A Measure of Directional Outlyingness With Applications to Image Data and Video

Peter J. Rousseeuw*, Jakob Raymaekers, Mia Hubert

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Functional data analysis covers a wide range of data types. They all have in common that the observed objects are functions of a univariate argument (e.g., time or wavelength) or a multivariate argument (say, a spatial position). These functions take on values which can in turn be univariate (such as the absorbance level) or multivariate (such as the red/green/blue color levels of an image). In practice it is important to be able to detect outliers in such data. For this purpose we introduce a new measure of outlyingness that we compute at each gridpoint of the functions’ domain. The proposed directional outlyingness (DO) measure accounts for skewness in the data and only requires (Formula presented.) computation time per direction. We derive the influence function of the DO and compute a cutoff for outlier detection. The resulting heatmap and functional outlier map reflect local and global outlyingness of a function. To illustrate the performance of the method on real data it is applied to spectra, MRI images, and video surveillance data.

Original languageEnglish
Pages (from-to)345-359
Number of pages15
JournalJournal of Computational and Graphical Statistics
Volume27
Issue number2
DOIs
Publication statusPublished - 3 Apr 2018
Externally publishedYes

Fingerprint

Dive into the research topics of 'A Measure of Directional Outlyingness With Applications to Image Data and Video'. Together they form a unique fingerprint.

Cite this