Stationary Subspace Analysis

Abstract

Non-stationarities are an ubiquitous phenomenon in time-series data, yet they pose a challenge to standard methodology: classification models and ICA components, for example, cannot be estimated reliably under distribution changes because the classic assumption of a stationary data generating process is violated. Conversely, understanding the nature of observed non-stationary behaviour often lies at the heart of a scientific question. To this end, we propose a novel unsupervised technique: Stationary Subspace Analysis (SSA). SSA decomposes a multi-variate time-series into a stationary and a non-stationary subspace. This factorization is a universal tool for furthering the understanding of non-stationary data. Moreover, we can robustify other methods by restricting them to the stationary subspace. We demonstrate the performance of our novel concept in simulations and present a real world application from Brain Computer Interfacing.