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

TL;DR

This paper introduces a new directional outlyingness measure for functional data that accounts for skewness, enabling effective outlier detection in image and video data with efficient computation.

Contribution

The paper proposes a novel outlyingness measure for functional data that considers skewness and provides a practical outlier detection method with heatmaps and outlier maps.

Findings

Effective outlier detection in spectra, MRI images, and videos.

Computational efficiency with O(n) time per direction.

Outlier maps reveal local and global outlyingness.

Abstract

Functional data covers a wide range of data types. They all have in common that the observed objects are functions of 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 O(n) 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.