Detecting Relative Anomaly

System states that are anomalous from the perspective of a domain expert occur with high density in some anomaly detection problems. The performance of commonly used unsupervised anomaly detection methods may suffer in that setting, because they use density as a proxy for anomaly. We propose a novel concept for anomaly detection, called relative anomaly detection. It is tailored to be robust towards anomalies that have high density, by taking into account their location relative to the most typical observations. The approaches we develop are computationally feasible even for large data sets, and they allow real-time detection. We illustrate using data sets of potential scraping attempts and Wi-Fi channel utilization, both from Google.