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Background: EEG signals are extremely complex in comparison to other biomedical signals, thus require an efficient feature selection as well as classification approach. Traditional feature extraction and classification methods require to reshape the data into vectors that results in losing the structural information exist in the original featured matrix. Aim: The aim of this work is to design an efficient approach for robust feature extraction and classification for the classification of EEG signals. Method: In order to extract robust feature matrix and reduce the dimensionality of from original epileptic EEG data, in this paper, we have applied robust joint sparse PCA (RJSPCA), Outliers Robust PCA (ORPCA) and compare their performance with different matrix base feature extraction methods, followed by classification through support matrix machine. The combination of joint sparse PCA with robust support matrix machine showed good generalization performance for classification of EEG data due to their convex optimization. Results: A comprehensive experimental study on the publicly available EEG datasets is carried out to validate the robustness of the proposed approach against outliers. Conclusion: The experiment results, supported by the theoretical analysis and statistical test, show the effectiveness of the proposed framework for solving classification of EEG signals. EEG, Sparse PCA, Marix Classification, Support Matrix Machines.READ FULL ARTICLE ON IEEE XPLORE