Antimodes and Graphical Anomaly Exploration via Adaptive Depth Quantile Functions

TL;DR

This paper introduces an adaptive depth quantile function method for anomaly detection that leverages geometric insights and visualization, applicable to Euclidean and non-Euclidean data.

Contribution

It extends depth quantile functions with an adaptive approach, providing a novel geometric perspective and visualization for anomaly detection in diverse data spaces.

Findings

Competitive anomaly detection performance across datasets

Effective visualization of data geometry and anomalies

Theoretical insights into the shape of depth quantile functions

Abstract

This work proposes and investigates a novel method for anomaly detection and shows it to be competitive in a variety of Euclidean and non-Euclidean situations. It is based on an extension of the depth quantile functions (DQF) approach. The DQF approach encodes geometric information about a point cloud via functions of a single variable, whereas each observation in a data set is associated with a single such function. Plotting these functions provides a very beneficial visualization aspect. This technique can be applied to any data lying in a Hilbert space. The proposed anomaly detection approach is motivated by the geometric insight of the presence of anomalies in data being tied to the existence of antimodes in the data generating distribution. Coupling this insight with novel theoretical understanding into the shape of the DQFs gives rise to the proposed adaptive DQF (aDQF) methodology. Applications to various data sets illustrate the DQF and aDQF's strong anomaly detection performance, and the benefits of its visualization aspects.