Multiclass EEG motor-imagery classification with sub-band common spatial patterns

Recently, various machine learning (ML) approaches for BCI have been developed to circumvent the complexity of brain signals. These different methods have shown remarkable results for binary class EEG classification [10‐14] while for better and more control commands of real-time applications such as BCI controlled wheelchair, neuro-gaming, and prosthetics, binary class is not sufficient; therefore, a requirement for multiclass classification arises. Nicolas et al. implemented adaptive generalization method for classification of multiclass motor imagery (MI)-based EEG signals, by the selection of optimal extracted subband CSP features using mutual-information best individual features (MIBIF) [15]. Classification is done by using stacked regularized linear discriminant analysis (SRLDA) [16]. The resulted accuracy has shown better results for binary class rather than for multiclass, i.e., 85% and 74% respectively. Shiratori et al. [17] included “rest state” as a third class along with other two classes for MI movement of the left and right hand. They extracted CSP features from the EEG signal is divided into subbands. Support vector machine (SVM) [18] was used as a classifier to train the system on selected features based on mutual information. Although the implemented methodology has shown 88.7% results for classification of EEG signals produced as a result of finger tapping, it did not show good results for multiclass MI data, i.e., 56.7%.

A lot of research has been conducted for the classification of multiclass EEG signals of same limb movements. Yong and Menon [19] applied a bandpass filter to preprocess raw data while both CSP and Filter bank common spatial pattern (FBCSP) [11] were used to extract features from multiclass EEG signal acquired from the same limb. This approach showed better results for data acquired from the same limb than data from different limbs but the overall accuracy of the system was reported 60.7%. Shiman et al. [20] investigated that MI-based brain signals produced as a result of the imagination of movement from the same limb produce more results than the signals acquired from different limbs. They applied FBCSP having unique frequency cutoffs, i.e., (7 to 15 Hz, 15 to 25 Hz, 25 to 30 Hz) on the acquired same limb EEG data for feature extraction. Then, linear discriminant analysis (LDA) [21] is trained for classification on the basis of extracted features. The results show an accuracy of 69.1% and 62.75% for 3 and 4 class MI-based brain signal respectively.

Apart from feature extraction, classifier improvements have also been implemented to enhance the overall accuracy of the system. She et al. [22] implemented a multiclass posterior probability classification technique for twin SVM through ranking continuous output and pairwise coupling. Platt’s estimating technique and the ranking continuous output techniques were used for two class posterior probability approximation. Then, each pair of class probabilities were combined by using pairwise coupling for multiclass probabilistic outputs. This technique has not proven efficient for classification of multiclass MI-based EEG signal. Further, Gao et al. [23] tested the effectiveness of Adaboost extreme learning machine (AdaboostELM) for classification of features extracted by using Kolmogorov complexity (K_c). They followed the approach of Adaboost model, which states that by calling a base lerning algorithm rapidly, the performance of that algorithm can be enhanced. So, the features were extracted from muthe lticlass MI-based brain signal by using K_c after removing EOG artifacts from the signal using a single wide band filter, then classified by using AdaboostELM. Although, the results showed improved results for adboost approach on the classification accuracy, but these results were calculated by using one versus rest approach which is considered as a binary class classification technique [24]. Meisheri et al. [25] produced better CSP features after identification and removal of artifacts using joint approximate diagonalization (JAD) [26] in preprocessing of the MI-based EEG data. Fast Frobenius Diagonalization (FFDIAG) [27] was applied on the EEG signal for obtaining spatial filters by JAD then CSP is applied on the resulted signal for feature extraction. Self-regulated interval type 2 neuro fuzzy inference system (SRIT2NFIS) is used for classification of these extrated features. The implemented technique have shown good results on the produced algorithm, i.e., maximum of 74.65% accuracy for a single subject. Table 1 shows a brief comparison of previous researches for classification of multiclass MI based brain signals.

The related work for multiclass EEG classification shows that most of the results were evaluated by using one versus rest approach which is considered as a binary class classification. Therefore, for run-time control of BCI-controlled devices, multiclass classification is required [24]. This paper aims to implement multiclass classification to improve the results of motor imagery brain signals by using sub-band common spatial patterns with sequential backward floating selection (SBCSP-SBFS). Feature extraction and then selection of optimal features on the basis of the final performance of the classifier is the principle of this approach. The motor imagery-based EEG signal is decomposed into different subbands using a filter bank which contains filters of different frequency cutoffs. Once the signal is decomposed, then CSP is applied on it to extract sub-band CSP features, these features are fed into LDA for eigenvector computation. All of the features are not optimal for getting better accuracy from classifier; therefore, sequential backward floating selection (SBFS) technique is used to select ‘k’ optimal features from ‘n’ extracted features. Different classifiers SVM, k-nearest neighbor (KNN) [29] and naïve Bayesian Parzen window (NBPW), are trained and tested on these ‘k’ optimal features for evaluation of the proposed model.

For preprocessing, filter bank having each bandpass filter is implemented instead of applying one wide bandpass filter of 8–30 Hz on raw EEG signal. The proposed filter bank includes 12 filters of two distinct categories having unique frequency edges between 6 and 32 Hz. Every category in filter bank has 6 filters, and cutoffs of the filters in every category are different in a manner that there is an overlapping of 2 Hz between frequencies of both categories. One filter bank category has a gap of 4 Hz in a range of 8 to 32 Hz, at the same time another category has also a gap of 4 Hz ranging from 6 to 30 Hz. The overlapping of 2 Hz helps to avoid the possible information loss between two consecutive bands.

