Conformal prediction for anomaly detection and collision alert in space surveillance

Anomaly detection has been considered as an important technique for detecting critical events in a wide range of data rich applications where a majority of the data is inconsequential and/or uninteresting. We study the detection of anomalous behaviors among space objects using the theory of conformal prediction for distribution-independent on-line learning to provide collision alerts with a desirable confidence level. We exploit the fact that conformal predictors provide valid forecasted sets at specified confidence levels under the relatively weak assumption that the normal training data, together with the normal testing data, are generated from the same distribution. If the actual observation is not included in the conformal prediction set, it is classified as anomalous at the corresponding significance level. Interpreting the significance level as an upper bound of the probability that a normal observation is mistakenly classified as anomalous, we can conveniently adjust the sensitivity to anomalies while controlling the false alarm rate without having to find the application specific threshold. The proposed conformal prediction method was evaluated for a space surveillance application using the open source North American Aerospace Defense Command (NORAD) catalog data. The validity of the prediction sets is justified by the empirical error rate that matches the significance level. In addition, experiments with simulated anomalous data indicate that anomaly detection sensitivity with conformal prediction is superior to that of the existing methods in declaring potential collision events.