An anomaly detection method can enjoy some properties. The idea presented here is to apply an algorithm for anomaly detection to a dataset, to remove the discovered anomalous points, and then to apply to the remaining data the same algorithm again.
Let S be a set of points, F an outlier detection method, and A the set of outliers of S discovered by F. In this case we can write A=F(S). If F(S-A)={} (empty set), then F is an invariant algorithm for S (or S is invariant respect to F). In this case, F finds all the outliers of S in one fell swoop. If F is invariant for each set, simply F is invariant.
Do you know a method F that is invariant for each set?
Well all anomaly detection Methode I know rely on some kind of a threshold metric to separate between normal and abnormal observations. Usually this threshold is computed by comparing your objects inside your current set and recursive application of A would give you always a new Set of Anomalies but with smaller deviation to normal observations. One application i would suggest which is invariant to the remaining dataset are Cluster based techniques like DBSCAN which have the capability to assign abnormal data points to no Cluster. This would be your anomaly. And recursive application would not give you new anomalies.
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