Learning Minimum Volume Sets and Anomaly Detectors from KNN Graphs
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We propose a non-parametric anomaly detection algorithm for high dimensional data. We first rank scores derived from nearest neighbor graphs on n-point nominal training data. 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 real-data experiments. Our results demonstrate the superiority of our algorithm over existing K-NN based anomaly detection algorithms, with significant computational savings.
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