TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Linear Discriminant Analysis <s> Driven by the progress in the field of single-trial analysis of EEG, there is a growing interest in brain computer interfaces (BCIs), i.e., systems that enable human subjects to control a computer only by means of their brain signals. In a pseudo-online simulation our BCI detects upcoming finger movements in a natural keyboard typing condition and predicts their laterality. This can be done on average 100-230ms before the respective key is actually pressed, i.e., long before the onset of EMG. Our approach is appealing for its short response time and high classification accuracy (>96%) in a binary decision where no human training is involved. We compare discriminative classifiers like Support Vector Machines (SVMs) and different variants of Fisher Discriminant that possess favorable regularization properties for dealing with high noise cases (inter-trial variablity). <s> BIB001 </s> TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Linear Discriminant Analysis <s> The reliable operation of brain-computer interfaces (BCIs) based on spontaneous electroencephalogram (EEG) signals requires accurate classification of multichannel EEG. The design of EEG representations and classifiers for BCI are open research questions whose difficulty stems from the need to extract complex spatial and temporal patterns from noisy multidimensional time series obtained from EEG measurements. The high-dimensional and noisy nature of EEG may limit the advantage of nonlinear classification methods over linear ones. This paper reports the results of a linear (linear discriminant analysis) and two nonlinear classifiers (neural networks and support vector machines) applied to the classification of spontaneous EEG during five mental tasks, showing that nonlinear classifiers produce only slightly better classification results. An approach to feature selection based on genetic algorithms is also presented with preliminary results of application to EEG during finger movement. <s> BIB002 </s> TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Linear Discriminant Analysis <s> We use support vector machines (SVM) for classifying EEG signals corresponding to imagined motor movements. The parameters of an SVM Kernel are optimized for minimizing a theoretical error bound. Fourier features and correlative time-frequency based features are extracted from EEG signals and compared with respect to their discriminatory power. <s> BIB003 </s> TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Linear Discriminant Analysis <s> The t-CWT, a novel method for feature extraction from biological signals, is introduced. It is based on the continuous wavelet transform (CWT) and Student's t-statistic. Applied to event-related brain potential (ERP) data in brain- computer interface (BCI) paradigms, the method provides fully automated detection and quantification of the ERP components that best discriminate between two samples of EEG signals and are, therefore, particularly suitable for classification of single-trial ERPs. A simple and fast CWT computation algorithm is proposed for the transformation of large data sets and single trials. The method was validated in the BCI Competition 2003 , where it was a winner (provided best classification) on two data sets acquired in two different BCI paradigms, P300 speller and slow cortical potential (SCP) self-regulation. These results are presented here. <s> BIB004 </s> TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Linear Discriminant Analysis <s> An improvement of the information transfer rate of brain-computer communication is necessary for the creation of more powerful and convenient applications. This paper presents an asynchronously controlled three-class brain-computer interface-based spelling device [virtual keyboard (VK)], operated by spontaneous electroencephalogram and modulated by motor imagery. Of the first results of three able-bodied subjects operating the VK, two were successful, showing an improvement of the spelling rate /spl sigma/, the number of correctly spelled letters/min, up to /spl sigma/=3.38 (average /spl sigma/=1.99). <s> BIB005
The aim of LDA (also known as Fisher's LDA) is to use hyperplanes to separate the data representing the different classes   . For a two-class problem, the class of a feature vector depends on which side of the hyperplane the vector is (see Figure 1) . LDA assumes normal distribution of the data, with equal covariance matrix for both classes. The separating hyperplane is obtained by seeking the projection that maximize the distance between the two classes means and minimize the interclasse variance  . To solve an N-class problem (N > 2) several hyperplanes are used. The strategy generally used for multiclass BCI is the "One Versus the Rest" (OVR) strategy which consists in separating each class from all the others. This technique has a very low computational requirement which makes it suitable for online BCI system. Moreover this classifier is simple to use and generally provides good results. Consequently, LDA has been used with success in a great number of BCI systems such as motor imagery based BCI  , P300 speller BIB004 , multiclass BIB002 or asynchronous BIB005 BCI. The main drawback of LDA is its linearity that can provide poor results on complex nonlinear EEG data BIB003 . A Regularized Fisher's LDA (RFLDA) has also been used in the field of BCI [38]  . This classifier introduces a regularization parameter C that can allow or penalize classification errors on the training set. The resulting classifier can accomodate outliers and obtain better generalization capabilities. As outliers are common in EEG data, this regularized version of LDA may give better results for BCI than the non-regularized version  BIB001 . Surprisingly, RFLDA is much less used than LDA for BCI applications.