Investigation of Non-stationarity in Brain Activity via Robust Principal Component Analysis
Berlin Institute of Technology, Machine Learning Laboratory, Germany
Fraunhofer FIRST, IDA, Germany
Investigating non-stationarities is an important topic and a difficult problem in neuroscience. In this paper we propose a method that allows, visualizing the spatial pattern of the most prominent variability in the neuroscientific data (EEG in this case). A key feature of this procedure is that allows the study of the relevant brain activity by attenuating the influence of outlying signals. In this case we apply the method in .brain-computer interface (BCI) data. BCIs are systems that translate the users intent, coded by a small set of mental tasks, into control actions such as computer applications or prostheses. Fluctuations in BCI data may be caused by change of task involvement, fatigue etc., or by artifacts such as swallowing, blinking or yawning. Recently, Krauledat  applied principal component analysis (PCA) to session-wise average covariance matrices and discussed session-to-session variability of BCI signals. Inspired by the previous work, we investigate non-stationarity between single-trial covariance matrices by a novel robust PCA proposed in this research.Technically, our robust PCA is developed upon the theory of robust statistics. As in our previous work on the robust CSP , we replace the Euclidean error measure with an “outlier-insensitive” one for defining the desired low-dimensional approximations of observed data. From this robust objective function, we derive an iterative algorithm which can detect outlying trials automatically and which makes the PCA calculation robust by reducing their weights. The outputs of our procedure are eigen matrices, which indicate prominent changes in covariance matrices across trials. We can usually get further insight by showing the first eigen vectors of the eigen matrices as scalp maps (see Fig. 1).The data of the analysis were recorded in a one-day session from 1 healthy BCI-novice user. The subject was sitting in a comfortable chair with arms lying relaxed on armrests. Brain activity was recorded from the scalp with multi-channel EEG amplifiers using 119 Ag/AgCl electrodes in an extended 10-20 system sampled at 1000 Hz with a band-pass from 0.05 to 200 Hz. The subject performed a ‘calibration measurement’ in which every 8s one of three different visual cues (arrows pointing left, right, down) indicating which motor imagery to perform: left/right hand or foot. Three runs with 25 trials of each motor condition were recorded. Here we analyzed the data of two classes.
Figure 1. Comparison of robust PCA and PCA to analyze the spatial patterns of variability in brain activity in BCI.
The figure illustrates the first principal component of the direction of main variation for each class. This component is wrongly estimated using conventional PCA. We can see a strong influence of lateral electrodes in the motor area. However, robust PCA reveals that this direction is mainly caused by outlying trials. Our robust method is a powerful tool to study variations in brain activity and can be applied not only to data where difference in rhythmical power is to be expected but also to other activity such as evoked potentials.
1. M. Krauledat.Analysis of Nonstationarities in EEG signals for improving Brain-Computer Interface performance. PhD thesis, Technische Universität Berlin, Fakultät IV -- Elektrotechnik und Informatik, 2008.
2. M. Kawanabe and C. Vidaurre. Improving BCI performance by modified common spatial patterns with robustly averaged covariance matrices. InWC2009, pages 279-282, 2009
Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010.
Bernstein Conference on Computational Neuroscience
(2010). Investigation of Non-stationarity in Brain Activity via Robust Principal Component Analysis.
Front. Comput. Neurosci.
Bernstein Conference on Computational Neuroscience.
17 Sep 2010;
23 Sep 2010.
Dr. Carmen Vidaurre, Berlin Institute of Technology, Machine Learning Laboratory, Berlin, Germany, email@example.com