Learning Efficient Anomaly Detectors from K-NN Graphs

We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average KNN 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 α-false alarm level if the predicted score is in the α-percentile. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate α, its decision region converges to the α-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 realdata experiments. Our results demonstrate the superiority of our algorithm over existing K-NN based anomaly detection algorithms, with significant computational savings.