Antimodes and Graphical Anomaly Exploration via Depth Quantile Functions

Depth quantile functions (DQF) encode geometric information about a point cloud via functions of a single variable, whereas each observation in a data set can be associated with a single function. These functions can then be easily plotted. This is true regardless of the dimension of the data, and in fact holds for object data as well, provided a mapping to an RKHS exists. This visualization aspect proves valuable in the case of anomaly detection, where a universal definition of what constitutes an anomaly is lacking. A relationship drawn between anomalies and antimodes provides a strategy for identifying anomalous observations through visual examination of the DQF plot. The DQF in one dimension is explored, providing intuition for its behavior generally and connections to several existing methodologies are made clear. For higher dimensions and object data, the adaptive DQF is introduced and explored on several data sets with promising results.