the i-th column of matrix W has a relative variance of di (i-th element of D) for trials of class 1 and relative variance 12di for trials of class 2. If di is near 1, the filter given by the i-th column of W (i.e., the ith spatial filter) maximizes the variance for class 1, and since 12di is near 0, it also minimizes the variance for class 2. Typically one would retain projections corresponding to two or three of the highest eigenvalues di, i.e., CSP filters for class 1, and projections corresponding to the two or three lowest eigenvalues, i.e., CSP filters for class 2. For a detailed review of the CSP technique with respect to the application in BCI see [10]. C. Features and Classification. He were describe generally, how spatial CSP filters are used to calculate features for classification, and how the ongoing EEG is translated into a control signal. This method applies to both classical CSP and the proposed method. The EEG signals of the calibration measurement are band-pass filtered (subject-specific frequency band, see Section ‘‘Experimen- tal Setup’’ and Table 1) and spatially filtered with the selected CSP filters. From these signals the log-variance is calculated in each trial of the calibration data (interval is selected subject-specifically, typically 750 to 3500 ms relative to the presentation of the visual cue). This procedure results in a feature vector with dimensionality equal to the number of selected CSP filters (which was in this study 4 for classical CSP and 12 for the proposed method, see Section ‘‘Construction of Classifiers’’). For classification least squares regression (LSR) was used. For online operation, features are calculated in the same way every 40 ms from the most recent segment of EEG (sliding windows of 1000 ms width). CSP filters calculated from the initial calibration measurement are not adapted during online operation. Nevertheless the system allows stable performance even for several hours [15,16]. But for optimal feedback the bias of the classifier might need to be adjusted for feedback. Since the mental state of the user is very much different during the feedback phase compared to the calibration phase, also the non task related brain activity differs. For a thorough investigation of this issue cf. [17,18,19]. With regard to this study, the issue is discussed in Section ‘‘Experimental Setup’’. D. Preliminary Study. In [5], we have analyzed data from the same subjects in repeated BCI sessions, that were recorded with the same motor imagery paradigms. We could show that the proposed distance (which will be introduced in detail in Section Table 1. Subject-specific parameters. Subject #channels #past sessions zq ay zp al aw zk 46 46 46 44 44 46 7 4 5 9 13 7 Towards Zero Training ‘‘Prototype Filters’’) clearly groups corresponding spatial filters into clusters, and the clusters themselves could be interpreted as physiologically relevant groups of filters. We used this concept to extract prototypical filters from previous sessions of a particular subject. In an offline analysis, it could be shown that the proposed method outperforms the usual CSP routine even if the number of training samples for CSP is increased up to 30 trials per class from the same session. The encouraging result was that high classification performance for longterm BCI users can be established with no or very few calibration trials from the current session. In the current work, we expand this finding to the online scenario. 2. Prototype Filters The CSP filters are not just randomly drawn points from RC , but instead represent subject-specific neurophysiological condi- tions, which suggests that, for a given subject, similar filters should be found across all sessions. We will first define a meaningful notion of similarity in this space and then use this relation to explore the space. We expect that the regions with a high density of CSP filters contain examples for filters which are particularly stable and informative across sessions. We will call these regions ‘‘clusters’’, and we will introduce a method how to sample prototypical filters from the clusters, using a notion of ‘‘inlier’’ points which have a low distance to their nearest neighbors [20,21]. A. Metric in the Space of CSP Filters and c-Index. CSP filters are obtained as solutions of a generalized eigenvalue problem. Since every multiple of an eigenvector is again a solution to the eigenvalue problem every point in the space of CSP filters (RC ) on the line through a CSP filter point and the origin form an equivalence class (except for the origin itself). More precisely, it is sufficient to consider only normalized CSP vectors on the (C21)- dimensional hypersphere (cf. figure 2). This suggests that the CSP space is inherently non-euclidean. As a more appropriate metric between two points w1 and w2 (column vectors of a CSP filter matrix W) in this space, we calculate the angle between the two lines corresponding to these points: mðw1,w2Þ~arccos w12 jw1j1jw2j : 2 ð Þ When applying this measure to a set of CSP filters (wi)i#n, one can #train trials 845 324 704 684 1075 240 Classes LR LR LR FR LF LR FQ band (CSP) [9 14] [8 22] [10 25] [11 25] [11 17] [8 31] (ZT) [9 25] [9 25] [9 25] [9 25] [10 25] [9 25] Interval (CSP) [810 4460] [710 2650] [2750 5000] [1600 4690] [1500 4500] [920 4390] (ZT) [500 3000] [500 3000] [500 3000] [500 3000] [500 3000] [500 3000] The first until third column report the number of sensors and sessions, as well as the number of trials per class which were available in total from these previous sessions. The fourth column indicates the two motor imagery classes that have been used (L: left hand, R: right hand; F: right foot). The frequency band (FQ band) for CSP analysis was chosen for each subject individually. For original CSP (column 5) it was chosen on data of the actual session. For Zero-Training (ZT) (column 6) it was chosen on data from previously available sessions. The same holds for the time window used for the training of the classifier, denoted in milliseconds after stimulus presentation: for CSP (column 7), the window was optimized on the training data, while for Zero-Training, a fixed window was used for all subjects. doi:10.1371/journal.pone.0002967.t001 PLoS ONE | www.plosone.org 3 August 2008 | Volume 3 | Issue 8 | e2967