Cracks in KRX: When more distant points are less anomalous

We examine the Mahalanobis-distance based kernel-RX (KRX) algorithm for anomaly detection, and find that it can exhibit an unfortunate phenomenon: the anomalousness, for points far from the training data, can decrease with increasing distance. We demonstrate this directly for a few special cases, and provide a more general argument that applies in the large bandwidth regime.

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