A Rank-SVM Approach to Anomaly Detection

TL;DR

This paper introduces a non-parametric, adaptive anomaly detection method for high-dimensional data using rank-SVM, which is shown to be asymptotically optimal and effective in experiments.

Contribution

It presents a novel rank-SVM based anomaly detection algorithm that adapts to unknown densities and achieves asymptotic optimality in high-dimensional settings.

Findings

The proposed method is asymptotically optimal for anomaly detection.

It demonstrates strong statistical performance in synthetic and real data.

The algorithm is computationally efficient for high-dimensional data.

Abstract

We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on rank-SVM. Data points are first ranked based on scores derived from nearest neighbor graphs on n-point nominal data. We then train a rank-SVM using this ranked data. 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 and adaptive in that for any false alarm rate alpha, its decision region converges to the alpha-percentile level set of the unknown underlying density. In addition we illustrate through a number of synthetic and real-data experiments both the statistical performance and computational efficiency of our anomaly detector.