Anomaly Detection with Score functions based on Nearest Neighbor Graphs

TL;DR

This paper introduces a non-parametric, adaptive anomaly detection method using nearest neighbor graphs that is asymptotically optimal, computationally efficient, and effective in high-dimensional data environments.

Contribution

The paper presents a novel anomaly detection algorithm based on score functions from nearest neighbor graphs, with proven asymptotic optimality and adaptability to local data structures.

Findings

Algorithm is asymptotically optimal for specified false alarm levels.

Computational complexity is linear in dimension and quadratic in data size.

Effective on artificial and real high-dimensional datasets.

Abstract

We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on $n$-point nominal data. Anomalies are declared whenever the score of a test sample falls below $\alpha$, which is supposed to be the desired false alarm level. The resulting anomaly detector is shown to be asymptotically optimal in that it is uniformly most powerful for the specified false alarm level, $\alpha$, for the case when the anomaly density is a mixture of the nominal and a known density. Our algorithm is computationally efficient, being linear in dimension and quadratic in data size. It does not require choosing complicated tuning parameters or function approximation classes and it can adapt to local structure such as local change in dimensionality. We demonstrate the algorithm on both artificial and real data sets in high dimensional feature spaces.