Tracking and visualization of changes in high-dimensional non-parametric distributions

Abstract

Most real-world systems exhibit a non-stationary behavior, e.g., slow drifts due to wear or fast changes due to external influences. Extracting and quantifying these phenomena is often difficult due to the lack of a precise mathematical model of the underlying system. We here propose to model such high-level changes of a dynamical system solely on the basis of the observed measurements rather than by modeling the underlying system itself. In particular, we present a method to track and visualize changes in general data distributions. We approach the problem of how to represent continuous changes in high-dimensional non-parametric distributions by identifying anchor distributions and we model the transitions between those anchor distributions by defining a suitable similarity measure. Applications to a high-dimensional chaotic system and to a sleep-onset detection task in EEG demonstrate the efficiency of this approach