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 may be defined as those curves that exhibit a different shape from the rest of the sample. Whereas magnitude outliers, that is, curves that lie outside the range of the majority of the data, 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 measures of depth 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 assess the performance of the algorithm on a simulation study. Finally, we apply our method to identify outliers in real data sets of growth and mortality curves.