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Stationary Subspace Analysis

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Abstract: Multivariate non-stationary time series are encountered in many application domains, ranging from climate research to neuroscience. Often, the non-stationarity is a problem for classical data analysis methods. In machine learning, it might limit the generalization ability from training- to test set. So for accurate predictions, the goal is to control or eliminate the non-stationarity. On the other hand, temporal changes in the dynamics can be of high interest to understand the analyzed system. Often they allow to find change points (i.e. data points where the system switches between different states) that yield a temporal segmentation. Here, the stationary part of the data is uninformative and only makes the segmentation problem harder. To tackle these problems, we propose a novel technique, Stationary Subspace Analysis (SSA), that decomposes a multivariate timeseries into its stationary and non-stationary parts. The method is based on two assumptions: (a) the observed signals are linear superpositions of stationary—and non-stationary sources; and (b) the non-stationarity is measurable in the first two moments. We characterize the properties of the resulting algorithm and present results on simulated and real data.

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