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A measure of directional outlyingness with applications to image data and video

Journal Contribution - Journal Article

© 2018, © The Author(s). Published with license by Taylor & Francis. © 2018, © 2018 Peter J. Rousseeuw, Jakob Raymaekers, and Mia Hubert. 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.
Journal: Journal of Computational and Graphical Statistics
ISSN: 1061-8600
Issue: 2
Volume: 27
Pages: 1 - 36
Publication year:2018