Wasserstein Stationary Subspace Analysis

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

doi:10.1109/JSTSP.2018.2873987

Wasserstein Stationary Subspace Analysis

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

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

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 language	English
Article number	8481426
Pages (from-to)	1213-1223
Number of pages	11
Journal	IEEE Journal on Selected Topics in Signal Processing
Volume	12
Issue number	6
DOIs	https://doi.org/10.1109/JSTSP.2018.2873987
Publication status	Published - 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:,[email protected]; [email protected]).

Publisher Copyright:
© 2018 IEEE.

Keywords

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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10.1109/JSTSP.2018.2873987

Cite this

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abstract = "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.",

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author = "Stephan Kaltenstadler and Shinichi Nakajima and M{\"u}ller, {Klaus Robert} and Wojciech Samek",

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Wasserstein Stationary Subspace Analysis

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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