A Proposal for Formalization and Definition of Anomalies in Dynamical Systems

Although many scientists strongly focus on anomaly detection in different applications and domains, there currently exists no universally accepted definition of anomalies and outliers. Using an approach based on control theory and dynamical systems, as well as a definition for anomalies as described by philosophy of science, the authors propose a generalized framework viewing anomalies as key drivers of progress for a better understanding of the dynamical systems around us. By mathematically defining anomalies and delimiting deviations within expectations from completely unforeseen instances, this paper aims to be a contribution to set up a universally accepted definition of anomalies and outliers.