Wasserstein Stationary Subspace Analysis

Stephan Kaltenstadler, Shinichi Nakajima, Klaus Robert Müller, Wojciech Samek

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Learning under nonstationarity can be achieved by decomposing the data into a subspace that is stationary and a nonstationary one [stationary subspace analysis (SSA)]. While SSA has been used in various applications, its robustness and computational efficiency have 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 1) higher numerical efficiency by defining analytical SSA variants and 2) 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 nonstationarity is used for spatial filter regularization and gives rise to higher decoding performance.

Original languageEnglish
Article number8481426
Pages (from-to)1213-1223
Number of pages11
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number6
Publication statusPublished - 2018 Dec

Bibliographical note

Funding Information:
Manuscript received April 15, 2018; revised August 9, 2018; accepted September 17, 2018. Date of publication October 4, 2018; date of current version December 17, 2018. This work was supported by the German Ministry for Education and Research as Berlin Big Data Center BBDC (funding mark 01IS14013A) and Berlin Center for Machine Learning BZML (funding mark 01IS18037I). The work of K.-R. Müller was supported by the Institute for Information and Communications Technology Promotion Grant funded by the Korea government (MSIT) (No. 2017-00451, No. 2017-0-01779). The guest editor coordinating the review of this paper and approving it for publication was Prof. Thierry Bouwmans. (Corresponding authors: Wojciech Samek and Klaus-Robert Müller.) S. Kaltenstadler and W. Samek are with Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany (e-mail:,stephan.kaltenstadler@hhi.fraunhofer.de; wojciech.samek@hhi.fraunhofer.de).

Publisher Copyright:
© 2018 IEEE.


  • Subspace learning
  • covariance metrics
  • divergence methods
  • optimal transport
  • stationary subspace analysis

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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