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Anomaly detection is being regarded as an unsupervised learning task as anomalies stem from adversarial or unlikely events with unknown distributions. However, the predictive performance of purely unsupervised anomaly detection often fails to match the required detection rates in many tasks and there exists a need for labeled data to guide the model generation. The authors' first contribution shows that classical semi-supervised approaches, originating from a supervised classifier, are inappropriate and hardly detect new and unknown anomalies. They argue that semi-supervised anomaly detection needs to ground on the unsupervised learning paradigm and devise a novel algorithm that meets this requirement. Although being intrinsically non-convex, they further show that the optimization problem has a convex equivalent under relatively mild assumptions.
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