A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> SUMMARY The asymptotic consistency of cross-validatory assessment and the asymptotic efficiency of cross-validatory choice is investigated both in some generality and also in the context of particular applications. <s> BIB001 </s> A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> This paper studies the potential of six artificial intelligence (AI)-based approaches for classification of non-averaged EEG data that is on important issue for the building of a brain-computer interface (BCI). The effectiveness of the methods in terms of classification accuracy, stability and speed is reported. <s> BIB002 </s> A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> We present preliminary classification results for a real time brain-computer interface. Our approach seeks to build individual brain interfaces rather than universal ones. This means that the interface should adapt to its owner; as it will incorporate a neural classifier that learns user-specific features. Three feature sets extracted with Fourier transform, autoregressive models and wavelets were evaluated with early stopping MLP committee. The goal was to classify EEG patterns related to imagined hand movements and relax. The best results were obtained with the autoregressive special features. The results so far are not satisfactory for their intended use as basis for robust EEG classification but they give us valuable basis for future work. <s> BIB003 </s> A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> Intention of movement of left or right index finger, or right foot is recognized in electroencephalograms (EEGs) from three subjects. The authors present a multichannel classification method that uses a "committee" of artificial neural networks to do this. The classification method automatically finds spatial regions on the skull relevant for the classification task. Depending on subject, correct recognition of intended movement was achieved in 75%-98% of trials not seen previously by the committee, on the basis of single EEGs of one-second duration. Frequency filtering did not improve recognition. Classification was optimal during the actual movement, but a first peak in the classification success rate was observed in all subjects already when they had been cued which movement later to perform. <s> BIB004 </s> A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> The information transfer rate, given in bits per trial, is used as an evaluation measurement in a brain-computer interface (BCI). Three subjects performed four motor-imagery (left hand, right hand, foot, and tongue) and one mental-calculation task. Classification of the EEG patterns is based on band power estimates and hidden Markov models. We propose a method that combines the EEG patterns based on separability into subsets of two, three, four, and five mental tasks. The information transfer rates of the BCI systems comprised of these subsets are reported. The achieved information transfer rates vary from 0.42 to 0.81 bits per trial and reveal that the upper limit of different mental tasks for a BCI system is three. In each subject, different combinations of three tasks resulted in the best performance. <s> BIB005 </s> A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> Parametric modelling strategies and spectral analysis are explored in conjunction with linear discriminant analysis to facilitate an EEG based direct-brain interface for use by disabled people. A self-paced typing exercise is analysed by employing for feature extraction, respectively, an autoregressive model, an autoregressive with exogenous input model, and a time-frequency decomposition of the data. Modelling both the signal and noise is found to be more, effective than modelling the noise alone with the former yielding an accuracy of 70.7% and the latter an accuracy of 57.4%. Experiments, using the raw samples of a short-time power spectral density estimate of each trial as features, yielded an accuracy of 62.5%. <s> BIB006 </s> A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> At the recent Second International Meeting on Brain-Computer Interfaces (BCIs) held in June 2002 in Rensselaerville, NY, a formal debate was held on the pros and cons of linear and nonlinear methods in BCI research. Specific examples applying EEG data sets to linear and nonlinear methods are given and an overview of the various pros and cons of each approach is summarized. Overall, it was agreed that simplicity is generally best and, therefore, the use of linear methods is recommended wherever possible. It was also agreed that nonlinear methods in some applications can provide better results, particularly with complex and/or other very large data sets. <s> BIB007 </s> A survey of signal processing algorithms in brain?computer interfaces based on electrical brain signals <s> Feature classification <s> Most EEG-based BCI systems make use of well-studied patterns of brain activity. However, those systems involve tasks that indirectly map to simple binary commands such as "yes" or "no" or require many weeks of biofeedback training. We hypothesized that signal processing and machine learning methods can be used to discriminate EEG in a direct "yes"/"no" BCI from a single session. Blind source separation (BSS) and spectral transformations of the EEG produced a 180-dimensional feature space. We used a modified genetic algorithm (GA) wrapped around a support vector machine (SVM) classifier to search the space of feature subsets. The GA-based search found feature subsets that outperform full feature sets and random feature subsets. Also, BSS transformations of the EEG outperformed the original time series, particularly in conjunction with a subset search of both spaces. The results suggest that BSS and feature selection can be used to improve the performance of even a "direct," single-session BCI. <s> BIB008
Linear classifiers are generally more robust than nonlinear ones. This is because linear classifiers have fewer free parameters to tune, and are thus less prone to over-fitting . In the presence of strong noise and outliers, even linear systems can fail. One way of overcoming this problem is to use regularization. Regularization helps limit (a) the influence of outliers and strong noise, (b) the complexity of the classifier and (c) the raggedness of the decision surface . It is always desirable to avoid reliance on nonlinear classification methods, if possible, because these methods often involve a number of parameters whose values must be chosen appropriately. However, when there are large amounts of data and limited knowledge of the data, nonlinear methods are better suited in finding the potentially more complex structure in the data. In particular, when the source of the data to be classified is not well understood, using methods that are good at finding nonlinear transformation of the data is suggested. In these cases, kernel-based and neural-networksbased methods can be used to determine the transformations. Kernel-based classifiers are classification methods that apply a linear classification in some appropriate (kernel) feature space. Thus, all the beneficial properties of linear classification are maintained, but at the same time, the overall classification is nonlinear. Examples of such kernel-based classification methods are support vector machines (SVMs) and kernel Fisher discriminant (KFD) . For a more detailed critical discussion regarding linear and nonlinear classifiers in brain-computer interfaces, refer to BIB007 . Some BCI designs have used classification algorithms such as FIR-MLP and TBNN that utilize temporal information of the input data (Haselsteiner and BIB002 . The motivation for using such classifiers is that the patterns to be recognized are not static data but time series. Thus, the temporal information of the input data can be used to improve the classification results (Haselsteiner and Pfurtscheller 2000) . Utilizing the temporal information of features is not necessarily performed directly in the classification stage, and can be done with a static classifier like MLP and a mapping of the temporal input data to static data. However, using classifiers such as FIR-MLP and TBNN that directly utilize temporal information may yield better performances as they are much better suited for exploiting temporal information contained in the time series to be classified. Regardless of the method that is used for exploiting temporal information, these approaches are preferred over static classification as they may increase the performance of BCI systems. Using a group (committee) of classifiers rather than using a single classifier might also yield to better performances of BCI systems. Only a few BCI designs have employed such an approach in classifying features and achieved performance improvements  BIB004 BIB003 . The classification accuracy of the committee depends on how much unique information each committee member contributes to classification. A committee of classifiers usually yields better classification accuracy than any individual classifier could provide, and can be used to combine information from several channels, i.e., from different spatial regions BIB004 . As the number of epochs available for evaluating a BCI system is small, using a technique that reduces the bias of the estimated performance on a specific dataset is highly recommended. This is especially important when different architectures of a certain design are being compared. K-fold cross-validation and statistical significance tests are especially useful for these cases (e.g. refer to Anderson et al (1998) , BIB006 , Lalor et al (2005) , BIB005 and BIB008 ). K-fold cross-validation can be used simply to estimate the generalization error of a given model, or it can be used for model selection by choosing one of several models that has the smallest estimated generalization error but it is not suitable for online evaluations. A value of 5 to 10 for K is recommended for estimating the generalization error. For an insightful discussion of the limitations of crossvalidatory choice among several evaluation methods, see BIB001 .