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Stationary Common Spatial Patterns for non-stationary EEG data

^{
1}
Technical University of Berlin, Machine Learning Group, Germany
^{
2}
Fraunhofer Institute FIRST, Computer Architecture and Software Technology, Germany

**Introduction**

Projecting EEG data using Common Spatial Patterns (CSP) [1, 2] is a standard step in brain-computer interfacing (BCI). However, non-stationaries in the data i.e. variation of the signal properties within and across experimental sessions coming from electrode artefacts, alpha activity or fatigue, can negatively affect the performance of CSP. We alleviate this problem by regularizing CSP towards stationary subspaces, calling this method *stationary CSP or sCSP*.

**Method**

Let Σ+ and Σ- be the average covariance matrices from the entire data, while Σ+(k) and Σ-(k) denote the covariance matrices in the k-th chunk. In order to evaluate non-stationarity, let us consider the difference matrices Δ+(k) = | Σ+(k) - Σ+ | and Δ-(k) = | Σ-(k) - Σ- | where |M| denotes the matrix with the negative eigenvalues flipped, i.e. |M| = R diag(|di|) RT. We propose to use their averages (see figure 1,2).

For regularizing CSP towards stationary subspaces, i.e. we project data in directions w computed as (see figure 3,4).

**Results**

We compare CSP and sCSP on a data set containing 36 subjects performing motion imagery tasks. We use log-variance features, a LDA classifier and error rate to measure performance. λ is set using 5-fold cross-validation.

In our experiments 14 subjects had the same error rate, 16 subjects performed better and 6 did a bit worse than the CSP baseline. The average gain in error rate was 4.25 (or 17.3 \%), the average loss was -1.1 (or 8 \%). Subjects which perform badly (~ 30 \%) using CSP had the larger gain than subjects which did very good (~ 4 \%). We conjecture that this is because subjects which do very good have much less non-stationarities in the signal.

In Figure 1 we see the CSP and sCSP pattern of a subject which had the largest performance gain, an error rate eR of 27 when using CSP, but eR = 15 when applying sCSP. As can be seen this is due to non-stationarities (probably visual or electrode artefacts) appearing in the training data which are suppressed by sCSP.

Figure 5: CSP pattern (left) contains artefacts in the F6 and F8 electrodes which are removed by sCSP (right).

##
References

[1] B. Blankertz, M. K. R. Tomioka, F. U. Hohlefeld, V. Nikulin and K.-R. Müller. Invariant common spatial patterns: Alleviating nonstationarities in brain-computer interfacing. *In Ad. in NIPS 20*, page 2008, MIT Press, 2008.

[2] B. Blankertz, R. Tomioka, S. Lemm, M. Kawanabe and K.-R. Müller. Optimizing spatial filters for robust EEG single-trial analysis. *In IEEE Signal Proc. Magazine*, pages 581–607, 2008.

Keywords:
computational neuroscience

Conference:
Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010.

Presentation Type:
Presentation

Topic:
Bernstein Conference on Computational Neuroscience

Citation:
Wojcikiewicz
W,
Vidaurre
C and
Kawanabe
M
(2010). Stationary Common Spatial Patterns for non-stationary EEG data.
Front. Comput. Neurosci.
Conference Abstract:
Bernstein Conference on Computational Neuroscience.
doi: 10.3389/conf.fncom.2010.51.00051

Received:
17 Sep 2010;
Published Online:
23 Sep 2010.

*
Correspondence:
Dr. Wojciech Wojcikiewicz, Technical University of Berlin, Machine Learning Group, Berlin, Germany, wojwoj@mail.tu-berlin.de