Functional data covers a wide range of data types. They all have in commonthat the observed objects are functions of of a univariate argument (e.g. timeor wavelength) or a multivariate argument (say, a spatial position). Thesefunctions take on values which can in turn be univariate (such as theabsorbance level) or multivariate (such as the red/green/blue color levels ofan image). In practice it is important to be able to detect outliers in suchdata. For this purpose we introduce a new measure of outlyingness that wecompute at each gridpoint of the functions' domain. The proposed DirectionalOutlyingness} (DO) measure accounts for skewness in the data and only requiresO(n) computation time per direction. We derive the influence function of the DOand compute a cutoff for outlier detection. The resulting heatmap andfunctional outlier map reflect local and global outlyingness of a function. Toillustrate the performance of the method on real data it is applied to spectra,MRI images, and video surveillance data.
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