  In many real-world applications data exhibits non-stationarity, i.e., its
distribution changes over time. One approach to handling non-stationarity is to
remove or minimize it before attempting to analyze the data. In the context of
brain computer interface (BCI) data analysis this may be done by means of
stationary subspace analysis (SSA). The classic SSA method finds a matrix that
projects the data onto a stationary subspace by optimizing a cost function
based on a matrix divergence. In this work we present an alternative method for
SSA based on a symmetrized version of this matrix divergence. We show that this
frames the problem in terms of distances between symmetric positive definite
(SPD) matrices, suggesting a geometric interpretation of the problem. Stemming
from this geometric viewpoint, we introduce and analyze a method which utilizes
the geometry of the SPD matrix manifold and the invariance properties of its
metrics. Most notably we show that these invariances alleviate the need to
whiten the input matrices, a common step in many SSA methods which often
introduces errors. We demonstrate the usefulness of our technique in
experiments on both synthesized and real-world data.
