FuRIA: a new feature extraction algorithm for brain-computer interfaces using fuzzy and inverse models
When using Brain-Computer Interfaces (BCI) based on ElectroEncephaloGraphy (EEG), the identification of mental tasks relies on two main points: feature extraction and classification [MAM(+)06, BFWB07, LCL(+)07]. Feature extraction aims at describing EEG signals by a few relevant values called "features", whereas classification aims at automatically assigning a class to these features. In this paper we focus on feature extraction, as the BCI community has stressed the need to explore new feature extraction algorithms [MAM+06]. Recently, inverse models have been revealed as promising feature extraction algorithms for BCI [QDHO4, GGP(+)05, WGWB05, CLL06]. Such models aims at computing the activity in the whole brain volume, by using only scalp EEG signals and a head model representing the brain as a set of voxels (volume elements). The activity computed in a few brain regions has been used as features for BCI systems. Despite good results, some limitations remain. Indeed, it seems that current methods cannot conciliate genericity, i.e., the capability to deal with any kind of mental task, and the fact of generating few features. On one hand, methods that are generic and automatic tend to generate a large number of features, as they extract several features for each voxel [GGP(+)05], The activity in neighboring voxels can be correlated and, as such, it would be more appropriate to gather these voxels in brain regions. On the other hand, methods that generate few features have been proposed, but they are not generic anymore as they need a priori knowledge on the mental tasks used, and are currently limited to motor imagery-based BCI [QDH04, WGWB05]. Recently, we have proposed a method which is generic and which generates few features, as voxels whose activity is correlated are gathered into Regions Of Interest (ROI) [CLL06]. However, this method is not completely automatic and is limited to the use of two ROI whose spatial extension is hard to define [CLL06]. In this paper, we propose a generic feature extraction algorithm which can automatically identify any number of relevant ROI and can properly define their spatial extension thanks to the new concept of fuzzy ROI. This algorithm is known as FuRIA, which stands for "Fuzzy Region of Interest Activity". The FuRIA algorithm FuRIA is a trainable feature extraction algorithm. Indeed, it can automatically identify what are the relevant ROI to discriminate mental tasks, and what are the frequency bands in which these ROI react. The FuRIA training is performed in 5 steps: Statistical analysis: This step consists in comparing, using a statistical test, the activity in each voxel, possibly averaged over a given time window, between the different classes. This analysis is performed for each of the N(f) frequencies considered, Once the analysis is achieved, we obtain N(f) statistical maps, each one revealing which voxels are significant for discrimination. Clustering: For each statistical map computed at the previous step, a clustering algorithm is used in order to gather significant voxels into ROI. To perform this clustering, a 4-dimensional vector [x, y, z, s] is associated to each significant voxel. The x, y, z coordinates are the 3D coordinates of the voxel in the head model used and s is the voxel statistic obtained at the previous step. Once the clustering is achieved, all voxels whose associated vector belongs to the same cluster are gathered into the same ROI. Fusion: Once the relevant ROI are identified for each frequency, we have to identify which ROI are relevant in which frequency band. To do so, ROI obtained at similar positions (i.e., with an overlap of more than 50%), for consecutive frequencies, are merged, simply using the union set operator, and identified as reactive in the frequency band resulting from the concatenation of these frequencies. Adaptation: Because of the use of the union as the fusion operator, a ROI Q identified as reactive in the frequency band [f(a); f(b)] can contain voxels which were significant for a single frequency belonging to [f(a); f(b)] but which are not significant anymore for the whole [f(a); f(b)] frequency band. Consequently, we perform another statistical analysis for each ROI, in order to remove voxels that are not significant anymore. Fuzzification: In the ROI defined so far, it can be noticed that all voxels do not have, statistically, the same discriminative power. However, all these voxels contain a given amount of information. Moreover, the brain regions of a given subject are not well defined but are rather naturally fuzzy. Hence, identifying which voxels should be kept in a ROI, and which ones should be removed is a difficult problem. We believe that all voxels that contain information should be in the ROI, but that those