Figure 2. Projection of CSP filters onto the (C21)-dimensional hypersphere. Distances between filters are defined by the angles between the projected filters. doi:10.1371/journal.pone.0002967.g002 generate the distances (m(wi, wj))i,j#n, which can then be used to find prototypical examples of CSP filters. Once a suitable distance function is established, it can be used to find regions in the data space consisting of CSP filters, which are more densely sampled than others (‘clusters’). In particular, by identifying points located in the middle of clusters, it is possible to select them as typical CSP filters. We apply a clustering concept which has been introduced by [21] and consider the average distance (according to metric m) of a filter to its k = 5 nearest neighbors. Let nn1(w),…,nnk(w) be the k nearest neighbors to point w according to metric m (Eq. (2)). Then the average distance of w to its neighbors is called the c-index of w, i.e. cðwÞ~ 1 Xk k i~1 mðw,nniðwÞÞ: The CSP filter with the lowest c-index can clearly be regarded as ‘‘inlier’’-point of a cluster. In order to find other regions of the filter space which are also densely populated, we applied a heuristic which is presented in the next section. B. Finding Cluster Prototypes. We first calculated the c- index of each filter to obtain a ranking according to the distance function explained above. The lowest c-index indicates that the corresponding filter is inside a region with many other filter examples and should therefore be chosen as cluster prototype. The same applies to the second-to-lowest c-index, but in this case it would not be recommendable to select this filter, since it is highly probable that the filter is from the same region as the first one. To ensure that we also sample prototypes from other clusters, an incremental procedure of choosing and re-weighting is applied to determine a predefined number of cluster prototype filters. The search starts with one prototype only, that is chosen as the filter with the minimal overall c-index. The chosen filter point is removed from the set of all filter points. Then the average distance of each remaining filter to its neighbors is re-weighted by the inverse of the distance to the removed point, as explained in [21]. Due to this re-weighting, all points in the vicinity of the chosen cluster prototype receive a larger c-index. The re-weighting is driven by the assumption that these neighboring points belong to the same cluster with high probability. Due to their increased c- index, they are less likely chosen as prototypes in the next iteration. Towards Zero Training The iterative procedure ends, when a predefined number of cluster prototypes has been determined. 4. Experimental Setup To demonstrate the feasibility of the Zero-Training approach, a BCI feedback study was designed to compare the proposed approach with the classical CSP approach in terms of feedback performance. The specific construction of the two classification setups is described in Section ‘‘Construction of Classifiers’’. The BCI experiments were performed with 6 healthy subjects, 5 male and one female, aged 26–41. These were all the subjects who previously had performed at least 5 BCI sessions with the Berlin Brain-Computer Interface (BBCI). They were members of the department and volunteered for the participation in this study. The availability of a large amount of experimental data is a prerequisite for the extraction of prototypical CSP filters as described in Section ‘‘Prototype Filters’’, since the cluster density in the CSP filter space can only be estimated reliably with a sufficient number of sample points. The visual feedback consisted of the presentation of a computer cursor which was controlled by the output of one of two different classifiers. The goal of each trial was to steer the computer cursor in eleven feedback runs that were grouped in five experimental blocks (see Figure 3). In block I, continuous visual feedback was given by a classifier that had been pre-computed with the Zero- Training method, see Section ‘‘Construction of Classifiers’’. Data collected in these initial three runs were used to determine spatial filters and a classifier using the ordinary CSP method (as described in Section ‘‘Construction of Classifiers’’) for use in the following blocks. Blocks II to V each contained one run with Zero-Training feedback and one run with CSP feedback. Within a block, the order of the two feedback methods was chosen randomly and remained unknown to the subject. The use of continuous visual feedback and no continuous visual feedback alternated regularly between blocks II to V, as indicated in Figure 3. During the experiment the subjects were sitting in a comfortable chair in front of a computer screen. EEG was recorded with 64 Ag/AgCl electrodes, acquired at a sampling rate of 1000 Hz, then downsampled to 100 Hz. The resulting data was bandpass-filtered at a subject-specific frequency band (see Table 1), and spatial filters, as described in Sections ‘‘Prototype Filters’’ and ‘‘Common Spatial Patterns Analysis’’, were applied. Finally, the logarithmic band power of the spatially and temporally filtered signals was estimated by calculating the logarithm of the squared sum of the filter outputs. These features were fed into a linear classifier. We used least squares regression (LSR), in order to force the classwise mean of the linear classifier output to be +1 and 21, respectively. At a rate of 25 Hz, graded classifier outputs were calculated for the last 1000 ms, and averaged over 8 samples. A scalar factor was multiplied to the result, and finally a real-valued bias term was added. Guided by our experience with non-stationary bias, a bias adaptation was performed at the beginning of every run. Therefore, the subject controlled the cursor for 20 trials (10 per class), and the bias was adapted at the end of this period. The procedure corresponds to the initial calibration of the bias as presented in [18]. In the following 100 trials (50 per class), the subject controlled the cursor in a feedback application. At the beginning of each trial, one of two boxes on either side of the screen was visually highlighted to indicate a new target. After being fixed in the middle of the screen for 750 ms, the cursor was released (see also the description in [2]). During these 3.5 seconds, the subjects were instructed to now imagine the associated motor movement (see PLoS ONE | www.plosone.org 4 August 2008 | Volume 3 | Issue 8 | e2967