Learning Efficient Anomaly Detectors from $K$-NN Graphs

TL;DR

This paper introduces a non-parametric anomaly detection method using $K$-NN graphs that is asymptotically optimal and computationally efficient, outperforming existing algorithms on synthetic and real data.

Contribution

It develops a novel $K$-NN based anomaly detection approach that learns to rank anomalies efficiently with theoretical optimality guarantees.

Findings

Outperforms existing $K$-NN anomaly detection methods.

Achieves significant computational savings.

Demonstrates asymptotic optimality in anomaly detection.

Abstract

We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average $K$-NN distance, and rank them accordingly. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as an anomaly at $\alpha$-false alarm level if the predicted score is in the $\alpha$-percentile. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate $\alpha$, its decision region converges to the $\alpha$-percentile minimum volume level set of the unknown underlying density. In addition, we test both the statistical performance and computational efficiency of our algorithm on a number of synthetic and real-data experiments. Our results demonstrate the superiority of our algorithm over existing $K$-NN based anomaly detection algorithms, with significant computational savings.