Backward Degree a new index for online and offline change point detection based on complex network analysis

How to identify an upcoming transition in a time series continues to be an important open research issue. In various fields of physical sciences, engineering, finance and neuroscience abrupt changes can occur unexpectedly and are difficult to manage during the temporal evolution of the dynamic system. In this work, we developed a new unsupervised method called “Backward Degree” based on a new topological graph index that we introduce, which can be used to detect not only offline point of change, but also can effectively be used as an early warning system for online detection of upcoming abrupt changes. Specifically, based on the well-established algorithm “Visibility graph”, which was introduced by Lacasa et al. (2008) we convert a time series into a complex network and then we apply our proposed approach. The results, on a number of synthetic and financial datasets demonstrate that the proposed methodology correctly identifies change points during the evolution of time series validating the advantages of the proposed methodology for effective detection an upcoming abrupt transitions.