Data Discovery and Anomaly Detection Using Atypicality: Signal Processing Methods

Abstract: The aim of atypicality is to extract small, rare, unusual and interesting pieces out of big data. This complements statistics about typical data to give insight into data. In order to find such "interesting" parts of data, universal approaches are required, since it is not known in advance what we are looking for. We therefore base the atypicality criterion on codelength. In a prior paper we developed the methodology for discrete-valued data, and the the current paper extends this to real-valued data. This is done by using minimum description length (MDL). We show that this shares a number of theoretical properties with the discrete-valued case. We develop the methodology for a number of "universal" signal processing models, and finally apply them to recorded hydrophone data.