Network representations of attractors for change point detection

Abstract

A common approach of monitoring the status of physical and biological systems is through the regular measurement of various system parameters. Changes in a system's underlying dynamics manifest as changes in the behaviour of the observed time series. For example, the transition from healthy cardiac activity to ventricular fibrillation results in erratic dynamics in measured electrocardiogram (ECG) signals. Identifying these transitions -- change point detection -- can be valuable in preparing responses to mitigate the effects of undesirable system changes. Here, we present a data-driven method of detecting change points using a phase space approach. Delay embedded trajectories are used to construct an `attractor network', a discrete Markov-chain representation of the system's attractor. Once constructed, the attractor network is used to assess the level of surprise of future observations where unusual movements in phase space are assigned high surprise scores. Persistent high surprise scores indicate deviations from the attractor and are used to infer change points. Using our approach, we find that the attractor network is effective in automatically detecting the onset of ventricular fibrillation (VF) from observed ECG data. We also test the flexibility of our method on artificial data sets and demonstrate its ability to distinguish between normal and surrogate time series.