* and Sebastian Kurtek
• Companies: The Ohio State University and The Ohio State University
• Keywords: Functional Data Analysis ; Functional Boxplot ; decompositon of functions ; warping ; outlier detection ; visualization

Abstract

We define a new method for construction and visualization of boxplots for functional data. In particular, we utilize a recent functional data analysis framework, based on a special representation of functions called square-root slope functions (SRSFs), to decompose observed functional data into three main components: amplitude, phase, and vertical translation. While vertical translation is easy to extract, the amplitude and phase components are found by aligning all given functions to the geometric amplitude median, which is computed, under an appropriate metric, using an iterative algorithm. We then construct a separate boxplot for each component using the geometry and metric of each space to compute the median, the two quartiles, and the two extremes, and to detect outliers. The main advantages of this approach are: (1) we are able to decompose the display of functional data into natural components of translation, amplitude and phase, and (2) we can identify different types of outliers. We provide various types of display for the generated boxplots, including surface plots, and apply the proposed method on simulated and real data.