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This paper presents a new approach called clustering technique-based least square support vector machine (CT-LS-SVM) for the classification of EEG signals. Decision making is performed in two stages. In the first stage, clustering technique (CT) has been used to extract representative features of EEG data. In the second stage, least square support vector machine (LS-SVM) is applied to the extracted features to classify two-class EEG signals. To demonstrate the effectiveness of the proposed method, several experiments have been conducted on three publicly available benchmark databases, one for epileptic EEG data, one for mental imagery tasks EEG data and another one for motor imagery EEG data. Our proposed approach achieves an average sensitivity, specificity and classification accuracy of 94.92%, 93.44% and 94.18%, respectively, for the epileptic EEG data; 83.98%, 84.37% and 84.17% respectively, for the motor imagery EEG data; and 64.61%, 58.77% and 61.69%, respectively, for the mental imagery tasks EEG data. The performance of the CT-LS-SVM algorithm is compared in terms of classification accuracy and execution (running) time with our previous study where simple random sampling with a least square support vector machine (SRS-LS-SVM) was employed for EEG signal classification. We also compare the proposed method with other existing methods in the literature for the three databases. The experimental results show that the proposed algorithm can produce a better classification rate than the previous reported methods and takes much less execution time compared to the SRS-LS-SVM technique. The research findings in this paper indicate that the proposed approach is very efficient for classification of two-class EEG signals.