which contain less information should be less in the ROI. Thus, we propose the concept of fuzzy ROI, which relies on the fuzzy set theory of Zadeh [Zad96]. A standard (crisp) ROI Omega(c) is defined by the set of voxels it contains. The activity gamma(Omega c) in this ROI Omega(c) is classically computed from the activity gamma(v) of the voxels v of this ROI (see Equation 1). A fuzzy ROI Omega(f) is not defined by a set of voxels anymore, but by a fuzzy membership function mu(Omega f). This function provides the membership degree (in [0; 1]) of any voxel into the ROI Omega(f). The activity in a fuzzy ROI is computed as described in Equation 2, where N(v) is the number of voxels in the head model used. This formalism enables use to weigh each voxel according to the importance of its contribution within the ROI, and, as such, to use efficiently the available information. To complete the training of FuRIA, all ROI Omega are turned into fuzzy ROI by associating to each of them a fuzzy membership function mu(Omega) which uses the statistics obtained at the previous step. Once the training of FuRIA is completed, a set of discriminant fuzzy ROI should have been identified together with the corresponding reactive frequency bands. The activity in these ROI and in these frequency bands, possibly averaged over time, can be used as features for any classifier. Evaluation In order to evaluate FuRIA, we used sLORETA (standardized low resolution electromagnetic tomography) as the inverse model [PM02], a multiple comparison randomization t-test as the statistical analysis [HBWF96] and the "Mean Shift" algorithm as the clustering algorithm [CM02]. Concerning the fuzzy membership functions, it appears that, due to the low resolution of sLORETA, significant voxels with a relatively high probability of type I error are much more numerous that significant voxels with a relatively low probability of type I error. Consequently, for each ROI Omega, we used a membership function mu(Omega) which assigns a membership degree which decreases exponentially with the voxel statistics, as described in Equation 10. In this equation, N(Omega s) is the number of voxels in the ROI Omega; p(min) and p(max) are respectively the minimum and maximum probability, among the ROI voxels, of correctly rejecting the null hypothesis H(0); and p(v) is the probability of correctly rejecting H(0) for voxel v. In order to evaluate FuRIA, we have used the data set IV of the "BCI competition 2003" [WZL(+)04]. These data contain EEG signals recorded 500 ms before a subject hits a keyboard key with a finger from his left or right hand, The goal of the competition participants was to identify, for each trial, the hand that was used. We trained the FuRIA algorithm on the training set provided, by considering the frequencies between 3 Hz and 45 Hz, with a step of 1 Hz, and by considering the time window comprising the last 250 ms of each trial. FuRIA has found 5 discriminant fuzzy ROI (see Figure 1), hence generating 5-dimensional feature vectors. These features has been classified using a linear support vector machine. The recognition rates obtained after 100 training/testing repetitions are displayed in Table 2 and compared with two other methods: the method of the competition winner [WZL+04] and a method using inverse models that we proposed previously [CLL06]. The results obtained withouth the fuzzification step (step 5 of the training, see previous section) are also displayed as a comparison. We can noticed that the method that use FuRIA with fuzzification reached the best results with a recognition score ranging from 85% to 86%, These results suggest that the features extracted with FuRIA are very discriminant, as they are not numerous (there are only 5 features) and still enable us to reach good classification results. It is also interesting to notice that when using FuRIA without fuzzification, the results are significantly lower. This stress the advantage of using efficiently the information contained in any significant voxel, thanks to the concept of fuzzy ROI. In addition to this evaluation, we also proposed a first step towards the design of an interpretable BCI system. To this end, we proposed to classify FuRIA features, which are interpretable features, with a Fuzzy Inference System (FIS), which is an interpretable classifier. Indeed, FIS are a set of fuzzy "if-then" rules that can be learnt from data. By combining FuRIA features with FIS, we can obtain a set of rules describing which activity in which brain regions and frequency bands is related to which mental task. An evaluation of this method on the EEG data mentioned above suggested that the obtained rules were consistent with the literature (see Figure 3).
feature extraction inverse model brain-computer interface (bci) electroencephalography (eeg) classification fuzzy set interpretability source localization