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Wasserstein stationary subspace analysis

: Kaltenstadler, S.; Nakajima, S.; Müller, K.-R.; Samek, W.


IEEE journal of selected topics in signal processing 12 (2018), Nr.6, S.1213-1223
ISSN: 1932-4553
ISSN: 1941-0484
Fraunhofer HHI ()

Learning under non-stationarity can be achieved by decomposing the data into a subspace that is stationary and a non-stationary one (stationary subspace analysis (SSA)). While SSA has been used in various applications, its robustness and computational efficiency has limits due to the difficulty in optimizing the Kullback-Leibler divergence based objective. In this paper we contribute by extending SSA twofold: we propose SSA with (a) higher numerical efficiency by defining analytical SSA variants and (b) higher robustness by utilizing the Wasserstein-2 distance (Wasserstein SSA). We show the usefulness of our novel algorithms for toy data demonstrating their mathematical properties and for real-world data (1) allowing better segmentation of time series and (2) brain-computer interfacing, where the Wasserstein-based measure of non-stationarity is used for spatial filter regularization and gives rise to higher decoding performance.