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Activity Number: 220 - Robust Multivariate and High-Dimensional Analysis Using Functional Data Ranking
Type: Topic Contributed
Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #322862 View Presentation
Title: Total Variation Depth for Functional Data
Author(s): Ying Sun* and Huang Huang
Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology (KAUST)
Keywords: data depth ; functional data ; total variation ; outlier detection ; shape outliers

There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation depth, for functional data. As a measure of depth, its properties are studied theoretically, and the associated outlier detection performance is investigated through simulations. Compared to magnitude outliers, shape outliers are often masked among the rest of samples and harder to identify. We show that the proposed total variation depth has many desirable features and is well suited for outlier detection. In particular, we propose to decompose the total variation depth into two components that are associated with shape and magnitude outlyingness, respectively. This decomposition allows us to develop an effective procedure for outlier detection and useful visualization tools, while naturally accounting for the correlation in functional data. Finally, the proposed methodology is demonstrated using real datasets of curves, images, and video frames.

Authors who are presenting talks have a * after their name.

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