Common spatial pattern (CSP) is applied after filter bank in order to extract the features which are utilized for classification of multiclass data. It yields excellent outcomes by means of extracting considerable EEG features for MI-based signal. The goal of CSP is to grasp the spatial filters for maximizing the converted data variance ration among distinctive classes in EEG data. Basically, CSP is used for a binary class problem, but in the proposed approach, it is used for the multiclass problem by using one-vs-rest (OVR) algorithm.

Multiclass EEG data is generally assumed to be centered without generality loss, i.e., E_{j, 1}, E_{j, 2}, and E_{j, n}. Shape of the acquired data matrix represents “channels by number of samples,” where j = unique trail in data. For ‘n’ classes, Eq. (1) can be used to compute the composite spatial covariance matrix E.

Where, M_n = All trials in ‘n’ classes

Here, the classification of three classes is done; therefore, n = 3 results three covariance matrices, i.e., E₁, E₂ and E₃ which results in the composite covariance matrix, i.e., E = E₁, E₂ and E₃. This matrix is further factored by using (2).

Where, P₀ = L × L unitary matrix of principal components

∂ = L × L diagonal matrix of eigenvalues

The major goal of CSP is to find transformed data variance between distinct multiclass data which is computed by using (3)

Where, W(s) = Rayleigh quotient maximization

‖s‖₂ = the n₂ normal

E_c1 = Covariance matrix of class 1

E_c2 = Covariance matrix of class 2

The solution of the generalized eigenvalue Eq. (4) results in W(s).

Finally, from the learned spatial filter matrix ‘S’, the eigenvectors are calculated to compute the projection of an EEG signal using Eq. (5).

Where

G = EEG signal

After CSD, sub-band scores are generated by applying LDA which are then used as features. These features are computed by using the projection matrix that guarantees maximum separability by maximizing the ratio of the variance between and within different classes [21]. The cost function for the projection matrix is generated by LDA using Eq. (6).

S_lda = Projection matrix generated by LDA

V_B = Variance among MI-based right and left hand classes

V_W = Variance within MI-based right or left hand classes

V_B and V_W are calculated by (7) and (8) respectively.

Where f₁ and f₂ represent means of CSP computed features for empirical classes. Finally, the one-dimensional score by LDA can be calculated by (9). These scores are then sent to the feature selector.

Optimal features are selected using selection using sequential backward floating selection (SBFS). It is a feature selection technique which selects among all the provided features in such a way that the overall performance of the system could be improved. For example, ‘k’ optimal features are selected from ‘n’ total features in a way that the performance of the classifier should be maximized due to selected features. Let us assume F is a set of all features,

If ‘F’ set is given to the SBFS technique as input then the selection of set ‘P’ (set of output features) is done in such a way that, first of all, the classifier will be trained on all of the provided features, i.e., set ‘F.’ In the next iterations, those features are removed from the input set which causes the low average accuracy of the system. These iterations for feature elimination are carried out until the ‘k’ number of features is not obtained. Once the iterations are finished, then the set ‘P’ (a subset of ‘F’) containing ‘k’ selected features is returned.

After feature selection, the classifier is trained which estimates the accuracy of the system by predicting each class label from the testing model. The classifiers used in the proposed methodology are explained in this section.

Support vector machine (SVM) is called the supervised technique of machine learning because it requires labeled training dataset. It acts as a linear classifier because it draws a separating line known as hyperplane between data samples of different classes in a dataset. For margin maximization of training data, measurement of an optimal hyperplane is the goal of SVM. Hyperplane can be calculated by equation (10),

Where v and y = vectors containing EEG samples

As the hyperplane is a line which separates different classes in data, the equation for hyperplane is the same as the equation of a line which can be calculated by the dot product of v and y where

Once the hyperplane is computed then the distance among hyperplane and the closest data sample is calculated, which is known as margin value. Double of the calculated margin value is known as margin, no data sample occurs in this region. After hyperplane calculation, the classifier is considered ready for classification purpose. Now, when a test data is passed through the trained classifier it calculates the distance of the data sample from the margin. Then that class label is assigned to the data from which the computed distance is nearest.

The k-nearest neighbor (KNN) algorithm works on the principle of forming a majority vote between the ‘k’ most similar instances and a given test data sample (an unseen data). While ‘k’ represents a positive integer, which should be small. The performance of this algorithm depends on two factors, i.e., a suitable similarity function and an appropriate value for k. This similarity is found according to a distance matrix between two data samples. Euclidean distance is used as the most popular way to find the distance between the data samples. The equation for this method is

The algorithm is also known as lazy learning algorithm because it refers to the decision to generalize the training data samples until a new query is faced. The major assumption of this algorithm is that the class probabilities are locally constant approximately, so it is one of the simplest machine learning algorithms.

Naïve Bayesian Parzen window (NBPW) is a fast classification algorithm as compared to other classification algorithms which follow the principle of Bayes theorem of probability. A major assumption in this algorithm is that one feature in the data does not relate to any other feature. As NBPW is based on Bayes theorem which provides the methodology to calculate posterior probability P (a | y) from P (a), P (y) and P (y | a) using Naive Bayesian equation

Where

P(a | y) = posterior probability

P(a) = prior probability of class

P(y) = prior probability of predictor

P(y | a) = probability of predictor given class

The working principle of NBPW is that, firstly the dataset is converted into a frequency table then probabilities are computed to create a likelihood table. In the end, the posterior probability is computed by using the naïve Bayesian equation.