Shape Outlier Detection and Visualization for Functional Data: the Outliergram

Abstract

We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis we observe curves defined over a given real interval and shape outliers are those curves that exhibit a different shape from the rest of the sample. Whereas magnitude outliers, that is, curves that exhibit atypically high or low values at some points or across the whole interval, are in general easy to identify, shape outliers are often masked among the rest of the curves and thus difficult to detect. In this article we exploit the relation between two depths for functional data to help visualizing curves in terms of shape and to develop an algorithm for shape outlier detection. We illustrate the use of the visualization tool, the outliergram, through several examples and asses the performance of the algorithm on a simulation study. We apply them to the detection of outliers in a children growth dataset in which the girls sample is contaminated with boys curves and viceversa.